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STANDARD HANDBOOK 



FOR 



ELECTRICAL ENGINEERS 



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PUMISUCRS or SOOKS FOR^ 

Coal Age » Electric Railway Journal 
Electrical Ufarld -^ Er\gineering News-Record 
American Machinist -^ The Contractor 
Engineering 8 Mining Journal ^ Power 
Metallurgical £i Chemical Engineering 
Electrical Merchandising 



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STANDARD 
HANDBOOK 

FOR 

Electrical Engineers 

PREPABED BT A 
STAFF OF SPECIALISTS 



FRANK F. FOWLE, S. B. 

EDlTOB-IN-CHlEy 

CDXSULTINa VIJCCrmiCAL KNOIKKBB, MBMBCB AMBKICAN INaTITUTS 

or ZI.BCTBtCA.1. BNOINXBM, ILLCHINATINa BNaiHBBRIHO 

SOCIBTT AND HAHOHAL BLBCTBIO UORT AUOOIATIOH 



total. issue, pipty-bioht thousand 

Fourth Edition 
Rkwritten and Greatlt Enlarged 

Fifth Impression 

WITH Corrections, and Revision op the 

Standardization Rules 

TO 

JANUARY, 1917 



McGRAW-HILL BOOK COMPANY, Inc. 
239 WEST 39TH STREET. NEW YORK 



LONDON: HILL PUBLISHINQ CO., Ltd. 

e & 8 BOUVBRIB ST.. B.C. 

1915 ^ • 



OopTmoHT. 1907. I90«, bt thb McOraw PtniLtsinNa Cohpamt 

COPTHIQHT, 1910, BT THB McGbaw-HiLL BoOK CoHPANT 

CopTRiauT. 1915, BT TUB AIcGbaw-Hili, Book Coupant, Ino. 



FiBBT Edition 
Pint Printing, Decembtr, 1907 



Second Edition 

FirttPrintine, May, 1908 

Steond Priming, March, 1910 



TmsD Edition 
Firtt Printing, September, 1910 
Second Printing, September, 1911 
Third PritUing, December, 1912 



FouBTH Edition 

Firel Printing, July, 1915 

Second Printing, Novembtr, 1915 

Third Printing, December, 1916 

Fourth Printing, April, 1918 

Fifth Printing, May, 1919 

Total Ibsub, Fiptt-eioht Thousand 



TMEAfAt>I.K PKCSM TOBKPA 

Digiii^edb, Google 



PREFACE TO THE FOURTH EDITION 



The present edition of the Standard Handbook for Elec- 
nacAL Engineers, preparation of which was undertaken early 
in the year 1913 under the editorial direction of the writer, em- 
bodies so many changes and so much new matter that it is 
virtually a new bocdc, retaining, however, the general features 
and scheme of arrangement which have received extensive en- 
dorsement in the prior editions. As heretofore, the Standard 
Haxdbook is intended primarQy as a reference book of practical 
information and data for practising engineers and a supplement 
to the standard text-books employed in teaching electrical en- 
iqneering in colleges and universities. It is well recognized that 
limitations <rf space within ^ single volume of this character, even 
of the present size, render it impossible to treat each subject 
exhaustively. Our efforts have been concentrated chiefly on 
the task of presenting as much information and data of a prac- 
tiral nature as space would permit, reducing descriptive mat- 
ter to the reasonable minimum and relying on references to 
standard works for extended dissertations on theory and highly 
q>e(rial topics. Perhaps- the most difficult task of all, in the 
picsent revision, was that of keeping the subject matter within 
the confines of a volume which would not be impossible in 
either the physical or the commercial sense. 

Owing to the numerous advances in electrical science and the 
dectrical arts since the appearance of the third edition in 
tlWi, and owing also to certain criticbms which had been 
made concerning the earlier editions, the Publishers approved 
at the outset a broad and liberal editorial poKcy which greatly 
facilitated the work and minimized the burdens of a task that 
at best is a difficult one. 

The first problem was the rearrangement of the sections 
for the purpose of securing a rational classification of major 
subjects and insuring a well-balanced presentation. A great 
deal of time was spent in consideration of this question 
before undertaking the details of the work. In the same 
manner much attention was given to the grouping of subjects 
under minor divisions in each main section, in order that the 



35792 « L'«-- byGoogk 



PRBFACg 

information on each subject might be presented in reasonably- 
compact form, and at the same time be easily located. 

Thus each numbered paragraph opens with a descriptive title 
or phrase in bold-faced type, while in other respects the use of 
such type has been limited to subheads and important key- 
words which should catch the eye upon a casual glance over 
the pages. An entirely new feature is the consistent use of sub- 
heads throughout each section and the grouping of thebe on 
each section title page, for the double purpose of describing 
the contents in some detail and serving as a ready guide to any 
particular subdivision or minor subject. This general scheme 
of presentation is not intended to relieve the necessity for a 
thorough and complete index, but rather to supplement the 
latter and make the book of maximum usefulness. Another new 
feature is the addition of bibliographies at the end of each sec- 
tion or subsection, and the insertion of numerous references 
throughout the text to more extended or specialized literature. 

In retaining the sectional or unit system of arranging a refer- 
ence work of this character, both the Editor and the Publishers 
are convinced from past results that there is no other form of 
arrangement which is so well suited to the production of a useful 
and convenient handbook, or which makes possible the segrega- 
tion of all the material relating to each subject, presented in 
logical sequence and so displayed as to give it the desired 
prominence. 

. Sections 1 to 5 inclusive cover the same general ground as in 
the third edition, but have been almost completely rewritten and 
considerably extended. 

Sections 6 to 9 inclusive embrace the same subjects as Sections - 
6 to 8 in the third edition, but conform to a revised classification 
which is believed to be preferable to the former arrangement. 
These sections have also been entirely rewritten and substan- 
tially enlarged. 

Section 10 covers the same general subject matter as the cor- 
responding section in the last edition, but is entirely rewritten 
and greatly enlarged. 

Sections 11 and 12 cover the same ground as Section 11 in 
the third edition, but are entirely new and much more 
comprehensive. 

Section 13 replaces Section 18 in the old edition, being entirely 

vi 

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PREFACK 

lewrittcn; Section 14 replaces Section 12, with entirely new 
material', Section 15, Industrial Motor Applications, is a new 
section with entirely new subject matter. 

Section 16 covera the ground of Section 13 in the third edi- 
tion, and has been thoroughly revised. Section 17, Electric 
Vehicles, and Section 18, Electric Ship Propulsion, are both new 
sections. 

Section 19 replaces Section 14 in the third edition, many por- 
tions of it being rewritten. Section 20 takes the place of old 
Section 9 with new material, and Section 21 replaces old Sections 
15 and 16, also rewritten and altered somewhat in scope. 

Section 22 takes the place of Section 17 in the old edition, 
with almost exclusively new materiaL Section 23, Mechanical 
Section, is a new section; Section 24 corresponds to Section 19 
in the last edition; Section 25, General Engineering Economics 
and Central Station Economics, is entirely new. Section 20 in 
the former edition has Been abandoned and its contents, or 
their revised equivalents, have been distributed among other 
aeetions. 

The Editor takes this occasion to thank his numerous associ- 
ates far their cooperation and enthusiasm throughout a long 
and difficult task, and to acJcnowledge the painstaking efforts 
of the Publishers concerning the mechanical features and their 
patience over the unexpected but seemingly unavoidable delays 
in completing the editorial portion of the work. Acknowledg- 
ment is also due to my assistant, Mr. J. C. Bogle, who has pains- 
takingly performed a large share of the routine editorial work; 
to Mr. Walter Jackson, Associate £^tor of the Electric Railway 
Journal, who has read the complete proofs before going to 
press; and to Mr. O. A. Kenyon, who has prepared the index. 

FnANK F. FowLE, 
Chtcago, June 15, 1916. Editor-inrCkieJ. 



Tii 



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PREFACE TO THE THIRD EDITION 



The preface to the first edition of the Standard Handbook, 
which appears on another page, describes the "unit" system on 
which the work was developed. The present edition, the 
publishers believe, is somewhat of a triumph for this system. 
The thorough revision of a book of this size, when manufac- 
tured according to the usual plan, is commercially impossible 
except at long intervals when the changes in the art become so 
great as to demand an entirely new book. The "unit" system 
employed in the Standard Handbook permits thorough revision 
in part or as a whole without any of the usual limitations. 

In the present revision the authors of the various sections 
were allowed a free hand in so far as mechanical details were 
concerned. They were not restricted in space or compelled to 
cut and prune material to fit pages. The result is a book that 
has been thoroughly revised from cover to cover so that it could 
be fairly called a new Standard Handbook. 

The following synopsis gives a brief outline of the changes 
and additions that have been made to the various sections. 

Section 1, Units, is corrected and slightly enlarged. 

Section 2, Electric, Magnetic and Dielectric Circuits, is 
greatly enlarged. The general theory of electric and magnetic 
circuits is entirely rewritten and the calculation of inductance 
and capacity is given in greater detail than before. 

Section 3, Measurements and Measuring Instruments, is 
greatly enlarged. Several new instruments are described, tests 
of self and mutual inductance have been added and a section 
devoted to pjrrometers and high temperature measurements has 
been included. The design of rheostats and motor starters has 
been transferred to Section 5. 

Section 4, Properties of Conductor, Resistor and Insulating 
Materials, is enlarged more than any other section. Many 
tables have been added giving data on the latest types of 
conductors and cables. An entirely new section giving the 
properties of a large number of commercial resistor alloys has 
also been added and the magnetic testing of iron has been en- 
tirely rewritten and now forms a very comprehensive tTeatment 
of the latest practice in this important subject. 

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Section 5, Magnets, Resistors, Ck)nden8er8 and Reactors, has 
been enlai^^ed in scope to include resistors, condensers and react- 
ors. In the sections on magnets, a discussion of the energy 
relations in a plunger magnet has been added. The section on 
resistors contains the design of rheostats, formerly in Section 3. 
To this section have been added the design of induction motor 
starters, the heating of wires, cables and embedded conductors, 
the calculation of fuses and tables for use in heating calculations. 
A new skin effect for various metals has also been added. In the 
condenser and reactor sections, the electrical calculations are 
given, and considerable space is devoted to the electrolytic 
eondraaer. Almost all of the material in this section is entirely 
new. 

Section 6, Transformers and Converters, is thoroughly 
revised and considerably enlarged. The use of silicon steel has 
mrolutionized transformer design and hence this section has 
been completely overhauled. As the book goes to press it 
is the Mily available up-to-date treatment of transformers. In 
the converter section numerous additions are made, the most 
important being a discussion d the split-pole converter. 

Section 7, Generators, has been corrected and slightly revised. 

Section 8, Motors, has been revised, discussions of new motors 
being added to the alternating current commutating motor sec- 
tion. Xew design data are given for both a.c. and d.c. motors. 

Section 9, Batteries, has been corrected and revised, with 
aii^t additions. 

Section 10, Central Stations, has been thoroughly revised 
and largely rewritten. The scope is the same. Many cost data 
have been added. 

Section II, Transmission and Distribution, excepting the 
underground construction and mechanical transmission, has 
been entirely rewritten. It is believed now to be thoroughly 
abreast of the times in the calculation and construction of trans- 
mitBion and distribution systems. Many tables have been 
calculated especially for this section. Practically all of the old 
tables have been discarded. Inductive reactance and charging 
current for ail sizes of wire and cable and all spacings are given 
for 25 and 60 cycles. Tables giving the stresses in wires and 
cables of various sizes for wind, and wind and sleet conditions 
4*e abo among the additions. 

Sectioa 12, Illumination, has been corrected and revised. 

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DigilizedbyV^iUUyiC 



PREFACE 

Section 13, Traction, has been corrected, revised and enlarged. 
The locomotive section has been entirely rewritten, and more 
space has been given to the method of constructing speed-time 
curves. 

Section 14, ElIectrochemLstry, has been thoroughly revised 
and somewhat enlarged. 

Section 15, Telephony, has been entirely rewritten. It is now 
a comprehensive treatise and represents a new method of pre- 
senting the subject. 

Section 16, Telegraphy, is corrected. 

Section 17, Miscellaneous Applications of Electricity, ia 
corrected and somewhat enlarged. 

Section 18, Wiring, is corrected and brought to date. 

Section 19, Standards, is considerably enlarged. The 
latest changes in the A. 1. E. E. Standardization Rules have been 
noted, and standard specifications for rubber insulation, copper 
conductors and transformers have been added. 

Section 20, Tables and Statistics, has been corrected and 
enlarged by adding telephone, telegraph and central station 
statistics and by general revision. 



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PREFACE TO THE FIRST EDITION 



In the preparation of the Standakd Handbook the pub- 
lishers have adapted the "unit" system to bookmaking. The 
entire field of electrical engineering was divided into twenty sec- 
tions or units, each complete in itself. These twenty sections 
were arranged in what seemed to be a logical order and each 
was assigned to a specialist. Each author was supplied with 
a detailed outline of all the sections, thus avoiding repetitions 
and duplication of material as far as desirable. All of the 
material thus brought together was carefully edited to obtain 
uniformity of style, symbols, abbreviations, units, etc., and to 
eonnect the various parts by cross-references. 

Some repetitions are purposely made to save the time of the 
user. For instance, transformer oil is treated under Insulating 
Materials in Section 4, but a brief outline of its important 
qualities is again given in Section 6 under Transformers, with a 
cnm-rtsference to guide the reader to the fuller treatment in 
Section 4. 

The Index embodies some new features. All references are 
made to section and iiaragraph. In each section the para- 
giaphs are numbered from one to the end, and the section and 
paragraph numbers are set at the head of the page; the page 
number appearing in an inconspicuous place at the foot, for the 
guidance of the printer only. Cross-references are always made 
throu^ the index to avoid errors and to guide the user to all 
other parts of the book where that subject may be treated. 

The studied use of bold -face type is also intended to save time 
by bringing out in a prominent way the real subject of each 
paragraph. 

Recognized standards have been followed wherever pos- 
sble. Those recommended by the national societies or organi- 
lations have usually been followed. Section 19 is entirely 
given up to Standardization Rules and Reports, including the 
full report of the American Institute of Electrical Engineers of 
June, 1907, and that of the American Street and Interurban 
Railway Engineering Association, ratified in October, 1907. 

The publishers cannot hope for absolute accuracy in this 

Digiii.MbjV^iOOgle 



PRBFACE 

first edition of a work containing such a mass of figures and 
data, although the greatest care has been exercised in its prepa- 
ration. Any suggestions, criticisms, or corrections from users 
will be of great service in making The Standard Handbook a 
standard in fact as well as in name. 

December 12, 1907. 



PREFACE TO THE SECOND EDITION 



No new material has been added to this edition of the Stan]>- 
ARD Handbook, with the exception of directions for resus- 
citation from electric shock, which have been inserted at the end 
of the book. However, every page has been most carefully read 
and every possible effort made to insure the accuracy of all data 
and perfection of the typographical work. Several of the ta- 
bles, which were especially prepared for this book, have been 
recalculated and others have been checked by plotting the values 
and recalculating those which did not fall on a smooth curve. 

The success of the Standard Handbook has been phenome- 
nal. The general interest in the work has been manifested by 
the many letters received from prominent men commending its 
general character and offering suggestions and criticisms. It 
has already been adopted for use as a text-book in thirty 
universities and colleges. 

The publishers take this occasion to express their appre- 
ciation of its reception by the profession, and to thank those 
who by their kindness in pointing out typographical and other 
errors, have materially assisted in the work of correction. 

New York, May, 1908. 



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SECTIONS AND AUTHORS 



SECTION 1 
man, COHTUSIOH FACTOBS AHD tabus. By Arthur K. 

XannaUr, A.M., Bo.D. 
i^ymtetoM of UnitB, Historical Sketch. Evolution of Practical Electromag- 
■Flic Sygtem of UnJtA. Definitioiu, Dimensional Formulas, WeiEhts and 
, CoDTeraion Tables and Mathematical Constants and Taoles. 



SECTION 2 
ILBCTBIC AHD KAOnTIC CIBCUIT8. By VUdlmir KarapatoS 
Eteetrie Potential, Electric Currents, Continuous-euirent Circuits, Eloctro- 
nuicn«tie Induction, The Magnetic Circuit, Inductance, Hysteresis, Eddy 
Currents, The Dielectric Circuit, Transient Currents, Alternatinp-current 
Cireuita, Complex Wares, Polyphase Systems and Transmission Circuits. 

SECTION 3 

MXABinaiCBim ABO KBASOBIHO APPABATVB. By T. Haleolm 

Fannar; Oaorn K. BurcaM, Be.D.; Paul O. Voota, A.M.: 

Baclnald /. 8. rigott and WUUam J. DrUko, 8.B. 

Gahranometers, E.M.F. and Current Measurements, Resistance Measure- 

nents. P o wer and Energy Measurements, Curve-drawing Instruments; 

Measorements of Inductance, Capacity, Wave-form, Frequency, Slip, Torque 

aad Speed; Magnetic Measurements, Thermometry, Pyrometry, Heat 

CotHloctivity, Fuel and Gas Analysis; Water, Gas, Air and Steam Meters; 

Precjaum of Measurements. 

SECTION 4 
PBOFBBTnS or MATIBIAU. By Frank F. FowU, I.B. 

f" r_.iLftor Materials. Wire Gaged, Wire Tables, Copper, Aluminum, 
Copptrr-^ia*! St*?el, Iron and Steel, Bronze, Miscellaneous Metals, Resistor 
Materials, Carbon and Graphite, 8kia Effect; Magnetic Material.s, Composi- 
tioo and Properties, Core Losses, Sheet Gages, Conimercial .Shet-ta, Magnet 
Mad; lasulating Materials, Classification, Discussion of Properties, Solid 
■Satval Materuls, YitriBed Materisilii, Fibrous Materials, Molded Com- 
psatMos, Rubber and Its Derivatives, Varnishes and Compounds, loBulat- 
■ag Oik, G a ses : Structural Materials, Cast Iron, Wrought Iron, Steel, 
Aaaeafing, Hardening. Tempering, Steel Wire and Cable, Non-Ferrous 
Metab. Conrrete, Brick. Stone. Timber, Belting and Rope, Properties of the 
Omenta, Atomic Weights, Densities, Specific Heats, Properties of Water 
aad Air. 

SECTION 5 

luaBxn, nrovcnox coiu, condbmbbbs and bbbistobs. 

By Charlaa M. UndarhlU and Iiaonard Kablar 
Pffmaaent Magnets, Electromagnets, General Theorr, Tractive Electro- 
Bsgnets, Conditions for Maximum Work, Standard electromagnets. Por- 
tative Eketromagnets, Polyphase Electroma^ets, Heating, Magnet Wires, 
CslcolatioBS, Construction, Testing; Induction Coils, Types, Windings, 
latemxpters; Condensers, Types, Plate Condensers, Electrolytic Condeii- 
•m. Reaiatan, Fldd Rheoatats, Speed-regulating Rheostats, Dimmers, 
''urting Rheoatats, Battery-charging Rheostats and Resistance Units. 

SECTION e 
TBABBFOBUU AHD BBCTIFIBB8. By Charlaa La O. Forteacua 

Tbecry, Design, Insulation, Cooling, C<h1 Grouping, Transformers for 
Poacr Stnriee ana Distribution Systems, Multiple Operation, Polyphase 
Traa^ormations, Constant-Current Transformers, Auto-transformers, Instru- 
mm TrsMfomera, Miscellaneous Applications, Testing, Installation, Carp 
ud (>j«ation; Potential and Current Regulators, Reactors and Rectifiers. 

xiii 

D,jiii_.,ih,*^ii.)uyie 



SECTION S AND AUTHORS 

SECTION 7 

ALTIBKATnrO-CCBSENT OKMKBATOBS AMD MOTORS 
By Oomtort A. Adanu and Henry M, Hobart 

Synchronous Mschioes, Armature Winding, E.M.F. Generation, The 
Magnetic Circuit, Characteristics of Synchronous Alternators, Synchronous 
Motors, Parallel Oi>eration, Design, Insulation, Efficiency, Ventilation, Con- 
struction and Testing; Induction Machines, Theory of Polyphase Motors, 
Characteristics, Magnetising Current, Leakage Reactance, Circle Diagram, 
Efficiency^ Standard Polyphase Motors, Induction Generators, Design, 
Hiogle-phase Motors and Tlieir Speed Control; Commutator Motors, Auxil- 
iary Commutating Maohines, Phase Modifiers, MoU>r«eneratora and 
Frequency Changers. 

SECTION 8 

DiaiCT-CUaSXRT aEHZBATOSS AKS MOTOBB. By Alexander 
Oray, B.Bo., Whit. Boh. 
Types, Windings, Armature Reactions, Commutation, Armature Design, 
Field Design, Construction, Insulation, Cooling, Efficiency, Characteristics, 
Regulation, Weights, Costs, Standard Machines, Thury System, Motor- 
generator Sets, Operation and Testing. 

SECTION 9 

CONVXBTKBS AIO) DGUBLI-CUBBXITr OINBBATOBS. By F. D. 
Mewbuiy, M.X. and Alexander Oray, B.Be., Whit. Boh. 
Synchronous Converters, Theory, Design, Characteristics, Applications, 
Operation, Testing; Inverted Converters, Motor Converters, Direct-current 
Converters, Dynamotors and Double-current Generators. 

SECTION 10 

POWIB PLAHTB. By Reginald J. B. Plgott, Arthur T. BaSord and 
Oeorge I. Bhcdei 

Steam Power Plants, Laws of Heat Transfer, Boilers, Furnaces, Stokers, 
Chimneys, Mechanical Draft, Fuel, Water Supply, Coal and Ash Handling 
Engines, Turbines, Condensers, Heaters, Economisers, Pumps, Piping and 
Testing; Gas Power Plants, Producers, Superheaters, Condensers, Scrubbers, 
Purifiers, Holders, Properties of Gas, Engines, Piping and Testing; Oil Power 
Plants, Engines, Testing; Hydraulic Power Plants, Hydraulics, Flow For- 
mulas, Stream Flow^ Dams, Headworks, Water Wheels and Testing; Build- 
ings and Foundations; Electrical Equipment, Generators, Excitation, 
Voltage Control, Switching, Station Transformers, Lightning Arresters and 
Wiring; Power-plant Economics. 

SECTION 11 
POWXB TBAimMIBBION. By Harry B. Cliflord, B.B. and Chester 
L. Dawei, B.B. 
Transmission Systems, Electrical Calculations, Tables of Reactance and 
Charnng Current, Design, Corona, Insulators, System Connections, Switch- 
ing, Spans and Supports, Construction, Cables, Substations, Operation, 
Economics and Cost Data. 

SECTION 12 
DUTBIBUTION 8T8TBM8. By Harry Bamei Gear, A.B., M.B. 

Classification, Applications, Types of Circuits, Circuit Design, Substations, 
Regulation. Secondary Distribution, Transformation, Protection, Construo- 
tion and Economics. 

SECTION 13 
niTIBIOB wnnro. By TerreU Croft 
Fire Risk, Methods of Wiring, Wires and Cables, Fittings and Accessories, 
Calculations, Lay-outs, Installation, Protection and Misoellaneoua. 

xiv 



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SSCTIONS AND AVTHORB 

SECTION 14 
lUVICIITATIOir. By rraaton B. imiar 

Production of Lisht, Inesndeuent Lamps, Carbon Filament, Mctallifed 
Ctfboo'Filainent, Tantalum, Tnngsten, Gaa-filled Type; Arc Lamp Char- 
acteristics, CarboD-eleetrode, Flame Arc, Metallic Electrode, Tube Lamps, 
tithtinc Aeeoaories, Reflectors, Indirect and Semi-indireet Lichtinc; 
niuDiination Calculation, Flux, Candle-power, Intensity, Brightness, 
Efficiency ; Apdiied Illumination, Fundamentals of Vision, Characteristics of 
lUnmination. Physiological and PssrchologiGal Effects, Methods, Design, 
Costs; Photometry, Fundamentals, Standards, Apparatus, 8psotropli» 
tometers, Coharimeters and Testing. 

SECTION 15 

VKOVWTKUJ. KOTOB APPUCATIOin. By tiM foltowinv 

ipadalista: 

Leon P. Alford Chester W. Drake Arthur C. Eastwood 

Wilfred Bykes David L. lindquist Fred J. Postel 

Joseph H. Brown, Jr. Merton S. Leonard C. D. Gilpin 

B. McL. Harding Graham Bright Augustus C. Smith 

Wilfiam W. Crosby Joseph H. WaUace Charles £. Carpenter 

John F. Harrison Wirt S. Scott Frits Balser 

Bernard Lester Clark T, Henderson 

Machine Tools, Wood-working Machinery, Traveling Cranes, Electric 
Boista, Elevator*. Power Pumpe, Air Compr e ssor s , Fans and Blowers, Coal 
and Ore Handling Machinery, Telpherage Systems, Steel Mills, Cement 
iClls, Coal Mining, Refrigerating FlanU, Textile Mills, Paper and Pulp 
Mills, IVinting, Binding and Linotype Machinery, Flour Mills, Beet-sugar 
Mills, Laundry Machinery, Small-motor Applications and Motor Control. 

SECTION 16 
naOTBtO ftULWATS. By Albart B. Arnutronf, MannMi W. 
Stonr, Aaal Amaa and Albsrt r. Oani. 
EleeCHe 'IVaetion,l^«in Reaistanoe, Speed-time Curves, Motor Character- 
istics, Energy and Power Consumption, Motor Control, Types of Motors, 
Braking, Trucks and Car Bodice, aelf-wopelled Cars, Locomotives, Distri- 
butioB, Substations, Track Switches; JtaUway Si^naUinc, Types of Fixed 
Sgssls, Trolley-operated Systems, Track Circuits, Interiocking, Block 
System: Electrolysis, Surveys, Means of Prevention, Municipal and State 
Regulations. 

SECTION 17 
ILKCTBIO OOmCBBOIAL VXBICLBS. By SUphan O. ThompMn. 

^ Classification, Chassis Construction, Vehicle Resistance, Energy Consump- 
tMD, Transmission Gear, Motors, Controllers, Batteries, Instruments, Ga- 
rage Equipment and Comparative Performance and Economy. 

SECTION 18 
KLBCTUC SHIP PBOPULSIOll. By Henry M. Bobart 

Ship Resistance, Propeller Characteristics, Systems of Propeller Drive, 
Tvpes of Vessel For Different Service, Electric Propulsion and Examples of 
Electrically Propelled Shipa. 

SECTION 19 
SLSCTSOCBUnSTBT. By B. t. ftoeber, Ph.D. 

Interpretation of Chemical Equations, Laws of Gases, Laws of Solutions, 
Energy Relations, Electric Furnaces and Their Products, Electrolytio Proc- 
esses and Reactions, Industrial Electrolytic Processes, Electroplating, 
Rsfining of Metals; Electrolysis of Water, Alkalins Chlorides, Copper, 
Kiekd, ^ne. Aluminum, Sodium, Magnesium and Calcium; Discharges 
through Gases, Fixation of Atmospheric Nitrogen, Electromagnetic and 
Electrostatic Prooesaea. 



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SSCTIONS AND AUTHORS 

SECTION 20 
BATTBUn. By Wtltm M. Wlnihlp, Ph.D. 
Primary Batteries, Wet Cella, Dry Cells, Storage Batteries; livad Stornge 
Batteries, Eleotrolyto, Testing, Stationary Batteries, Vehicle Batteries, 
Train-lighting Batteries. MisceUaneous Applications, Battery Rooms, 
Regulating Equipment, Operation, Depreciation and Maintenance; Alka- 
line Storage Batteries. 

SECTION 21 ' 

TBUPHOinr, TBLIOSiiPRT AHD BADIOTKUOKAPHT. By 

Trajik T. Fowl*, 8.B., and LouU W. Auftin, Ph.D. 

Telephone Instruments, Switchboards. Xntercommunieating Systems, 
Phantom Circuits, Manual Telegraph Systems, Simplex and Composite Sets, 
Dispatching and Patrol Systems, Fire and Police Alarm Systems, Cables, 
Protectors, Cross-talk and Inductive Disturbances, Transmission, Construc- 
tion, Testing; Radiotelegraphy, Antenna, Receiving Circuits, Detectors. 
Wave Transmission, Undamped Oscillations, Arc-wave Generator, Continu- 
ous Oscillations, Wireless Telephones, Directive Antennaa and Measuring 
Instruments. 

SECTION 22 

HnSCXLLAHIOITB APPLICATIONS OF BLICTBIOITT. By the 

following spedallita: 

W. S. Hadawsy, Jr. Otia Allen Kenyon John C. Bogle 

Harry B. Oear H. A. Hornor Capt. Edw. D. Ardery 

John E. Newman Frank F. Fowie Milton W. Franklin 

Edwin P. Adams Ernst J. Berg. Eugene W. Caldwell, M.D. 

Resuscitation, Eleetrio Heating and Cooking, Electric-Welding, Electrical 
Equipment for Gas Automobiles, Thawing Water Pipes, Marine Applica- 
tions, Electricity in the U. 8. Army, Electricity and Plant Growth, Windmill 
Electric Plants, Osone Production, Radioactivity and the Electron Theory, 
Roentgen Rays, Lightning Rods, Electrostatic Machines, Electric Piano 
Players, Telegraphone, Telharmonium, Train-lighting Systems, Statistics 
of the Electrical Industry, Specifications and Contracts. 

SECTION 23 
HIOHANICAL 8KOTION. Compilad from itandard authoritiai. 

Elements of Sections, Beams, Columns, Shafting, Gearing, Chain Drives. 
Belts, Rope Drives, Pipe and Screw Threads. 

SECTION 24 

ITAMDA&DIZATIOir BULBS OF THK AMXRIOAIT IV8TITVTX OF 

ILIOTKICAL KNaurUBS. Approved edition of Dec. 1, 1«14 

SECTION 25 
QXNEBAL XNaiNBXBINa BOOMOBnOS AMD CBNTBAL STATIOH 
XOONOHICS. By Frank F. Fowle, 8.B., and Jamei Raley Cravath 
General En^neering Eeonomics, Definitions, Value, Price, Cost, Capital, 
Rent, Interest, Annual Charges, Depreciation, Social-economic Investiga- 
tions, ViUuBtion and Rate Making; Central Station Economics, Factors 
Relating to Utilisation of Investment, Factors Relating to Territory Served, 
Typic^ Earnings of Companies, Rate Making and Valuation. 



xvi 

Digitized by CjOOQIC 



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SECTION 1 



xmrrs, conversion factors, 

AND TABLES 

BT AKTHUK B. KEITNSLLT, A.U., ScD. 

Prtfnitr of EUitricdt Snguuering, Banard Unittrntv, and Man, 

ImL TetkHalan; FtOoti and Pott Pmidmt, AuMrioait 

InMtuU of SUdrieai Enginooro 

ooKmrTS 

(Nutnboro rtfer to Paratrapk*) 

I of UnHa 1 Deflnhioiia of Photometiio VoiU 81 

al Sketch of Eosiufa Definitioiu of Thermal tinita 87 

Uaita 6 Dimenaonal Formula* S8 

Hbtotical Sketch at the Interna. Tabular Summary of Definl- 

tioaal Metric Syetem 9 tione of Unite 110 

BTointiaa of the Pimetical Beo- Weight* and Measures 110 

tromacnetie System of Units 15 Conveirion Tables Ufl 

Dcinitiaai of Fundamental Mathematical Constants and 

Uaita 2t Tables 14S 

IMahiaas ct Eleetrie aad Ma«- BibUography 1S8 
iCaits 4S 



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SECTION 1 



UNITS, CONVERSION FACTORS, AND TABLES 

STSTKHB or TTKITB 

1, Ilktun of unltf. EnsineeriDg makes lue of physical quantitiea in 
tha broadest sense of that term, >'.«., including meohanioal, cbemioal, physical, 
thermal and physiological quantities. In order adequately to compare the 
magnitudes of physical quantities of the same kind, unit magnitudes, or 
units, are necessary for each kind of physical quantity dealt with. 

t. CiMlifleatlon of unit*. The subdivisions and species into which 
units may be divided are indicated in the scheme shown in Fig. 1, with ex- 
planations which follow in Par. t. 



Ca27laplilid 




(/,) I1-U(/,)^1bW/i)- ' 



SlMB tjmmt SfMM WjMmm 



Fio. 1. 

•(•■) Ituidard unlU (see Fi|[. 1) may be said to include all units which 
haTe received the stamp of recognition in technical literature. 

t(ai) Kinplrioal units, on the other hand, are units which have sprung 
into existence locally, ordinarily without any pretense to scientific deriva- 
tion, and wliich have not been sanctioned by general usage. At various 
times during Tecorded" history, empirical units have appeared. Thus, in 
the early history of electrical units, a unit of conductor resistance was used ss 
representing the itostanoe of a certain length pf » ««rV>u> ■>*« of telcfrapl) 



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VNITS, PACTOBS, AND TABLES Sec* 1-S 

wire, aM embodied in a oertain vUndard reMiaiwe 0(h1« Similarly. (Im 
aTcran «iia-f- of a Daaiell cell was originally an empirical unit of e.m.1. 

S(bi) Ibstematlc units are units of any definitely related sroup. Thus 
the onita pint," "quart,'* "peck," and "buafael" entering into "dry mesa- 
Bie" are Qyatematic units; be^uae they stand in definite quantitative mutual 
relation as a icroup or system. Again, the units "mill, "cent," "dime,** 
sod "dollar" entering into American currency are systematic units. 

S(bi) Hondeseripv units may be defined as standard units which are 
not sywtematic, or do not enter into any tmit system. Thus, in Pennsylvania, 
a "bushel" d coarse salt, as a weight-unit, is 80 lb. avoirdupoist* but in 
Dfinns it is 50 lb. avcnrdupois. 

<(B) Hybrid ff^l*f^, in contradistinction to systematic units, are units 
which (io not bdong to any one system, but which are derived say from 
s plurality ci different systems; from a systematio and a generu unit; 
or from any combination of standard and empirical units. Thus, a **kUo- 
gram" may be defined as a unit of weigiit in the international metric system; 



the use of a hybrid unit may outweigh the diudvantage of its unsystematic 
derivation. No stigma necessarily attaches to the use of a hybrid, as distin- 
giushed from a systematic unit; but great caution has to be used in pursuing 
new and unf&miuar quantitative reasoning processes involving hybrid units, 
lest Domerical errors be introduced by neglect of coefficients. 

Kci) Absolute units are units of pfaysiail quantities selected In a compre- 
bensiTe scientific system based upon three or more fundamental phyncal 
properties, such as length, mass, time, energy, epedfio gravitational force, 
etc.; BO that simple and fundamental quantitative relations may subsist 
between the members of the system and that each physical quantity may have 
one and onlv one unit in the system. The particular basic units from which 
s srstem <H absolute units is derived are called the tundanantAl unltg 
cf that system;t while the units so derived are called the dsrlTsd unlts in 
correlation thereto. In a dynamical syatsn, the fundMnent*! units 
are tlirss only and are: a unit of length, a imit of mast, and a unit of 
ttms.t Consequently, unless otherwise specified, the term "absolute units'* 
is taken as referring to a scientific system based on fundamental units of 
length, mass, and time. But whereas only one set of fundamental units has 
come into recognition — the length-mass-time set above mentioned — several 
Bpecies of this act have been used to some extent; nam^, the "foot-graln- 
second" system, { the "meter-kilogram-second" system* the "osntlmstsr- 
fram-ieeond*' (C.O.B.) system, and the "qnadrant-elsTsntli-gram- 
■ssond'* (Q.X.S.) system. Only the last two have come into extensive 
practical use. The C.Q.S. system has become the international scientific 
qntem, and the Q.E.S. system an international electromagnetic system in 
uectrical engineenng. Any complete electromagnetic absolute system 
involves five fundamental units, two of which mav be constants of the ether. 
S(ei)Ustrie units are units pertaining to the International mstrlo 
system. This system, which was created in France in 1792, was adopted 
in France in 1840, Q in Germany in 1872, in Austria In 1876 and so on from 
OM rivilijwd country to another; until at the present date, the only great 
eonimimities which have not yet adopted the metric system are the British 
Enqxre. the United States and the Russian Empire. The advantage of 
the system is its simplicity. It is a decimal system, using a single f unda- 
MS Dtalu nit of length (the meter) and one of mass (the ^cram). The dsoimal 
noltlplss of these are distinEuished by Greek and Latin preflzss common to 
sU branches of the system (Par. lOS). 

•"The World Almanac," 1913, New York, p. 81. 

tEverett, J. D. "C.G.S. System of UniU,'' Macmillan Co., 1891, p. 15. 

I Strictly speaking, a dynamical system of absolute units may employ 
ny desired acceferation as unit acceleration, when the unit force acts on 
vdt mass, yet, if the unit of acceleration be the unit of length per unit of 
time squared as in the C.G.S. system, the system Is called an absolute kinetic 

I "British Association Report on Electrical Standards,'* 1863. 
^ I HaQoek and Wade. " Evolution of Weights and Measures and the Mstrie 
West,*' Macmilton Co., Nsw York. 1906. 



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Sec 1-3 UNITS, FACTORS, AND TABLES 

a(e<) Onitomarrliicllili tmlta u« the nniu of the Eniliih taA Anuii- 
cftD meaaures, tU., lenxth measure, aquare meaaure, land meaauie, oubie 
measure, cord measure, dry measure, liquid measure, aToirdupois weight, 
troy weight, apothecaries weight and Jeweler's weight. Each of these mew^ 
ures may be regarded as a system. The complete list may be re^rded aa a 
oongeriea of imperfectly oonneeted systems. Empirical and hybrid units ar« 
mingled with tne rest. 

t(di) O.O.S. unlti are the units of that particular system of abaolute 
units which is baaed on the Intammtional oantiiiutar, the Intamatlonal 
cram and the mean lolar leoond. That is, they are absolute unita 
employing tlie metric system in a definite way. A reason for the centimeter 
having been selected in place of the meter as the fundamental unit of length 
was that the mass of the cubic centimeter of water (at the temperature of 
u^t density) is the fram or unit mass; whereas the masa of a cutnc meter of 
water would be a million grams. 

I(dt) Q.I. 8. nniti are unita pertaining to the quadrant-deventh-cranrt- 
seeond absolute system; {.«., the nrstem In which the unit of lencth la lO* 
cm. or 1 theoretical quadrant of the earth as measured from a pole to the 
equator, tiie unit of mass is 10^» g.,* and the unit of time the mean aolar 
second, or the l/86,400th part of the annual mean d«ly period of revo- 
lution of the earth with respect to the sun. This is the system to which the 
international ohm, volt, ampere, Joule, watt, coulomb, farad and beniy, 
belong. The system was not intentionally established aa a Q.B.8. (ystam; 
but the ohm having been arbitrarily selected, for convenience of magaituda. 
aa 10* C.O.S. eleetromagnetio units, and the volt similarly as I0*C.O.S. 
units, the reat of the system necessarily coincides with the Q.B.8. system; 
or is such a system as would be produced by the selection of the quadrant, 
•levonth-gram and second aa fundamental units, together with unity for 
the permeability and unity for the dielectric constant of the ether. 

•(dt) Oiorgl uatt* are units in a combined absolute and practical system 
devised by Prof. O. Oiorgi,t in which the fundamental units are: the meter- 
IdlogTam-eeeond-intemauonal ohm, and the further assumption that tba 
permeability of free ether, instead of being unity as in the C.G.8. magnetie 
•ystem, is m«~^X10-' henry/m. On this oasis the ohm-volt-ami>ere 
aeries of practical units become also absolute units. The electric inductivity, 
instead of being unity, as in the C.Q.S. electric system, becomes k, — l/SOr 
X 10~* farad/m. No distinction arisea in the Qioni system between electrie 
and magnetie units. The system is also rectified in regard to 4*' factoio, 
or is *^ationaU>ad" in the Heaviside sense; so that a number of fundamental 
equations in the system differ from thoee of the CO. 8. system in regard to 
such 4t factors. 

S(d4) H.O.B. nniti, ete. Units in an absolute system whose fundamental 
units are the meter«ram-second, the millimeter-milligram-eecond, the foo^ 

Gain second, etc. None of these extraneous absolute systems have coma 
to extensive use. 

S(«i) B.A. nnitt are the units of the C.O.8. system as established by the 
British Association for the Advancement of 8eiencet in 1863. The electro- 
static subsystem was established on the basis of the unit quantity of ele<v 
trieity such that it repelled ita prototype at a distance of I cm. with a force 
of 1 dyne. The electromagnetic sub^stem was similarly established on the 
basis of the unit magnetic pole such that it repelled ita prototype at a dis- 
tance of 1 cm. with a force of 1 dyne. This procedure led to the anomaloua 
nault that every electromagnetic qnantity has a unit both in the electro- 
static subsystem and in the magnetic subsystem. 

>(•«) Heaviside unita are units in that form of the C.Q.S. system which 
was first suggested by Mr. Oliver Heaviside in 1882. | He showed that it a 
unit electric point charge and a unit magnetic point pole had been respect- 
ively defined such that unit total flux emanated therefrom, the strength of 

* Maxwell, J. C. "A Treatise on Electricity and Magnetism," 1881, 
Chapter X. 

t Ascoli, M. "On the Systems of Electrical Units," Trans. Int. Electrical 
Concress of St. Louis. 1904, Vol. I, p. 130. 

t "British Association Report on Electrical Standards," 1863. 

I Heaviside, O. "The Relations between Magfletic Force and Eleatrie 
Curtent." The Eleetriciaa, London. Nov. 18, 1882. 



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UNITS, P ACTORS, AND TABLSS ScC 1-4 

ikt field St nait diatauoe would be 1/(4t), and this, not onity, ihould be the 
force in djmca tlukt the prototjrpe would develop in repulsion. Ai a. eonee- 
qneBee of this nnnsturml definition of the B.A. unit charce end pole, the 
fwwliifnfintal equations of the B.A. system become InterUrded with iw 
laeton in rectihneur problems and denuded of them in spherical problems 
where they should naturally be expected to occur. Mr. Heaviside proposed 
to l ec tifj the system by changing the fundamental definitions in the manner 
auaeeted, and enunciating a new list of units in both the electrostatic and 
inacnatie aubsystems; all related to the corresponding B.A. units in simple 
ra or roota of 4r. He aimilafly propoeed rectifying the practical or 
3. system of units by adopting a new ohm, volt, ampere, etc., all bearing 

x^o of simple power or root of 4r to the corresponding existing 

vafaiea. If Mr. Heaviside's proposals had been formulated and considered 
piior to international adc^tlon of the ohm-Tolt-ampere series of units, and 
Mgalisad standards, they might have been adopted. * At the present Ume 
a very few phyddsts employ Heaviside's "rational" ttnits in theoretical 
aiialyais.t 

4. FnndaoMntel prlndplaa ooneemlnc anltg in eqiMitioiis. Many 
of the equations re p re s e n ting propositions in pure mathematics maybe satie- 
fisd by quantitiee m any Una. Thus taking the very simple equation 

2(.a+b)-2a+3b 
h is dear that the qnantitiea a and b may be of the same kind or of different 
Uada, and their respective units may be any whatsoever, without affecting 
the identitr expressed, so long as a and b have respectively the same meanings 
SB Um two sules of the equation. 
Vhco, however, as ordinarily in en- 
gineeruw, physical magnitudes are 
oealt with in an equation; then three 
ruiisequeiiofe ensue; namely: 

(1) Ths equation can only be tnter- 
tnUd in Isnns «/ wm* unit aflkt par- 
(teslar pkytieal guttnUti/ diaU with. 
This is toe unit of the equation. 

CO Tk« SHtiC emplovM on tad 
tfAo toaalion mutt be the sams.t 

(3) 1/ either eide of the equation am- 
tauu a atapls swai of foeiliee or netoHte terme; tiien each of thete (emu muet 
emalett the saaw tmit ae the eguation. 

far eample, oonaideiliig toe case of a uniform pipe, discharging water at 
a ntdfarm velocity * meters pa see., from a reservoir A into a river B 
ifit- 3i. Let B be the total head or elevation in meters between the water 
levda i and B at the two ends of the i>ipe, and let a vertical pressure pipe 
be inserted C^- 2) at say point P. Then we have the well-known hydraulic 
tdatioa: 

B-f+^+hi+h, (meters) (1) 

where / is the loss of head due to friction in the length of pipe AP, a is the 
suedeiatiop doe to gravitation in meters per second per second, t'/^e i> the 
loss cl head due to velocity at the point P, ai is the remaining head above the 
local levd, and At the height of P above the reservoir level at B. Then 
acconfing to the jiropositioDS above stated, each of the four terms on the 
right hand of the equation must be a head, or height, in meters, and both sides 
of the equation miist be expressed in terms of the same unit. The left-hand 
term H eannot be in meters and the right-hand terms or any of them in feet 
or centimeteis. The second term on the right hand (I'/ig) contains a 
vslodty s, sad an acceleration a; yet the term as a whole must be a height, 
if the eqnstioa is correct. 

The equation might evidently be expreesed in term* of any unit of length 
such as inehes, feet, eubits, yards, miles or millimeters. As an algebraic 
•qnaiion entirely by itself, ttere i s no reason for selecting one unit rather 

■ Bssviside, O. "Eleetrieal Papers." Macini]laii.Co., 1892, Vol. II, p. 675. 

tLorents, H. A. "The Theory of Eleetrons." B. O. Teubnar, 1909, p. 2. 

t An exception is found in aa equation expressing the relation between dif- 

'srent unit* of the same speciee, as for example, in the equation lib. - 16 os. 




^is is toe onit of tbe equsnon. 
CO The tntiC employed on each eide _ „ 



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Sec. 1-5 UNITS, FACTORS, AND TABLES 

than ftDother. The numerical values applyinji to any particular case cov- 
ered by the equation will vary greatly according to the unit Bolected. If, 
however, any one of the terms is oxpresaed in a particular unit, all the other 
terms must adopt the same unit. In all cases, noweveft it is helpful to the 
reader to have the unit of the equation written out at the end of ita line, as 
above, in order to assist the numerical interpretation. 

HIBTOBXCAL SKKTCH OF ENOLI8B UiriTS 

6. The Knffllih weighto and zneasurei are based upon old Roman 
weights and measures. * The troy pound is supposed to have been a weight 
of suver referred to as a "pound sterling." This pound would be coined into 
240 silver pennies or "pennyweights," each of 24 gr. (barley grain weights). 
It would, therefore, contain 5.760 gr. Heavy bodies (auostancea in gross 
outside of coins or bullion) were weighed by ** avoirdupois" weight, authorised 
by law early in the fourteenth century. Several slightly different avoirdu- 
pois pounds were in use. . Since Queen Elisabeth's reign the avoirdupois 
pound has been fixed at 7,000 troy grains. 

6. In regsrd to British lenffths, the earliest seems to have been the 
cubit or half yard. The cubit is a very ancient measure, and corresponds to 
a forearm length from elbow to middle finger-tip. The royal iron standard 
ysrd was constructed in the thirteenth century, after which the cubit or half 
yard gradually fell out of use. The foot was standardised at one-third of 
the yard. The mite was a relic of the Roman "millia passuum," or thousand 
paces; the Roman pace was two of our paces, or counted between the lifts of 
one and the same foot. 

7. Oallon mouiuret of volume existed at different times in England in 
six different forms, such aa the corn-gallon, the ale-gallon, etc. Among these, 
the wine-gallon of Queen Anne contained 231 cu. in. This gallon was brought 
to America by the early colonists and remains to-day the U, S. gallon. In 
1824, the British enacted a new *' impsrial gallon '* to eupersede all pre- 
existing gallons, and defined it as the volume of 10 avoirdupois pounds of 
distilled water at the temperature of 62 deg. fahr.^ with the barometer at 
30 in. It was further defined aa a measure containing 277.274 cu. in. of 
distilled water. There is thus a diiference between British and American 
gallons in the ratio 277.274 to 231 » 1.204 : 1; so that the British gallons, 
quarts, and pints are respectively about 20 per cent, larger than American 
gallons, quarts and pints, a large discrepancy that has frequently led to 
misunderstandings. 

8. In land measure, since Anglo-Saxon times, a "perch" or "pole*' 
was 11 cubit* in length - 10} ft., and such a pole was the surreyor't unit* 
A length of 40 perches was a furlong, and 8 furlongs the Statute mile. 
An acre of land was the area of a rectangular strip a furlong in length and 
4 perches in breadth, which breadth was known as the "acre's breadth." 
An acre therefore included 40X4 » 160 sq. perches. Eight such stripe end 
to end made the statute mile, and SO such strips side by side made a statute 
mile breadth; so that a square statute mile contained 640 acres. Early 
in the seventeenth century. Prof. Edmund Gunter of Gresham College 
decimalised acre measure by inventing a 100-link "chain" of outstretched 
length equal to 4 perches or the acre's breadth (66 ft.). The acre thus becams 
10 sq. chains. 

HIBTOKICAL SKKTCB OF THX ZKTERirATIOirAL MXTBIC 
8T8TIM 

9. Prior to 1790, differences existed between the weights and measures 
of different Departments of France. ^ Reform in the directions of simpli- 
fication and unification was promised in a decree of the National ABsemoly 
under the sanction of Louis XVI in 1790. The metric system was actually 
developed under the authority of the French Republic in 1793, in the hands 
of a committee of scientists and engineers. 

10. The decimal sntem, at the base of the metric system, was originally 
extended to angles and to time, the right angle being divided into 100 gradee. 
each subdivided into 100 min. and again into 100 sec. The day was dividea 
into 10 hr.. each subdivided into 100 min. and again into 100 see. The deci- 
mal subdivision of time never came into extended effect, and the decimal 
subdivision of angles has only been used to a limited extent. 

* Watson, Sir C. M. "British Weights and Measures.** London, 1910. 



UNITS, FACTORS, AND TABLES S«C 1-11 

11. Tlia mtttar wss selected ai a length equ&l to the ten millionth part 
yl the ZMWthAm qnadrant of tlM OBTthi or distance from pole to equator 
k.t the meridian of Paris. Lat«r measuromenta have shown that the inter- 
oational atandard meter finally adopted is shorter than the 10"' quadrant 
by 0.O2* per cent. The advanta^ of such a basis for the met«r is that by 
the U£e of the decimal subdivision of angles; i.e., by the aubetitution of 100 
grades for 90 deg., the kilometer becomes the natural nautical unit of dis- 
tance, or the hundredth of the grade; just as the English nautical mile is 
the sixtieth of a degree. 

IS. Tl&a metric syatom is universally used in all European countries, 
except Great Britain and Russia. The quantitative literature of the scien- 
tific irorld is almost exclusively written in the metric system. To express 
quantit&tive relations exclusively in the English units is to conceal their 
meaning to a great extent, from all but English-speaking peoples; and also 
to discredit them scientifically, by implication. 

IS. In tiie United States, the metric system has been a legally recognized 
system since July 28, 1868. In 1893, the U. 9. Office of Standard Weights 
fl^ Measures waa authorised to derive the yard from the mct^Tt at the ratio 
1 yd. =» 3G00/3937 meter. The customary weights are likewise referred to 
the kilogram. The customary weights and measures of the United States 
are thus defined in terms of, and maintained with reference to, the intcr- 
national metric sj'stero. 

14. Tbe international metrio standard!, i.e., the standard meter 
bar and the standard kilogram, are maintained at the International Bureau 
of Weights and Measures at Sevres, near Paris, France, in a building which 
h&B been declared internationally neutral or outside of French territory. 
Copies or prototypes of these standards are maintained at the various 
oationiJ laboratories and are occauonally intercompared. 

EVOIiVnOK or TBS PEACTICAL KLICTKOBCAaHXTIO 
STSTBM or TTRITSt 
IS. Brief higtorleal outline. In 1861 a committee of the B.A. (British 
Association for the Advancement of Science) was appointed to consider 
standards of electrical resistance. The committee decided to adopt a Hcrics 
of electrical units in the C.G.S. absolute system. The unit of resistance in 
the C.G.S. magnetic system was so small (one-billionth of an ohm) that it 
wu considered unfit for practical use and a unit 10* times greater than tho 
C.G.S. unit was selected as of convenient magnitude. This decimall>^ derivr*d 
unit was called the ohm after the German scientist Dr. Ohm. Similarly, 
the C.G.S. magnetic unit of electromotive force waa regarded arf unfit for 
rceommendation, and a unit 10* tim^ greater than the C.G.S. unit was 
■dected, and called the volt, after the Italian electrician Volta. The ohm 
Ittving been selected as a unit, standard resistance coils had to be produced 
and adjusted — a work of great labor. In 18ti4 and 18G5, certain standards 
of renstance or B.A. ohms were produced and put into servico. In 1K72, 
Mr. Latimer Clark produced the well-known dno-meroury standard cell 
which bears his name. 

U. B.A. ohm too imall. In 1878, it was realised that the B.A. ohm 
was too small by over I per cent. That is, the B.A. ohm is now taken to 
be •.i8M of the existing International ohm. 

IT. In 18S1 an international eleetrleal congress at Paris recommended 
that the standard ohm should be represented as the resistance of a uniform 
column of mercury, 1 sq. mm. in cross-section, at deg. cent., the length of 
such a column for the B.A. ohm being approximately 104.9 cm. The Paris 
Congress of 1881 also adopted the ampere, coulomb and farad, as the prac- 
tical units of current, quantity and capacity. The practical syfltom based 
<m the ohm and volt thus became virtually the Q.E.S. (quadrant-Hovoiith- 
gnun-seeond) system, in place of the C.G.S. system: t.e., as thouRh 10* cm. 
were substituted for 1 em. as the unit length, and 10~" g. instead of 1 g. an 
tbemut mass. 

"AniJuaire pour Tan 1913, Paris. Gauthier'Villars. 

t Tables of Equivalents of the U. S. Customar>- and Metric Woights and 
Meuures. Department of Commerce and Labor, Bureau of Stundardu, 
Publication. 

t Wolff, F. A. "The So-called International Electrical Units.** Trans. 
{si £1 Concres** St. Louie. 1004. Vol. I, p. 148. 



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Sec 1-18 UNITS, FACTORS AND TABLgS 

II. In IMS, >n intem*tloiutI oommlMlon met at Farii and adopted 
a lencth of 106 cm. as the length of the merouiy column defining the ohm, aa a 
closer approximation to the true ohm than the B.A. ohm. This 106-em. 
ohm was called the "laral" ohm, as distinguished from the B.A. ohm. 
Legal ohms, volts, etc., have at the present date almost eompletebr dia- 
appeared. They represented an intermediate stage of appronmatton to 
the present international unit values. 

It. In 16M, an international eleetrloal oongran at Paris adopted 
the joule, the watt, and the quadrant, aa the practical units of energy, power 
and inductance, respectively. 

to. Xdlnburgh conference. In 1892, a eonferenea was held in conneo- 
tion with the B.A. meeting at Edinburgh. It was then decided to adopt 
106.3 cm. as the length of mercury column whose resistance should embody 
the ohm. 

M. In un, the International alaetrlcal confraai of Chicago adopted 
the 106.3-cm. ohm, which was called the intemationml ohm. The other 
units of the practical system adjusted in conformity to tliis value were called 
correspondingly the International ampere, volt, oonlomb, etc. The 
name of the umt of inductance was changcKl from the quadrant to the henry, 
in honor of the American physicist of that name. 

tf . In IMO, an internationml electrical oongreu at Paris, aftw some 
debate, adopted the maxwell aa the unit of magnetic flux and the (aua* 
as the unit either of magnetic intensity or of flux-density in the C.Q.S. mag- 
netic system. 

tt. In Itot, an International oommlaaion at London considered the 
order of leauenoe of resistance, current and voltage rtandarda, which 
had been left indefinite at precediiig congresses. It was decided that the 
ohm should be the llrtt unit, and tne ampere the lecond, as determined 
by the rate of electrodeposition of silver under specified conditions. The 
volt was to be determined from the ohm and ampere. 

simnTioHB or ruiTDAMurTAL uiriTS 

M. Length. (L.) Linear distance between any two points. Thennitot 
length in the metric system is the meter, in the C.Q.8. system the centi- 
meter, in the customary system it is any one of the following:— inch, foot, 
yard, pole, furlong, statute mile, nautical mile. 

The fundamental luit of length of the United States ia the international 
meter, the primary standard of which is deposited at the International 
Bureau of Weights and Measures near Paris, France. This is a platinum- 
iridium bar with three fine lines at each end: and the distance between the 
middle lines of each end when the bar is at the temperature of deg. cent., 
and is supported at the two neutral points 28.fi cm, each side of the centre ia 
1 m. by definition. Two copies of this bar (protot3rpe meters) are in the 
pos s es si on of the United States and are deposited at the Bureau of Standarxls. 

The United States yard is defined by the relation 
1 yd. - 3600/3937 m. 

The legal equivalent of the meter for commercial purposes was fixed ■■ 
89.37 in. by the law of July 28, 1866, and experience having shown that this 
value was exact within the error of observation, the United States Office of 
Standard Weights and Measures was, by executive order in 1893, authorised 
to derive the yard from the meter by the use of this relation. 

18. Maaa. (M.) The quantity of matter in a body is estimated either by 
its inertia or by He weight. In the metric system, the unit of mass la 
the CTMn, which was originally defined aa the mass of a oubia centimeter 
of distilled water at deg. cent., although in practice it is taken as the 
thousandth part of a standard kilofl^m. In the customary system, the 
unit is ordinarily any one of the following: avoirdupois grain, ounce, pound, 
or ton (long or short) : occasionally, it is one of the Troy; system (ounce, 
pound). In the use of drugs, it is usually stated in apothecarise weight. The 
mass of precious stones is commonly estimated in carats. 

M. Time. (7*.) The interval elapsing between any two events. In the 
C.Q.8. system, the unit of time is the mean golar leoond, or 86,400th part 
of the mean solar day. In the customary system, it is either the second, min- 
nte, hour, day, week or year of mean solar time. 



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VNITa, PACTOBS, AND TABLES See 1-27 

V. ATM. (A.) Spaoe ooenpted in two dimeniioiu. In th« metric *y»- 
tun, tba unit u primarily tha iquar* OMtw; but the squue dekameter or 
ve ie oaad in und measure; while square millimeter; square centimeter; 
ud square decimeter are also used. In the ouatomary English system the 
unit may be the Kniars mil, the square inch, square loot, square yard, square 
ekain or square mUs. 

tS. TalanM. (T.) Space oecnpied in three dimeodons. In the metric 
■fstem. the unit is piimanly the ouDio meter or itare; but the cubic deci- 
meter or liter is much usea, as well as the cubic centimeter and the cubio 
nnllimeter. In the customary English system, the unite are tha cubic inch, 
nHs foot, enUa yard, cubic mile. 

H. Demltr. (<. ) Ratio of mass to the Tolnme it oecuiuM. In the met- 
ric sjnMem tha onii is primarily tha cram per cubic meter; but decimal deriva- 
tives an vaan common. In the C.Q.S. system, the unit is the (TMn par 
(oUo eanUmatar. 

M. Vore«. (f .) That which tends to change the energy eiisting in a 
(iv«n renon of apace. In mechanics, foit» is that which tends to produce 
ekaaga of motioii in matter. In the C.O.8. system, the unit is the ayna, or 
tkat fona whieh after acting on a free gram during 1 sec., creates therein 
a vsloct^r ol \ em. jiar sec. In mechanics, the unit force is the force 
isquired to support unit msa sgainst atsodard gravity; i.t., gravity at the 
•laadard locality ; the weight, at standard latitude and level, of a gram, a 
UkgTsm, a poand, etc., aooording to tha system considered. 

tl. Tha ir«i|(lit of a bodjr is the gravltatloBal (orea acting upon it. 
Its slasdatd wocht ia its- weight under standard gravitational force. Its 
loeal waigbt ia ita wright xmoer local gravitational force. In the C.O.S. 
•jislem the unit for weight ia the dyna. It is also expressible in the various 



•jstama as the armm weight, Ulogram weight, the pound weight, etc. 

laqxartMit diSaraneaa of uaaga and terminology freauently exist be- 
twaan text-books on physics and text-books on api^ed mecbanics, ia regard 



to the units of mass uul of force. These dilferencee are not eaaentially con- 
nected with Enriish weights and measures, because they exist in the text- 
books of aeveralEnropean countries where the metric system is exclusively 
employed. In phyrics, it is customary to regard the terms gram, milu- 
Bam, kilogram, pound, etc., as deaignating a mass in the sense above 
oafincd. Tha force exerted gravitatlonally on such a unit is called the weight 
cf the unit, and is derived from the product of the mass and the gravitational 
seeeleratioa constant q. Thus in an absolute kinetic system, if a body has 
s mass of si gimioa, its local weight or gravitational force P is 

P -mg (dynes) (2) 

( being the local cravitational aeceleiation. If the body is transferred to a 
place where there is standard gravitational acceleration ft, then: 

Pt - si«t (dynes) (3) 

la appBad meebjudea, it ia customary to regard the terms gram, kilo- 
gram, pound, eto., as designating a wisight or gravitational force In the 
sense above defined; that is, to say ona and tha same term, " kilogram " say, 
is used with a cUfferent meaning in the two cases here compared. If a body 
kaa a standard weight of Wt grama, then by (3), 

Pt - (.Wt/Qti)9t (grams standard weight) (4) 
so that in the books on applied mechanics, where a mass has to appear in 
aa aquation, it ia rapreaented by such a term as Wt/g*. The same is true 
far any system of unite. Thus in (3), if ai is a mass expressed in pounds, 
sad n is the gnvitational eonatant in eustomary measure, then we might 
tad m' a test-book on phyrice: 

Fo — mot (poundals) (5) 

wbareaa in a text-book on applied mechanics (4) would have to be written 

Pt — i.V»/Q»)ll» (standard pounds weight) (6) 

Tba eantrUocal forea of a mass m pounds whirling with a peripheral 

nlodty > feet per sac. at a radius of r feet would be, according to (S) 



y-«(^) (•poundals) (7) 



* Everett. " C.O.S. System of Units." New York, Macmillan Co., 1891, 
P.2>. 



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Sec. 1-32 UNITS, FACTORS, AND TABLES 

a poundal being the foroe which acting on a pound maaa for 1 aeo-i develop* 
in it a velocity of 1 ft> per seo. A pound weight ia equal to 32.2 poundaU. 
But if we oonaider a pound to be a force, represented by a weight W, 

f - — • - ( • pounda force) (8) 

It i> evident that there is no difference between the two contrasted modes of 
presenting the facts, provided that we distinguish carefully between a 
" pound-mass " and a "pound-force." If, however, we use the same word 
"pound " to do duty in the two cases, contradictory and illogical results may 
be obtained. 

It follows that the terms gram, kUogram, pound, ton, etc.. are bus- 
ceptible of either of two distinct meanings; namely, a unit of mass of 
matter or a unit of force equal to the gravitational force exerted on that 
mass by the earth. Confusion can be avoided in all cases, however, by usins 
distinguishing terms, as "gram-mass/' "gram force," or "gram weight." 

SS. Linear velocity Cv). ^ Rate of movement along a line, and ordinarily 
along a straight line; also, time rate of change of space. The unit in the 
C.G.S. system is thecentimeter-per-second, in the metric system the meter- 
per-second, or per minute or per hour. In the customary system, it would 
be any of the customary English units of length per second, minute, hour 
or day, etc. Velocities may be either + or — with respect to a selected 
point on the line of motion. 

SS. Linear acceleration (a). Time rate of change of linear velocity. 
The C.G.S. unit ia the (cm. per seel per sec. ; or the cm. per sec.'. The 
metric unit may be a meter per sec.', or a meter per hour*, or any decimal 
derivative of the meter, per square of the second, minute, hour, etc. A 
useful hybrid unit is the (kilometer per hour) per second. AcceleraUona 
may be either + or — . 

S4i. Plane ani^le ia,p,y). In plane circular trigonometry, the ratio of 
a circular arc to its radius. The C.G.S. unit is the radian, or 1 cm. of arc 
drawn with a radius of 1 cm. The metric unit is the ^ade or one-hundredth 
of the quadrant with unit radius. The customary umt ia either the degree — 
one-ninetieth of the unit-radius qxiadrant— or the revolution of four 
quadrants. 

SS. Angular velocity (») . In plane circular trigonometry, the time rate of 
change of angle at any given instant. The C.G.S. unit is the radian per 
second. The customary unit is either the degree per second, or the revolu- 
tion per second, or per minute, etc. Angular velocities may be either + or — . 

86. Angular acceleration. In plane circular trigonometry, the time 
rate of change of angular velocity. Tne C.G.S. unit is the radian per second 
per second. Customary unita are the degree per sec.', the revolution per 
sec.*, or per min.*, etc. 

t7. Energy (W). The capacity of doing work. Energy may be consid- 
ered as the fundamental entity in terms of which all dynamical quantitiea 
may be downed. In the C.G.S. system, the unit is the erg, or dyne-oentl- 
meter. In mechanics, it may be any product of a unit weight and unit, 
distance such as kilogram-meter, foot-pound, etc., according to the system. 
An industrial unit in the meter-kilogram-eecond system is the watt-hour. 

58. PoWOT (P). Activity or the rate of working. The rate of expending 
enerf^y. The C.G.S. unit is the erg per second. The metric gravitational 
unit is the gram-meter oer second, or a decimal derivative, such as the kilo- 
gram-meter per second. The absolute unit in the meter-kilogram-second 
system is the watt. The customary unit ia the foot-pound per seoond, 
or the horse-power of 560 ft.-lb. per sec. It may be either local or 
standard. 

59. Momentum. The product of the mass of a body and its velocity. 
The C.G.S. unit ia the gram-centlnieter per second. A customary unit 
ia the pound-masa X (foot per second). 

40. Torque (r). Twisting e^ort. The moment of a twisting couple 
ordinarily exerted about a shaft axis. The C.G.S. unit is the dyne-i>erpen- 
dicular-centlmeter; t.«., a dyne acting at right angles to a radius arm 1 cm. 

• Prof. W. J. M. Rankine. "Applied Mechanics," 9th edition, 1877. page -491. 

10 



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UNITS, FACTORS, AND TABLES Scc. 1-41 

In length. The customary nnit is the pound-welcht pen>«ndicnlu' foot. 
If the word "perpendicular" is omitted from the unit, care must be taken to 
distinBuifib from a dyne-centimeter or a foot-pound weight, which are untt« 
of work or energy. A torque is not a work, and can do Do work until it 
advances through an angle. 

41. Fr«niir« (p). A force integral, or summatioD of a force, over a 
■nrface. A pressure may be either total or SFpecific. A total prMture, aa 
itfl name suj^gesta. is the force intef^ral or totu force with reference to ttome 
particular direction or set of directions. A ipedflo preuure, or intensity 
of pressure, is the raiio of a pressure to the surface area over which it la 
ap^ed. or the preuuro per unit area. Unless otherwise sperificd. a 
prestfure ia ordinarily imderstood to be a specific pressure. TbeC.G.S. unit of 
prewure is the dyne per square centimeter, sometimes called a "bar."* 
The metric graTitation unit is the gram weight per square meter, or 
some decimal derivative, such as the kilogram weight per square milli- 
meter. The standard atmospheric pressure of 760 mm. mercury 
at sea-I^vel and deg. cent, at latitude 45 dcg., is 1.01321X10" bars or 
1.01321 mesrabar-t Pressures are thus frequently reckoned in ntmoaphores. 
They are also frequently expressed as heights of a column of uniform liquid. 

41. StrSiia. A change in the shape or mzc of a body due to the applicatian 
of a force or set of forces. In the simplest cases, strains arc (1) voluminal 
compressions or dilations; (2) extensions or compressions in one direction with 
corresponding lateral compressions or dilations (such an extension is cnllcd an 
elongation); (3) a twist or shear. These various strains, when sniiill, are 
expressed aa f<niall numerical fractions, in which the numerator expresses the 
distortion aod the denominator the origihal undistorted value. These strains 
are ordinarily independent of the system of units employed. 

4S. Streaa. The force or set of forces applied to a body, and which tend 
to produce a s^^n. They may be either umple forces, pressure intenaition, 
twists, or combinations of the foregoing, ana are expressible in the corre- 
sponding units. 

M. Young's modulus of elasticity. The specific tension which would 
have to be applied to a uniform prism of a substance in order to double its 
firiginal length, aa judged from a small extension under a measured tension. 
It is a specific tension or longitudinal force per unit area of prinm. The 
C.G.S. unit is the dyne per square centimeter. The metric gravitntion 
unit is the gram-weight per square meter or some decimal derivative. 
A customary unit is the potmd-weight per square Inch. 

4i. Moment of inertia of a body with respect to an axis <J). The 
product of the mass of the body and the square of its radius of gyration 
with respect to the axis conmdered. It is therefore the product of a nia.s.<4 and 
a distance squared. The C.G.S. unit is the g-cm.^ The metric unit is 
a grajn-masft-meter.i A customary unit is the pound-mass-foot.' 
The radius of gyration of a body with respect to an axis is the square root 
<rf the mean square of the distances of all the iMirticles of the bo<ly from the 
axis.^ It is therefore a length. The C.G.S. unit is the centimeter. A 
metric unit is the meter, or decimal derivative. A customary unit is the foot, 

DBFnriTioHt or xliotbio ahd magitetio TnnTS 

M. Blectric quaoti^ (Q). The amount of electricity present in any 
electric charge or passccf through a circuit during any time interval by an 
eleetrio current. The practical unit is the coulomb, the C.G.S. units are the 
abcoulomb and statcoulomb. 

47. Xlectric e.m.f. or pressure (K). That which tends to make an 
riectric current flow. E.m.f. is ordinarily accompanied by a difrcronce of 
electric potential; but an e.m.f. may occur without difference of potential, as 
for example, when a straight bar magnet is thrust-synimetrically into a cir- 
ct]Iar loop of uniform wire. A brief current will thus be set up in the wire 
due^ an e.m.f. induced by the. magnet's motion; but there will be no dilTor- 
encc tji electric potential in or abound the wire. The practical unit in the 
»olt. "fhe C.G.S. units a re the abvo lt and stat volt. 

* Richards- and Stull. Garnegie -Institution Publication No. 7, p. 43, l^ec. 
t Gautbier-Villara. "Les lUeeita Progrte du Systdme Mctrique." Paris, 

iWTrpp/aoeajK , : ../ :.->' - 



IX 



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Sec 1-48 UNITS, r ACTORS, AND TABLES 

E.in.f . may ba reckoned for • complete ctreuit or for Miy portion thareof : 
that ia, each and every portion of a closed drcvit in the iteiuly atata oberya 
Ohm's law. 

48. Potential dUIarance (Jlary). A condition in virtue of which an 
electric current tends to Bow from a place of higher to a place of lower poten* 
tial. The numerical measure of the jmtential oifFerenoe is the work done OB 
a unit quantity of electricity in passins between the two points. The prao- 
tioal umt ia the volt. The C.G.S. units are the abvolt and statvolt. 

4*. Potential gnwUent. The space rate of ehanse of potential, or th« 
change with reepect to distance. ^ An electric potential gradient is the apaoa 
rate of change of electric potential, and similarly for magnetic, thermal or 
gravitational potential. The systematic unit in the practical system is tha 
TOlt per quaorant, but a hybnd unit such as volt {Mr oantlmetar is gener- 
ally used. The C.Q.8. unit is either the abvolt or itatvolt per em. 

50. Ueotrle emreiit (I). The rate at which electricity flows throncb • 
conductor or circuit. The practical unit is the ampere, which is a current 
of one coulomb per second. . The C.Q.B. unit is either the abiainiiara or 
■tatampere. 

•I. Beetrle enrrant deniitf . The ratio of the eurrent flowing throiuh 
a conductor to the crosa-aectional area of that conductor. More strictly, 
the current density at a iwint in a conductor is the ratio of the current through 
a very small plane element of section containing the p<dnt and peniendiouiar 
to the current, to the area of the element. The systematic practioal unit in 
the ampere per iquare qnadraat. In piaotiee, a hybrid unit is preferred 
such as the ampere per iquare eaatlmeter or square inch. The C.G.8. 
unit is either the absampere or statampere par square centimeter. 

•1. nectrie realitaaoe (B). Obstruction to electric flow. The ratio 
of voltage to current in a conductor or dosed circuit. The praetieal nnit ia 
tlia ohm. The C.G.S. unit is either the abiohm or itatofim. 

M. Ueetrie reiiittvltj U). The ratio of potential gradient in a con- 
ductor to the current density thereby produced. Also the specific resistance of 
a substance numerically equal to tne resistance offered by a unit cube of the 
substance as measured between a pair of opposed parallel faces. The sys- 
tematic practioal unit is the ohm-quadrant or numerically equal to the 
resistanoe in a cubic earth-quadrant. A hybrid unit such as the ohm-cm. 
is usually preferred. The C.Q.S. magnetic unit is the absohm-cm. 

54. Kleotrio oonductance (Q). The conducting power of a conductor 
or circuit for electricity. The inverse or reciprocal of electric resistanoe. 
The practical unit is the mho. The C.O.S. umt is either the abmho or the 
■tatmho. 

55. Kleotrio conduetlvlty (y). The spedfio electric conducting power 
of a substance. The redprocal of resistivity. The systematic praetieal 
unit is the mho per quadrant. A hybrid unit, such as the mho per em. 
is usually preferred. The C.G.S. magnetic unit is the abmho par em. 

55. Indnotance (L). The capadty for electromagnetic induction poa- 
seesed by an active drcuit dther on itself or on neighboring circuits. The 
ratio of the magnetic flux linked with and due to an active conductor (num- 
ber of turns X total flux) to the current strength carried. The practical 
unit is the heni7. The C.O.S. units are the abhenrj and itatheaiy. 
The term "inductance" seems to have been first introduced by Heavitide* 
as a brief equivalent for " eoeffident of self^nduotion." Inductance may bo 
divided into two spedes; namely, lelf-indaotanoe and mutual Induetanoo. 
The unit is the same for both spedee. 

5T. Elsctrio capacity (C). Sometimes called parmlttanoa oroapaei- 
tanoe. The power of storiiig or holding an electric charge. The ratio of an 
dectric charge on a conductor to the electric potential £llerence produdnc 
the charge. The practical unit is the farad. The C.O.S. unit is dther the 
abfarad or the itatfarad. The term "permittance" was introduced by 
Heavisidct It should be noted that capadtance is used by a few writers as 
synonymous with eapadty-reactance. 

* Heavidde, 0. "The Electridan," 1884, May 3, p. S83; also "Electrical 
Papers," Macmillan Co., 1892, Vol. 1, p. 3M. 
T Hraviside, 0. "Electrical Papers.''^ 1892, Vol. II, pp. 802 and 837. 

W 

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UNITS. rACTOBS, AND TABLES Sm. l-fi8 



_ k the qwdfio pemuttanoe of a rabateiiM and numar- 
icaOy aqoal to the parmittanoe offered by a unit cube of the ■n«t«ri^l ^a 
■Maiiii ml between a pair of oppoaed parallel facea. In the C.Q.8. deetiie 
•jiUiiu it ia eqnal to I, the dielectric oonatant. Aoalogona to eleetiia 
■■ilui IJTity and macaeUo penneabilitjr. A term iatroduoed and defined 
by Hasraida. * 

n. DlatoBMe eooateat or ipaeUa IndneUT* eapaeltj (Jk). Tha 
laaio of the eapacitr of a oondenaer whose aoatinsa are aeparatad by a given 
aahatance, to the capacity of a aimilar oondenaer whoee platea are aeparatad 
by a TBCunm. A pure numeric in any ayatem of unite. 



Theredproaalof thecapadtf of aeondenMrordieleetrie' 
Na anit for rtaatanne haa Men agreed upim in any syatam. The term 
^ haa, howerar, been sugKcated for thia unit in the practical ayatem. 



so that a aandaoaar hsTing a capacity of one farad woiuid alao have an 
> of ooe daraf . 



U. ■taaUrlljF. The apecifio elastance of a anbatance, and numerically 
ej— I to the ala a tanne ogered by a unit cube of thesubataneeas meaaaredbe- 
t««aa a pair of oppoaed paraUel faees. In the C.a.8. electric ayatem It ia 
the M 'i ' of permittivity. Analofona to eleetrie reaiativity. 

W. »»qoaii«jj (f). In a aiinple altematinc-ounent circuit the number of 
■nWatiatiilwl by the current per aeeond. Tha unit is the oyela par laoond. 
AafOlar nHotttj M of a simple alternating-current circuit. The 
et of the nnmerie 2w and the frequency / of the eurieat in eydee per 
Tbe unit amplorad is the radian par aaooad. 
rtanca (X). In a simple altemating-curTent circuit, the reactiva 
j of ibe impedance, aa distin|piished from tbe active component, 
aaooL Beactanee may be divided into two s|>eciee of mutually oppoaite 
_ J Bamdy, imdnettra raactanea or that species of reactance developed 
ia aa indnetance, 2r/L, and eondanaiTe raaotanoa, or that speciea of le- 
•etanoe developed in a condenser, l/Tmfe. Inductive reactance is denoted 
(ali en us ing toe method of complex imaginary quantitiea) by t he rign + y or 
+V— I. and eondenaive reaetance by the sign —jot— V— 1. The unit of 
I in tbe nraetioal ayatem ia the ohm. The C.G.8. unit ia either the 
>r atatonm. 




(Z). The apparent resistance of an altemaUng-current 
dfcait or patli. Tbe Taetor ram of the railatanca and reactance of the 
path. The piaetieal unit is the ohm. The C.Q.S. unit is either the abnhm 



I (T). The reciprocal of the impedance of an altemating- 
nmat cireirit or path. A plane vector or complex quantity. 

tl. OailJlKitanna (O). In a direct-current cireuit, the reciprocal of 
the resiataiiee. The practical unit ia the mho. In Germany it ia called 
the aKmena. Tbe C.G.8. unit is either the abmho or the etatmho. 

Ia a simple altemating-curTent circuit, the conductance is the active com- 
paacart of the admittance, or the quantity which multiplied by tha root- 
■ SS B square impreaaed alternating voltage gives the active component of 
raot-nMaa-aqaare cmrent, or the component in phase with the e.m.f. The 
fraetieal nut ia the mho. The C.G.S. unit may be either the abmho or 



I (B) . The reactive component of admittance in a ample 

oreidt. Tha practical unit is the mbo. The C.Q.8. 

ay oe eitlaer the abmho or atatmho. 

M. WagiwMo polaa. Thoae portions of the surface of a magnetic source 

vbR the magaetie flux entera or leavea the surface. Magnetic poise apiwar 

a hta ie t there la an abrupt change of permeability. 

n. ■■•■•*'' pol* ■transth. The total flux entering or leaving a pole 
Crided by 4w. No name has been provided for this unit. The product 
d aiagnffir pole atrength and the length of the magnet (interpolar distance) 
iithe macaiaUe momant. 

n. Hacmatie floz (40- The magnetia flow or current that paaaaa through 
say magnarte drenit. The C.O.8. magnetic unit ia tha mazwall. 

tBwvWdc. O. "Elaetrieal Papers." 1803, ToL II, p. 82S. 

U 



.ligilizedbyCoOgle 



^ 



Sec. 1-72 UNITS, FACTORS, AHD TABLBS 

Tl. Hagnatlo fluz-denal^ ((B). ^ The ratio of the magnetic flux in any 
CTOBS B o otional element of a magnetic circuit to the area of that element. 
The C.O.S. magnetic unit is the gftUMi which is also a maxwell per square 
centimeter. 

TS. MagnetomotlTe force (m.zn.f.). That which produces magnetic 
flux. The analogue in the magnetic circuit of electromotive force m ^lie 
electric drouit. No name has been provided for the unit of m.m.f. either 
in the practical or in the C.O.S. magnetic system. The name of gUboz^ 
haSj however, been suggested for the latter. A convenient practical unit 
is the ampere-turn wmeh is Air/lO gilberts. 

74. BCeignetic field Intensity (3C) or gradient of magaette pot«nti«J. 
also termed magnetlaing force. The rate of change of magnetic potential 
with respect to distance. In a region of unit permeability, the field intensity 
is numerically equal to the magnetio flux density. The provisional naxno 
of the C.O.S. magnetic unit is the gilbert per centimeter. A numeric»Uy 
related hybrid unit is the ampere-tum per centimeter. 

Tf . Beluctance ((R). Obstruction to magnetic flow. In a simple mme- 
netic circuit, the ratio of the m.m.f. to the magnetio flux. A provisions,! 
name for the C.O.S. magnetic unit is the oersted. One gilbert m.m.f. acting 
on a magnetic circuit of one oersted reluctance produces one maxwell of flujc. 

T6. Kelnetlfl]^ (»). A specific reluctance, numerically equal to the 
reluctance of unit cube of a substance between any pair of oppoMMd parall«l 
faces. The C.O.S. magnetic tmit is the oersted-cm. 

7T. Permeance. The reciprocal of reluctance. Conducting power for 
magnetic flux. No name has been adopted for this unit. 

78. Permeabllltr (ji). The reciprocal of reluctivity, or tpeelflo pernto— 
anoe. No name has been adopted for this unit. In the dimcnsion&I 
formulas of the C.O.S. system, if the electric and magnetic constants of the 
0ther are considered as mere numerics; both permeability and reluctivity 
are also mere numerics. Also magnetic intensity has the same dimensioixs 
as flux densitjy;* so that on this basis, which was at one time undisputed, 
there would be no difference between gilberts-per-c^nti meter and gausses 
except namerically. It is now generally admitted, f however, that the electric 
and magnetio constants of the ather should not be taken as mere numerice; 
although their dimensional formulas are not defined. , On the latter basis, 
there is a dimensional difl^erence of some kind between magnetio intensity 
in gilbert s-per-cen time ter and flux-density in gausses. The permeability cad 
also be expressed n — 1 + 4«-« where k ia the lUSCeptlblUtjr. 

7*. Karnes for the units In the G.Q.B. magnetio and electric sub- 
systems. Although the practical ohm-volt-ampere series of units is uni- 
versally employed in the great majority of electrical applications, yet it is 
sometimes desirable to use the C.O.S. parent system of units and names for 
such units have only been assigned authoritatively in a few instances, such 
as the "dyne" for the unit of force, and the erg for the unit of work. It has 
been suggestedt that the C.O.S. magnetio units might be distinguished from 
their pr^otypes in the practical system by the prefix ab- or afos- and also 
that the C.G.S. electrostatic units might be similarly distinguished by the 
prefix abstat- or Itat-, as indicated in the following table. Par. 80. 

It should be borne in mind that the prefixes "ab and "stat" have never 
been authorised by any technical society or institution, and terms bearing 
these prefixes are therefore technically irregular. The excuse for this irregu- 
larity is that no proper terms exist by which to describe these units, since the 
phrases "C.O.S. magnetic unitt" or "C.G.S. electric unit/' are cumbersome 
and insuflSdently descriptive.^ Moreover, there can be no ambiguity con- 
cerning the meaning of these Irregular terms. 

* Maxwell, J. C. "A Treatise on Electricity and Magnetism." 1S8L 
Vol. II, p. 244. 

t RQcker, Phfl. Mag., Feb., 1889. 

1 Trans. A. I. E. E., July. 1903. Vol. XXII, p. 529. Franklin, W. 8. 
"Electric Waves," New York, MacmiUan Co.. 1909. p. 67. Bering, C. "Con- 
veraion Tablee," New York. John Wiley ft Sons. 1904. 

Pender, -Hafold. "American Handbook for Electrical Engtneerst" New 
York, John Wiley A Sons. Inc.. 1914. 

14 

Digitized by VjOOQIC 



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S«e. 1-81 VNITB, FACTORS, AND TABLKS 

DimnTzoira or PHOTomTuo toitb 

SI. Lnmlnoa* flnz (V), (Ufbt) b ths phymoal itiinaliis produced by ra- 
distion, which excite* Tiaon. it i< proportional to the nte of flow of r»aiant 
enerfy and to a sttmuliu eoeflelant which dmpenda chiefly on the meetral 
dittnbution of that energy,' The atimuliu coemcient for radiation ofm par- 
tioular wave-len^h is the ratio of the luminoiu flux to the radiant power 

Sroducing it. The conventional unit of luminoiu flux i« the luman or the 
uz emitted by one Intamatlonal Okndl* through one itanMliaa. 

SI. Luminoiu intansltr (I), or eandle-powar. The luminoni inten- 
nty of a point source of liglit u tiie eolid-angular density of the luminoua 
flux emitted by the aouroe in the direction considered; or it is the flux ii«r 
•teradian in that direction. The ooDTentional unit is the candle-power, or 
the (candle) lumen per eteradian. 

55. Intarjuktlonal eandle. A ttaodard of luminoua intensity, eon- 
rentionally equal to the boncle dedinml, maintained between the natioiuki 
laboratoriee of England, France and America through the medium of group* 
of standard incanoeaoent lamp* seasoned and intereompared. The intensity 
given by this standard is the conventional unit or candle. 

M. True ipeeifhi luminous IntaniltT Oh) of an element of a luminoua 
surface is the ratio of the luminous intensity of the element, taken normally, 
to the area of the element. The conventional unit is the oandle per gquar* 
eantlmatar ; or the lumen per sq. cm. 

SI. Apparent spaeiSe luminoua Intandtjr, or brlxhtneu (b), of an 
element of a luminous surface, from a given position, is the luminous intensity 
per unit area of the surface projected on a plane perpendicular to ths line <M 
sight, and including onlv a surface of dimensions small in comparison with 
the .distance from the observer. The conventional unit is the candl* p«r 
■qnara oentlineter of projeeted area; or the apparent lumen per sq. cm. 
For luminous surfaces obeying Lambert's law, or the "cosine law," the true 
and the apparent specific luminous intensities are equal. In practice, the 
apparent specific intensity is ordinarily observed. It has been proposed to 
call a brightness of one apparent lumen per sq. cm. one "lambert . 

56. ZUumination on a rarfa«* (I) is the luminous flux-density over 
the surface, or the flux per unit of intercepting area. The practical unit ia 
the lumen par square foot or the (oot-«andle. The conventional unit 
is the lunten per square oantimstar which has been termed the '^hot" by 
Blondel. It is a cm-candle. The meter-candle, or 10~*phot, is sometimes 
called the candle-lux. The milUphot (10'' phot — millilumen per equare 
centimeter) is roughly equal to a foot-candle, since 1 foot-candle —1.0764 
milliphots. 

Dniinnoin or tbkemal tjhits 

ST. Temperature. The thermal condition of a body considered with 
reference to its capability to communicate heat to other bodies. Bodi** 
at the same temperature do not communicate heat to oae another at their 
bounding surfaces. The conventional unit is the dagrea oanttgrada. 
Other units in practical use are the degree (ahrenltalt, and oecaaionslly tbe 
degree rtaumur. 

SS. QnantitT o{ heat. The amount of heat energy contained in a body 
or transferred from one body to another, by virtue of which temperaturee 
are established or changed. Since heat is a form of energy, a quantity of 
heat may be expressed in units of energy of any kind. Two types of uaita 
are employed, one thermal, the other dynamical. As thermal units the 
C.O.S. unit is the 'aesser-aalorie" or 'therm" or "watar-gram- 
dagrea centigrade," t.<., the quantity of heat required to raise 1 g. of 
water 1 deg. cent.; and as this differs sli^tly with the temi)eratura, the 
interval from 16 deg. to 10 deg. cent, is given in the definition. A larger 
' decimal multiple of this unit, called the ''graatar oalorie" or "Idlogram- 
ealorla" is much used and is equal to 1,000 lesser calories, A practical unit 
is the "British thermal unit'' (B.t.u.), or the heat required to raise 1 lb. 
of water 1 deg. fahr. Dynamic uniu are the erg, the joule, the watt-hr., 
etc. 

Digitized by VjOOQIC 



VNITS. FACTOBS, AND TABLES SeC. 1-80 

^ J liaat u th« ratio of th« qiuntity of best lequired to r*iw unit 
the ralMtmiioe through unit differanoe of temperstuie, to that t»- 
qairad to laiae unit man of water' the uune interval. In the C.Q.S. thermal 
Hatem tliia ia namerieaUr the Hune aa the quantity of heat reomred to ralM 
Is- (i< the aabatanee I dee. cent, at the tamperatura oonaideied. The unit i* 
lawnBUmerie in any ■ysteoi. 

M. Ttaamul eondaetMty. A ■|>eciflc thermal conducting power. It 
ii nnmetieally equal to the flow of heat occurring through a 1-cm. ilab of 
the material, through a eroae-eeetional area of 1 aq. cm., when the difference 
el tem|>erataie between the atufacea of the elab is I deg. eeot. The C.Q.S. 
4rBamieal unit ia the abwatt per centimeter und per degree centigrade. 

n. TlMrmal raciataiuw. Oppoaition to the flow of heat by conduction. 
Cait tbarmal reetstanee in a heat conductor permits unit flow of heat under 
■ait ^ffarenea of temperature. If the flow of heat is measured in abwatts or 
■IS per aeeoncL and the difference of temperature is in deg. cent., the unit 
kw bean called the thermal abaohm. If the flow of heat is measured in watts, 
dia unit haa been called the thermal ohm. 

(L Tharmal raaiatlTlty. The reciprocal of thermal oonduotivity, and 
iwaiaiisble ia. thermal ohm-cm. or absohm-cm. 

M. btant h»«t The quantity of heat required to change the physical 
•late of mnt maas of a substance without changing its temperature, as for 

cent, xnl 



J to convert 1 g. of water at 100 deg. cent, into saturated dry steam 

at 100 deg. eeni. The dynamical C.G,S. unit is the erg per gram. 

N. Xatropy. A quantitatiTe property of a body which is constant 
when the quantity of neat contained in it ia constant; but which increases 
•r deereaaes as the body gains or loaes heat. In any small change of the quan- 
tity tl heat contained in the body, the change in entropy is the ratio of the 
iMBge in qaaatity of beat to the absolute temperature at which the change 
took plaee. The C.G.S. unit is the erg per degree absolute. 

M. Ooaffldant of aspaiuloii, at any temperature, is the ratio of the 
•Hiffgr in dianenMona of a body to the original dimenrions, per dcj^ree centi- 
pads of temp«atar€ increase. The expansion may be linear, as m the ease 
af a mftalHr wire; or it may be Toluroinal as in the ease of a fluid. In either 
caas tks nmt is a nnmerie divided by a change of temperature. 

M. BinfiT''"T The rate of emission of heat from a body per unit of 
saiteee area andper degree centi^de elevation of temperature above its 
" igs. The C.G.8. dsrnamical unit is the erg per second, per square 
and per degree centigrade. 

vr. ICaehBiileal equlvalant of haat. The value in meehanieal units 
af CBsrgy earreapondini; to a given quantity of heat; and, in particular, the 
vafais in mechanical nmts eoiresponding to a unit quantity of heat such as 
a laassr calaria or a B.t.a> 

DnmUOKAL rOBKULAS 

n. Bash and mmaj dartrad imit in an absolute system is necessarily 
fill Hsil fmca the foadamental units of that system in one and only one eom- 
Hifatimi. The particular combination of fundamental unita antraing into a 
derived unit ejLprea s c e its dlmaiwloiu, and when presented algebraically, is 
aBsd the diaiaiaional fonnnla of the unit. Any statical or dynamical 
■nit ia a kinyti" abaolute system involves only three fundamental units, or 
tes iliiiieiMiiMis in three fundamental units. Eleotric or magnetic units 
■avaira Cva fnndanwBtal unita. 

M Aa > giiivl* •sampla, we may consider the unit of velocity. A 
nlactty ■ minrsssrily a lengtb divided by a time. The notion of mass is 
aet iavolvad ia the coneept of velocity. Consequently, if we denote the units 
(t leagtb, maar and time by L, If. and T, respectively, the nature of unit 
niaeityr is ezpraaaed by the f onnuU 

V-t/T-LT-i (velocity unit) (») 

• 17 



y Google 



Sec* 1-100 UNITS, FACTORS, AND TABLES 

The dimensioiu of Telocity are therefore LT'^^ or the firet positire power of 
length and the first negative power of time. Sinoe masa doee not appear in 
this dimenmonal formula we may write the formal diraensiona of TMOcity aa 
iAM^T~\ The three exponents 1, and — 1 completely define the nature of 
Telocity in any absolute system whose fundamental units are length, mass 
and time. Moreover, the dimensional formula of a unit assigns at once the 
■iie of a unit when systems employing different fundamental units are 
compared. Thus if we should compare the unit of velocity in the C.G.S. sya- 
tem with that, say, in the meter-kilogram-day system; then in the latter 
the unit would be the meter per day while in the former it would be the 
centimeter per second. 

100. TaUnff th« mor« complos case of the macnetle unit of, say. 
current-density in a system whose fundamental units are those of both the 
practical and C.G.S, systems; namely, length, mass, time, magnetic tether 
constant ^t and dielectric »ther constant k. Then the dimensional formula 

of current-density is L~*M ^T ^/i~ '. If now we compare the sise of the prao* 
tical unit with that of the C.G.S. unit the former has a unit length of a quad- 
rant or 10* cm., and a mass ximi of 10~" g. Consequently, the sise of the 

?ractical unit is to the sise of the C.G.S. unit in the ratio (10*)'^ X (10-i>)'- 
0~i*; so that the practical unit, the ampere per square quadrant. Is less 
than the C.G.S. unit or absampera per square centimeter in the ratio 10~i*. 
For praoUoal purposes, we should probably ignore the systematic practical 
unit of current density, the ampere per square quadrant, and select a hybrid 
unit, say the ampere t>er square centimeter or per square inch. By such a 
departure from the absolute system, however, the fundamental equations 
of the system involving lengths, areas, or volumes, may become erroneous 
unless we introduce compensating numerical coefficients. 

100a. Vector unltl and complex ouantttiea. As is explained in Sec . 
2, at Par. 163 and elsewhere, vector alternating quantities are much used 
in electrical engineering, and call for corresponmng vector units, as well as 
vector symbols, in the formulas relating to such quantities. Strictly speak- 
ing, such quantities and units are not vectors in the mathematical sense of 
that term, but are "complex" quantities and units, because when two such 
quantities are multiplied together, they do not possess both a "vector prod- 
uct" and a "scalar product as is the case when two mathematical vectors 
are multiplied. Nevertheless, such alternating quantities may be called 
"plane vectors" to avoid conflict with mathematical usage, and the word 
"vector," which is much used in alternating-current literature, may then be 
interpreted, in this sense, as subject to the algebra of complex quantities in a 
plane. 

It is not only logical but also very desirable to distinguish between simple 
and complex quantities, i.e., between scalars and vectors in alternating-our- 
rent formulas employing both. There are three ways in which this is done: 

1. Distinctive symbols, or types of symbol, are used to designate vectors. 
Thus a scalar e.m.f. in volts might be represented by E and a vector by X or 
V, i.e., by a black letter capital, or by a gothio capital, of the same letter. 
This method has the disadvantage of calling for and reserving special fonts 
in representing vectors. 

2. The same symbol may be used, but a distinctive mark, such as an 
**under dot," may be applied to symbols representing vector quantities. 
ThusaBOidare.m.!. in volts might be represented by £, and a vector e.m.f. by 
B. In any formula or equation, if any one term is a vector, all of its terms 
must be vectors; so that the under dot must be applied to each and every 
term of a vector equation. This method has the disadvuntages that it la 
difficult to print or to set up in type, and that a page containing many vector 
formulas presents a speckled appearance. 

3. No special symbolfi or symbol marks may be used for vector quantities, 
but the unit at the end of the line on which the equation appears may have a 
distinctive sign, such as an angle mark ( Z. ), to indicate that the equation 
employs vectora. Thus the equation 

J-/Zi+/Z>+I^i volts Z 

would indicate that the e.m.f. £ is a vector, and can be represented by the 
polygonal or vector sum of three vector elements. In this case the unit of the 
equation becomes a "vector volt." 

101. The Intoraatlonal metric iTitem. There an only three unite 

^ Lijli.cdby^^iUUyiC 



UNITS, FACTOBS, AND TABLBS Soc 1*102 



in the metric system — the meter, the gram and the liter, with decimal derira- 
tiTva denoted by prefixes common to all parte of the system, indudiBg all 
C.G^ unite azui electric or magnetio units. 



i or magneuo umts. 
101. Tha Metrlo PreflzM 



!§ 



Meg»- - 1,000.000- 10« 
Mrria.- 10,000 -10< 
KUo- - 1,000- 10> 
Becio- » 100- 10< 
,Oek»- — 01-I0> 
'Deci- -1/10 -lO-'-iV 
CenU- -I/lOO -l0-«-ii, 
MilU- - - ■ 



1 E 



Greek for gnttt 

Greek for 10,000 as in word myriad 

Greek for 1,000 

Greek for 100 

Greek for 10 

— Latin for 10 aa in U. S. dime 

— Latin for 100 ae in U. S. cent 
-1/1000 -lO-'-iit,- Latin for 1,000 a« in 0. S. mill 

Gredc Miero- - 1/1,000,000 - lO"' -fog^Qoo* °"^ '°' "™^ 

lOS. ■zamplu of lua of pratxm. The length of 1 itatute Engliah mile 
!• ezpreased in the metric system u 1609.33 meters or 1809.33 m. This 
mar also be expressed aa: 1.60933 kilometeia or 1.60933 km. 
or 16.0033 hectometeiB or 160933 centimeters 

" 180.933 dekametezs " 1609330 millimeters 

" 18003.3 decimeters " 1. 80933X10* microns 

The pre6x may be regarded either as designating a secondary 
iniit deeimaUy related to the primary unit, or as indicating a 
(iianfe in the decimal point of the number expressing the di- 
menawna, without changing the unit. Just as the unit of 
American currency, the dollar, may be expressed either as 1 
dollar, 10 dimes, 100 cents, or 1.000 mills, so each of the terms 
dime, oent, and mill may be regarded either as defining a sec- 
ondary unit decimally idated to the dollar; or as change the 
place of tha deramal in expressing a sum of money, without 
oeparting from the dollar unit; smce SI0.93 •• 109.3 dimes 

- 1093 oenta - 10,930 mills. 

104. Tig. t shows to aoale, a Uncth of 1 deelmotar, or 
about one hand's breadth. This is one-tenth of a meter. 
It is ^Tided into 10 parts, each 1/lOOth of a meter or 1 centi- 
Uffter. Each oentimeter is again divided into 10 parts, each 
1/IOOOth of a meter or 1 millimeter. 

IM. If • enbo li formed of dedmetor edges, the volume 
of the cube is. a cubic decimeter, and is called a liter. It is 
about midway between a dry U. 8. quart and a liquid U. S. 
quart: so that a liter may be regarded for rough purposes as 
a quart. One cubic oentimeter of water weighs 1 g. So 
that a liter of water weighs 1,000 g. or a kilogram, wmch is 
rougjily 2 lb. ardrdupois (2.205 lb.) 

IM. Kotrie length. 1 meter - 39.37 U. S. inches or 
roughly a yard or exactly 3 ft. 3 in. + } in. + A in- + sis in- 
Common deramal denvatives are the kilometer (km.) of 
roughly | statute mile; the centimeter (cm.) roughly {inch; 
the mulimflter (nun.) roughly ^ inch. 

lOT. Katrlo area. I sq. m. - 1.196 sq. yd. or roughly 
a square yard, and dednial derivatives, such as the square 
centimeter, or square millimeter. In land measure, a square 
dekameter or an area 10 m. by 10 m. — 100 sq. m. is called an 
ar. A aqnare 100 m. by 100 m. — 10,000 sq. m., contains lOO 
arsoris 1 bectar and forms the metric acre. 1 bectar — 2,471 
acres. The square kilometer contains just 100 hectais. 

105. Katrio Tolume. 1 cu. m., sometimes called a stere, 

— 1.308 cu. yd. or roughly li cu. yd. 
IM. Hetrle mass. 1 g. the mass of 1 cu. cm. of water. 

Common decimal derivatives are the kilogram, or the mass 
of 1 liter of water; the megagram, or mstaio ton, the mass 
of 1 cu. m. of water. The metric ton (1,000 kg.) is a little less 
than the long ton (0.084) so that for many purposes it may 
be taken u a Ions ton- 



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S«c. 1-129 



UNITS, FACTORS, AND TABLES 



COMTEBSION TABLES 
IW. Daniity • 





Grama per 
cu. cm. 


Reciprocal 


1 lb. av. per sq. mil. ft 

I lb. av. per circular mil-ft 


2.936X10* 
2.306X10* 
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Standards, pp. 31-35. 

ISO. Time IntarraU 





Mean solar 1 


days 


hours 


mins. 


sees. 


1 mean solar year. . 
1 week of 7 days . . 
1 mean solar day . . 

1 siderUl day 

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1 siderial hour . . . 
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365.2 
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1 


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right angle 


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Grama 
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Reciprocal 


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lib., weight avoird.. 


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0. 0010197 


0.002206 

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15.43 

1 
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980.6661 

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1 


0. 2248X10-* 

0. 7233X10-* 

0.01673 

0.0010197 

1. 124X10-* 

1 


1 grain, weight 

1 gram, weight 

1 short ton, weight. . 
1 dyne 





% The internatioaally accepted conventional value of gravitational ac- 
celeration at latitude 45 deg. and sea-level. This is usually adopted 
ftlthough later researohea have indicated a slightly different value. 



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^ rt SS -^ CO M 3 ^ t* t* 1*5; 



o o 

X X 

w « 

R !: 

CO CO 



— ooiBoeooeoee e e 



"SSxxxxxxxxxxx X X 



•OO _ 
Ooo a -a 

? V ? fc,2 oJ3-a 

- i i. ^r w 0-i m a) 

.» S3 »ij,ii-3 



CO 
CO 



E5 

.a « 

■ «a 

^•fdi. 



3 
O 



3 
*0> 



•2S J«o^Ef 



?3J 



£ « « 0) a 



I 

! 

"S 



3 
S 



1 

■s 

o •>• 
^ "■3 

""■2 

b h S 

0000 5-' 
H|§ 






40 



yGoogIc 



VHITS, FACTOS8, AND TABLEa S«e. 1-135 



e 



I 



eeooooSo 

xxxxxxSx 

^ ■« ^ 3 eq •-< « CO 
concocQo^aoco 



w^wAr^w^^^nOr^ ^< 



T 
o 



X 



XX»,XXXX(» X 



o ^ ^ 

r X X 
« S g 



SI.* 






-, * * 

■o ^ ^ 

»; X X 



dddodSSo d 



v4 v* '^ 

X o X 



XXXXXSgX X 
MGom09Ocooeo o 



o 
X 



9r*o*o»<-n^»« 






is £ 



siiiilS 

33 UUP. fi^ ^ ^ 9 3 
c <P O £ C S £ »r£ v.rl ^ 

o o 5 S 3- =* * oS a 
2 2° o -^ V E- o «-o 
•23'S''- "- *2 -S** 

pan g E(i.n.a ^sui » « 



Si S 

a a 



C o rt 

Its 



§ a 

•3 1 



•a 
S3 

S.2S.2B* 



5-2 g^ 



41 



^ 



lil 



9 Wd! 



Digilized by V^iOO*^ 



Ic 



S«C. 1-138 UNITS, FACTORS, AND TABLES 

ISS. Torque 





Grams parp. 
cm. 


Reciproeal 


Dynes perp. 
cm. 


Reciprocal 


1 lb.-perp.-ft.« 

1 g.-perp.-om , 

1 dyne-perp.-cm . . 


1.383X10* 

1 
0.0010197 


0.7233X10-* 

1 

980.665 


1.356X10' 
980.665 

1 


0.7375X10-' 
0.0010197 

1 



1ST. Un«ftr Velooity 





Metric equivalent 1 


Meters per sec. 


Reciprocal 




0.3048 

0.005080 

0.4470 

0.2778 

0.5148 


3.281 
196.9 
2.237 
3.60 
1.94.1 






1 km.-per-hr 







1S8. Linear Acceleration 






Meters per 
sec. per sec. 


Reciprocal 


Km. per hr. 
per sec. 


Reciprocal 


1 ft. per sec. per see 

1 mile per hr. per sec 

Standard gravitation ff. . 

1 m. per sec. per sec 

1 km. per hr. per sec. . . . 


0.3048 
0.4470 
9.80665 

1 
0.2778 


3.281 
2.237 
0.10197 

1 
3.600 


1.097 
1.609 
35.30 
3.600 

1 


0.9114 
0.6214 
0.02833 
0,2778 
1 





1S9. Convenion of Anglei (plane) 




Angles 


De- 
grees 


Recip- 
rocal 


Grades 


Recip- 
rocal 


Radian 


Recip- 
rocal 


1 degree 


1 

0.9 
67.30 
90° 

360° 

180° 
90° 
45° 

360° 


1 

1.111 

0.01745 

0.01111 

0.002778 

0.005556 

0.01111 

0.02222 

0.002778 


1.1111 

1 
63.66 

100 

400 

200 

100 
50 

400 


0.900 

1 

0.01571 

0.010 

0.00250 

0.005 

0.010 

0.020 

0.0025 


0.01745 

0.01571 

1 
./2- 1.571 

2r-6.283 
T-3.142 
»/2- 1.571 
W4- 0.7854 

2»-8.283 


57.30 
63.66 
1 

0.6366 
0.1592 
0.3183 
0.6366 
1 2730 
0.1592 


1 radian 

1 quadrant 

1 revolution 

I radians 

r/2 radians 

r/i radians 



140. 

1 lb. per linear yard.. 
1 lb. per linear toot. . . 



Linear Haas 

Gram per meter Reciprocal 

496.1 0.002016 

1488 0.0006720 



* A torque is the product of a force and a length taken perpendicul arly 
thereto. Its dimensions are therefore those of force X —jL where j^y/~^\ 
or —iL^M^T'*. Any element of angle is also the ratio of an element of arc 
length to the length of a radius perpendicular thereto, or has dimensions 
jL/L—j. The product of torque and the angle through which it advanoee 
IS thus —fL'Myr-'Xj='L'MiT-' which are the dimensions of work. If 
the foregoing direction symbols are neglected, a torque appears to have the 
same dimensioos and nature as a work, which is illo(3caI. A torque of 1 g. 
force acting at a radius of I cm. is thus correcily to oe expressed as a gram 
perpendicular oentimeter rather than as a gram centimeter. 



42 



yGoogle 



VNIT3, FACTORS, AND TABLKS 



Sec.] 



i-3 

i o 



A-5 

s> o 



li 



! 



•2 I 

3 



a 
4 









11 



Sow. 



-VK» 






■ " •« 
^ — N 



rr 
« 22 



bod 



XX 

^22 



00 



I I I I 
w« oooo 

gxxxx 

do CO 






,slis- 



00 
00 






TTl 



•| 1,2222 
SSxxxx 

dddd 



-li 



■^8 



tSSc 



S«25 



^ (DO« 



_^ g-woo 



ooa 

go SO SC X Xf^ "^ 



do 



■000 I 



?32 



g8S, 



'OS -a 



U 



ofe"o 



S2 C2S 
00 x.^ ■ 



-SO;! 



^1 









b'C bCb k"3 Uk^ 



as 



43 



TT 

00 

XX 

2" 



777777^ 7.7 

xxxxxxSxx 

tior-^os©oOM« 
b-«^--oe^o*<o 



x 

Ort 
oa> 



000000 00 o 



go SoS55 a 

xx|xxxxx '^"iSx 

o N 'H M rt r» oi r- o »^ « ^ ■ (« 
or- co(0<£iSiS^c«tfn2 



oogo o^^ p, 

xxSx^xS- Si«3 

do odd " 



«oX2f. N •*->»-«3 • 



T 

— O .^ 01 

S— _io2o»3' uiO«« 

V 3oS-"*o"«"' ■-< 
Mx^acisj-j-g • -a-w 

ODD M • . -O WCOW . 

on e> =» o 



NK no-*o- ■ •^'=:o 



© 000- 



1^ 















Diyilizc-ii hyV^iDD^lC 



S«c. 1-143 



VlflTS, FACTORS, AND TABLES 



141. ■tone* of Wftter 

1 Mr*-tt. -325,800 IT. S. gal. -43,560 ou. ft. - 1613 ou. yd. • 
Ifal. -0.3069X10-' aon-ft. 

1 en. ft. -0.2298X 10-< scre-ft. 
1 OU. 74. -0.00062 aere-ft. 
1 OU. m. -0.000811 aore-ft. 

144. Temp«ratur« 



1234 ou. 



Seals 


Ftaeiincpi^t 
of water 


Boiling point 
of water 


Int«rval 


Fahrenheit 

Centigrade 

lUaumur 


32 dec. 
Odeg. 
Odeg. 


212 dec. 

100 dec. 

80 dec. 


180 deg. 

100 dec. 

80 dec. 



1 dec. fahr. - 0.5556 or (|) deg. cent. - 0.4444 or (|) dw. lUa. 

1 dec. cent. - 0.8000 deg. lUa. - 1 . 800 dec. f a&. 

1 dec. R«a. - 2.250 dec. fahr. - 1 .250 dec. eant. 

Abaolnt* nro - -273.1 deg. cent. - -491.6 deg. fahr. - -218. J 
dec. rteumur. 

Td> - 273. 1 + deg. cent, (in cent, aoale) 
Tata — 491.6 + deg. fahr. (in fahr. scale) 
Tata — 218.5 + dec- r6aumur (in rteumur scale) 

TiM liit«m»tton»l t^drocan leale of tomiMratars. 

14f, MMhsnleal oqulTalent of heat. 

1 B.t.tl. - 1.054 Joules - 777.5 ft-lb. - 0.2928 watt-hr. -0.0003927 

1 Joule - 0.7^6 ft-lb. - 0.0009488 B.t.a. - 0.0002778 watt-hr. 
1 ft-lb. -1.356 iouIeB-0.001286 B.t.u. -0.0003766 watt-hr. 
1 watt-hr. -3,600 joules -2.655 ft-lb. -3.415 B.t.u. 
Also see Par. lit on energy conversion faotots. 



HATHUCATIGAL COH8TANT8 AITD TABLX8 

146. Viofnl Conitamti. Base of the hyperbolic system of locarithma 
— • — 2.7183 to the nearest unit in five sicmficant figures; it is not a com- 
mensurate quantity. 

Ratio of mroumference to diameter of circle — r — 3.1416 (incommensurate) 





Numerio 


Reciprocal 




2.7183 
0.434295 
3.1416 
6.2832 
9.4248 
12.566 
1.5708 
1.0472 
0.7854 
0.8696 
1.7728 
1.4142 
1.7321 


0.86788 

2.302585 

0.31831 

0.16915 

0.10610 

0.079877 

0.63662 

0.95493 

1.2782 

0.10132 

0.56419 

0.70711 

0.57733 






3r 


3r 


4t 


«/2 


w/a............. 


r/4 


r> 


^/i 


Z^:::::::::::: 


Vs 





Irodiaa- 57.296 dec- -57 dec., 17 min. and 45 sec. 

Aa are of 1 dag., in terms of its radius -0.017453. 

For further oonrenion factors of circular measure, see Par. 184 on antfes. 



44 



yGoogle 



UlflTS, FACTORS, AND TABLES SeC 1-147 

l«r. Vatima Bines And OodnM 
KoTB.— For ooaineB use risht-hand coluznn of degreee and lower tine of tenihe. 






D« tS "OJ "OJ '0.3 °0w4 "OJl 'O.* n).7 "0^ •0.9 



-r 



OjoaooDimrojogts 



OjOOSS 



llill7S0jDU2OjaS0»Ojlll27 



limi'OjOiw 
ojgsnojOMi 
ijmmsaK 

ojotsojota 

0J3H'OJ40g 
0JS«.0JSS2 

ojtm'ojtm 
JNS oans 

OJDTV.OJOM 

t asm sua 

OJdtOJttS 





OjO»8 

Oi>732 

OJIKW 
OJ080 
0J2E3 
0.14M 
OJSM 



OJMOl 

oisre 

0.07S0 
OjOt24 

0J2n 

0JM4 
OJU« 



J77! OJ78S 
JM2 0.19(9 
0.3113 



OJIM 
0J4S3 



U OJaSjOJtOS 0.2612 
M 0JW0J773 0J790 
n 0.aM,0.2»40 0.»S7 

» |OJ)M0.32RO.S»9 



tr o.Mio;o.Mi7 



0.1453 

o.3SMio.3aao o.3ais 



oirwooraz 

9J9II70J(I3 
twM7,0J083 



JOO 



twOWO 



0J778 



0.«»» 

OvOSS 



0.1300 
OJtTO 

0.2639 
0J807 
0.2974 
0J140 
0.3305 

0.3469 
0.3633 
0.3795 



ja39 0J«56 
0-4J15 



«.«4 0.43S»0A415 
0;I540,Oj45S6 0.4571 
04i«5O.inO 0.4726 
0JMB;Oj48(3 0^4879 



9 9 JOOOOJOI5 0.5030 

31 951500.5165 O.U80 

S »ja90J3l4 0A29 

a OJ4M0.5461 0^476 

N 0J592 0.5606 OJtU 



0J736'0J7SO 
04157,0.6170 

oj»,ojao7 



» 9J4tS0.«<41 
<I (JM1,0J674 

a tsmiajsm 

a SJnoO.6833 
M 0JK7Oj606« 



la 



•Oj» 



0Jt7M 
O.S906 
0.6046 
Oj«184 

oj6aio 

0.6455 
0.6687 
0.6717 
0.6645 
OJ972 



•«.8 



OJWTC 
0j0M4 
Oj0419 
Oi)593 
OJ0767 

OJ0941 
0JU6 
0J288 
0J461 
0J6a3 

OJ80S 

0J9n 



0.21300.2147 



0.^74 
0^4431 
0.4586 
0^41 
0.4894 

0.50U 
0.519S 
0A44 
0.H90 
0JMB5 

0JS779 





0.6198 

0.6334 

0.6468 

"" 
0.6730 





•0.7 



0.2317 
0.2487 

0.2(56 
0J!823 
0.2990 
0.8156 

oxm 

0.3486 
0.3649 
OJKll 
OJ971 
0.4131 

0.4289 
0.4446 
0.4601 
0.4756 
O.4909 

0.1060 
0JI210 
" " 
0.1506 
0J650 

o.c7n 

0J934 
0.6074 
0.f 
0.6347 



0.M81 
0.6613 
0.6743 
0.6871 
0J997 



•0.6 



OJ0OS7 

osaea 

0JB436 
OJ0610 

ojogss 

0J133 
0J305 
OJ478 
OJ650 

0J822 
0J994 
0.2164 
0.2334 
0.2504 

0JM73 
0.2840 
0J0D7 
0.3173 
0J338 

0.3503 
O.I«65 
OJ8S7 
0.3987 
0w4147 

0.4306 
04462 
0.4617 
0.4772 
0w4934 

0Ji075 
0.5225 



0.5373 
0M19 
0J664 

0.5807 

ojrns 

0.6088 



.«!11DJ325 
0.6361 



aMU 
0.6(26 
0.6756 
0.6884 
0.7009 



•Oi 



0X105 
0iB79 
Oi>454 
Oi)628 
Oj0802 

0X97( 
0.1149 
0J323 
0.1«( 
0J(68 

0.1840 
OJOll 
0.2181 
0.23(1 
0J531 

0.2689 
0.3857 
0J024 
0.3190 
0.3355 

0.3518 
0.3(81 
0J843 
0^006 
0.41(3 

Oj4331 
0^78 
0.4(33 
04787 
04939 

0.5090 
0.5240 



OJ534 
0M78 

0.5821 
0J963 
0.(101 
0.6239 
04374 

0.(508 



0.(7(9 

04896 

0.7021 



•04 



0j0122 
0j0397 
OJ0471 
Oil645 
OjOSM 

OJ0998 
0.1167 
OJ340 
0J513 
0J(85 

0J8S7 
0Ji028 
0^1(6 
0.23(8 
0.2538 

0J706 
0.2874 
04040 
04206 
04371 

0.3535 
0.3(97 
04859 
04019 
04179 

04337 
04493 
04648 
04802 
04955 

0410S 
04255 
04402 
04548 
04(03 

04835 
04978 
0.(115 
04252 
04888 

0.6521 
0.((52 
0.(782 

::: 

0.7034 



•04 



0.0140 
0JB14 
04488 
04((3 
04837 

OJOU 
0Jlg4 
0.1357 
0J530 
0J702 

0J874 
0J045 
04215 
04385 
04554 

04733 
04890 
04057 
04228 
04387 

0.8551 
0.8714 
04875 
0.4035 
04195 

04852 
04509 
04((4 
04818 
04970 

04120 
04270 

%^ 
04707 

04850 
04990 
0.(129 
042(6 
0.6401 

0.6534 
0.66(S 
0.(794 
0.(921 
0.7D4( 



•0 4 



04157 
04832 
04506 
04(80 
048(4 

0J038 
0.1201 
0J374 
0.1547 
0J719 

0.1881 
040(2 
04133 
04402 
04571 

04740 
04907 
04074 
04239 
04401 

0.3567 
0.3780 
04891 
040(1 
04310 

0.48(8 
0.4524 
04679 
04883 
04965 

04135 
04284 
04432 
04677 
04721 

04864 
0.(004 
0.6143 
0.(280 
0.6414 

0.(547 
0.(678 
0.(807 
04(84 
0.7059 



•oa 



87 
8( 
85 

84 
83 

83 
81 

80» 

79 
78 
77 
7( 
75 

74 
73 
72 
71 
70^ 

(9 
(8 
67 
(( 
(5 

64 
(3 

(1 
61 
(O* 

59 
58 

57 
66 
65 

54 
53 
52 
61 

nr 

49 
48 
47 
46 
45 



Dec. 



y Google 



f 



Sec 1-147 UNITS, FACTORS, AND TABLES 

Katnral Biaaa and Ootinas. — Cojtduded 



Deg. 


•OJ) 


•0.1 


•0J8 


•OJ 


•0.4 


•0.5 


•0.6 


•0.7 


•0.8 


•0.9 




45 


0.7071 


0.7083 


0.7006 


0.7108 


0.7120 


0.7133 


0.7145 


0.7157 


0.7189 


0.7181 


44 


40 


0.7193 


0.7206 


0.7218 


0.7230 


0.7242 


0.7254 


0.7266 


0.7378 


0.7290 


0.7302 


43 


47 


0.7314 


0.7325 


0.7337 


0.7349 


0.7361 


0.7373 


0.7385 


0.7396 0.7408 


0.7420 


43 


48 


0.7431:0.7443 0.745S 


0.7466 


0.747810.7490 


0.7501 


0.75130.7524 


0.7536 


41 


49 


0.7547 0.7559,0.7570 


0.7581 


0.769310.7604 


0.7615 


0.7627 


0.7638 


0.7649 


40» 


Uf 


0.7680 0.7672 0.7683 


.7694 .7705'o .7716'9 .7727 


0.7738 


0.7749 


0.7760 


30 


SI 


0.7771 0.7782 10.7793 


0.7804 0.7815 0.7826,0.7837|0.7848 


0.7859 


0.7869 


38 


S3 


0.7880 0.7891 


0.7902 


0.7912 O.7923,n.7934lo.7944lo.7955 


0.7985 


0.7976 


87 


53 


0.7986 0.7997 


0.8007 


0.8018 0.8028 


0.8039 


0.8049 


0.8059 


0.8070 


OJWWO 


36 


54 


0.8090J0.8100 


0.8111 


0.81210.81310.8141 


0.8151 


0.8161 


0.8171 


0.8181 


SS 


55 


0.8192 0.8202 


0.8211 


0.82210.82310.8241 


0.8251 


0.8261 


0.8271 


0.8281 


34 


5« 


0.829010.8300 


0.831010.832010.832910.8339 


0.8348 


0.8358 


0J368 


0X377 


33 


87 


0.8387 0.8396 


0.8406 


0.8415 0.8425,0.8434 


0.8443 


0.8453 


0.8462 


0X471 


32 


58 


0.8480 0.8490:0.8499 


0.8508 0.8517 0.8526 


0.8636 


0J545 


0.8554 0.8563 


31 


59 


0.8572 0.8581|0 .8590 


0.8599 0.8607 0.8616 


0.8826 


0.8634 


0.8043,0.8652 


SOP 


60» 


0.8660 


0.8669 


0.8678 0.888610.8695 0.8704 


0.8712 


0.8721 


0.8729 0.8738 


29 


61 


0.8746 


0.8755 


0.8763^0.877110.8780 0.8788 


.879610^805 


0.88130J821 


28 


83 


0.8829 


0.8838 


.8846,0 .8854 .8862,0 .8870 


0.8878 0.8886 0.889410.8902 


27 


63 


0.8910 


0J918 


0.8926;O.8934:o.8942.0.8949|0.8957!O.8965:0 .897310 .8980 


26 


64 


0.8988 


0.8996 


0.9003 


QMU 


0JI018 0.9036 


04)033 0.9041 0.9048 0.9056 


25 


65 


0.9063 


0.9070 0.9078 


0.9085 


0.9092 0.9100 


0.9107 0.9114 0.91210.9128 


24 


66 


0.9135 


0.9143]0.9160 


0.9157 


0.9164 0.9171 


0.9178 0.918410.91910.9198 


23 


67 


0.9205 


0.9212 0.9219 0.9225 


0.9232 0.9239 


J)245 J)252 .9259 jnes 


23 


68 


0.9272 


0.9278 0.928510.9291 


0.9298 0.9304 


0.931110.9317 


.9323,0 .9330 


21 


69 


.9336 .9342|0 .9348|0 .9364 


0.93610.9367 


0.9373 0.9379 


0JI385 0X391 


20» 


70° 


0.9397 


.9403 .9409;o .9415'o .942l!o .9426 


0.9432 0.9438 


0.9444'o.9449 


19 


71 


0.9465 


0.9461 


.9466 .947210 .9478 .9483 .9489 .9494 


0.950019.9505 


18 


73 


0.9511 


0.9516 


0.9521 0.9527 0.9532 D. 9537 0.9542 0.9548 


0X5530.9558 


•17 


73 


0.9563 


0.9568 


.9573 , J)578 , .9583 ! .9588 1 .9593 .9598 


0.9603 0.9608 


16 


74 


0M13 


0.9617 


0.9622 0.9627 


0.9632 


0.9636 0.96410.9646 


0X660 0.9655 


15 


75 


0.9669 


0.9664 


0.9668 0.9673 


0.9677 


0. 9681 '0. 9686 0.9690 


0.9694'o.9«99 


U 


76 


0.9703 


0.9707 


0.97110.9715 


0.9720 


0.9724 


0.9728 0.9732 


0.9736 


0.9740 


13 


77 


0.9744 


0.9748 


0.9751 0.9755 


0.9759 


0.9763 


0.9767 0.9770 


0X774 


oxm 


12 


78 


0.9781 


0.9785 


0.9789,0.9792 


0.9796 


0.9799 


0.980310 .9806 


0X810 


0X813 


11 


79 


0.9816 


0.9820 


0.9823 0.9826 


0.9829 


0.9833 


0.9836 


0.9839 


0.9842 


0X845 


10* 


80» 


0.9848 


0.9851 


0.9854 0.9857 


0.9860 


0.9863 


0.9866 


0.9869 


0.9871 


0.9874 


» 


81 


0.9877 


0.9880 


0.988210.9885 0.9888 


0.9890,0.9893 


0.9895 


0X898 0.9900 


8 


83 


OMm 


0.9905 


0.9907,0.9910 0.9912 


0.9914 OJW17;OJKI10 


0X9210X923 


7 


83 


0.9925 


0.9928 


0. 9930,0 .9932I0. 9934 


0.9936 


0.9938,0.9940 


0.9942 0X943 


6 


84 


0.9945 


0.9947 


0.9949 


0.99510.9952 0.9954 


0.9956 


0.9957 


0.9959 0X960 


5 


85 


0.9962 0.9963 


0.9965 


0.9966 0.9968 0.9969 0.9971 


0.9972 


0.9973 0.9974 


4 


86 


0.9978|0.9«VV|0.99-8 


.9979 .9980,0 .9981 ;0 .9982 


0.998310.9984^0.9985 


3 


87 


0.9986 0.9987 0.9988 
0.9994 0.9995|0. 9995 


.9989 .9990,0 .9990,0 .9991 


0.9992!o.9993|0.9993 


3 


88 


0.999610.9996 


0.9997 0.9997 


0J»997 


0.9998 


0.9998 


1 


89 


0.9998 


0.9999 


0J999 


0.9999 


0.9999 


1.000 


1X00 


1X00 


1X00 


IXCO 


0* 




"1.0 


•0.9 


"•0.8 


•0.7 


•0.6 


•0.5 


•0.4 


°0J |'0.2 


•0.1 


De«. 



y Google 



UNITS, FACTORS, AND TABLES S««. 1-148 



148. Natural Taacanta and Cotancanta 

KoTS. — For cotangents \uM right-hand column of dcgreon and lower Ud* of 
tenths 



D«K n>.0 °0.1 \°OJl °03 ■'0.4 "OJS •0.« "0.7 "O^ °0 



JMOO JM171O.0O3S .0052 
0.0175 0.em 0.0209 0J)227 
0.0349 0.0387:0.0384 0.0402 
.0524 .0542 .aM9 .0577 
.0*99 .0717 lO .0734i0 X7S2 

.0875:0 .0892 0.0910 X»28 
0.1051 i0.1069,O.I08f)0.11(M 
0.1228 0.124fi 0.1263,0.1281 
0.14(1.5 0.1423 0.1441 0.14.59 
0.1584 0.1602 0.1620,0.1638, 



0.0070 
0.0244 
0.0419 
0JO6M 
Oj0769 



OilC87 0.0105 0.0122 0.0140 
OU)262|0.0279iO .029710.0314 
.0437 .045410 .0472 .0489 
.0612 .0629 .0M7 .0664 



0.1122;0.U39 
0.12990.1317 
0.14770.1405 
0.166510.1673 



0.0187 
0.0332 
0.0507 

0.06K2 



!0787 !0805^0 !o822,0 !o840:o j)857 



0.17S3 0.1781 
0.1944 0.1962 
0.21260.21+4 
0.2:1(19 0.2.327 
0.24930.2512 

1 I 

0.2679 0.2698 
0J867 0.28S6 
0.31)57 0. .3076 
0-3349 0. .1209 
0.3443 0.3463 

I 

OJ«40 0.3659 
0JS39OJM9! 
0.4(rtC;0.40«li 
0.4245 0,4265 
0.4452,0.4473, 



lO .1799:0.1817' 
10.1980 0.1998 
10.2162 0.2180 
0.2343 0.2364 
J0.2530|0.2549, 

0.271710.2736 
0.2905 0.2924 
OJ0960J115 
0J2S8 0.3307 
,0^482 0.3502 

!o .3*79 0.3699 
0.3879 0.3899 

0.4C81 0.4101 
.4286 .43C7 
0.4494,0.4515 



l0.1835'0.18.W 
0.20160J035 

0.2199 0.2217 
.2382 .2401 
,0J568,0J586 



0.098110 
0.11570 
0J334 
0.1512 
0.1691,0 

0.1871 
0.20530 
0.22350 
0.2419 
0.2605,0 



0998:0.1016! 
.11750.1192 

.13.520.1370, 
.15.3(1 0.1.54S 
.1709 0.1727, 

1890 0.1908 
.2(171 J089 
J2,54 J272 
.243s .24.56 
J!623 0J!b42, 



0.1033 
0.1210 
0.1388 

0.1566 
0.1745 

0.1926 
0J1(I7 

0.2290 
0.2475 
0.2661 



.275410 J773 .2792'0 .281 10 .2»l.TO!o .2849 
0^943:0.2962 0J981 0.300(1 OJKIM) 0.30.38 
CJ134 0.3153 0J172 0J19I 0.3211 0.3230 
.3327 .3346|0 .33(i,5|0 .33K.5 .3404 .3424 
J622 .3541 J561 .3581 10 .3600 ,0 M20 

J719 J7.39 .3759 .3779;o .3799 .3819 
.3919 0.393910 .3959|0 .3979 .401X10 .4020 
0.4122 0.4142 0.4163 0.41H3 0.4204 0.4224 
.4327 .4348 .4369 .439(1 .4411 .4431 
.4536 .4557|0 .4578,0 .4599.0 .4621 .4642 



.4663,0 .4684 'o .4706 .4727 .474810 .4770 .4791 .48I3'o .4834 .48.56 
0.4877:0.4899 O.4921I0.4942 0.4964 iO .498610 JOOS 0.5029 .5051 0.5073 

J095;0 .5117,0^13910 .6161 |0J184 0.52(J6 0J228, 0.525(1 0.6272 0.5295 
0.5317 OJ340 0.5362 0J384 0.6407 0.5430 0.54,52 0J47,5 0.549X 0.5.52(1 
0i543|0.5566|O.i589OJi«12.0J635 0.5658 0.4681,0.5704 OJ727 0.5750 

OJ774'o.5797 0.5820 OJ)844'o.S867iO.S890,0.5«14 0.5938 0.S96I 0J9R5 
0.6009 0.6032 0.6058 0.60300.6104 0.6128 0.61.52 0.6176 0.62(WiO. 6224 

0.6249 0.6273:0.6297, 0.6322:0.6346 0.6371 0.6305 0.6420:0.6445,0 .6469 
0.6494 0.6519 0.6544 0.6569 0.6594 0.6619 ,6644.0. f.OfiO 0.6fi!l4 0.6720 
04745,0 .6771 .6796,0 .6822.0 .684710 .6873,0 .6899,0 .6924,0 .6950,0 .6976 

35 .7002 .7028 .7054 .7080 .7107 .7133 .7l.»'o .7186'0 .7212 .7239 

36 0.7265 0.7292 0.73I9O.7346,0.7373'O.740()O.7427;O.7454O.748llO.75(l« 

37 0.753(10.7563,0.7590 0.7618 0.7646 0.7673,0.7701 0.7729 0.7757 0.77S5 

38 0.7R13'0.7841'0.7S69 0.7898 0.7926 0.79,54 0.7983 0.8012 0.804110.8069 
J9 0.8098.0.8127j0.8156.0.8185 0.8214.0.8243,0.8273.0.8302 0.8332.0.8361 

«° !o«91 0.8421 0.8451 0.8481 0.8511 0.85410.8571 0.8601 0.86320.8662 

41 ;OJ!6930.8724 0.875410.8785 0.8816 0.8847 0.8878 0.8910 0J(94|.0 .8972 

42 i 0. 9004 :0.9a30 0.9067,0.9099 0.913r0.91M,0 .9195 .9228 .926(1 0.9293 

43 : .9315 .9:i58 .9391 .9424 .9457 .9490 .9,523 .9556 .9.5(K1 .9623 

44 10.9657 0.8691 0.9725 0.9759,0.9793,0.9827 0.9861 .9896 .9930 .9965 



•IjO 



•0.9 «0.8 



°0.7 °0.6 •OJ 



°0.4 



"VJ 



"0.2 



°0.1 



68 
67 
66 
65 

64 

63 

62 

61 
60° 

59 
68 
87 
56 
55 

54 

S3 
52 
51 
bO° 

49 
48 
47 
46 
45 



Deg 



«7 



yGoogle 



Sec 1-148 UNITS, FACTORS, AND TABLES 

Hatural Tuicanti and OotKotwatt—Cmeluded 



Deg. 


°0.0 


•0.1 


•0.2 


•0.3 


•0.4 


•0.6 


•0.6 


•0.7 


•0.8 


•0.9 






45 


IJKXm 


1.0035 


1j0070 


1X105 


1X141 


1X176 


1X313 


1X147 


1X288 


1X319 


44 




46 


lJ»5t 


1.0392 


11)428 


1X464 


1X601 


1X638 


1X575 


1X618 


1X649 


1X686 


4S 




47 


1J0734 


ijmti 


1J)799 


1X887 


1X876 


1X913 


1X951 


1X990 


1J038 


1J067 


43 




4S 


1JI06 


1.1145 


1J184 


1J234 


1.1368 


1J303 


1J343 


1.1383 


1.1423 


1.1463 


41 




4« 


1.1504 


1J644 


1J685 


1J626 


1.1667 


1.1708 


1.1760 


1.1792 


1.1833 


1J875 


4XP 




80° 


1J818 


1J960 


1.2(102 


1X045 


1X088 


1X131 


1X174 


1X318 


1X261 


1.3306 


39 




61 


1.2349 


1.2393 


1.2437 


1X482 


1X537 


1X572 


1X617 


1X662 


1X708 


1X763 


38 




ta 


1J7W 


1.2846 


1.3892 


1X938 


1X985 


1X083 


1X079 


1X137 


1X176 


1X233 


•7 




a 


1J270 


1J319 


1J367 


1X416 


1X466 


1X514 


1X664 


1X613 


1X663 


1X713 


U 




u 


1J764 


1.3814 


1.3866 


1X916 


1X968 


1X019 


1X071 


1X124 


1X176 


1X238 


3S 




u 


1.4281 


1j4335 


1.4388 


1.4442 


1.4496 


1.4550 


1X605 


1X669 


1X716 


1.4770 


34 




so 


1.4826 


1.4882 


1.4938 


1X994 


1X051 


1X108 


1X166 


1X224 


1X282 


1X340 


3S 




f7 


1.53W 


1JS458 


1JU17 


1X677 


1X637 


1X697 


1X757 


1X818 


1X880 


1X941 


*3. 




K 


IJHXB 


1.6066 


1.6138 


1X191 


1X355 


1X319 


1.6383 


1.6447 


1.6513 


1.6577 


*1 




M 


IMa 


1.6709 


1.6775 


1.6842 


1X909 


1X977 


1.7046 


1 .7113 


1.7183 


1.7361 


80» 




60° 


1.7321 


1.7391 


1 .7481 


1.7532 


1.7603 


1.7676 


1.7747 


1.7830 


1.7893 


1.7966 


19 




61 


1.8040 


1.8115 


1.8190 


1X265 


1X341 


1X418 


1X406 


1X573 


1X660 


1X738 


18 




82 


1J807 


1.8887 


1.8967 


1X047 


1X128 


1X310 


1X392 


1X376 


1X468 


1X643 


17 




43 


1.9626 


1.9711 


1.9797 


1.9883 


1X970 


2X067 


3X145 


2X233 


3X333 


3X413 


M 




M 


2.9(03 


2.4059 


2X686 


3X778 

- 


2X872 


3X966 


2.1060 


2J166 


3.1351 


2J348 


36 




«S 


2J445 


2.1643 


3.1642 


3J742 


3J842 


3J943 


2X046 


2X148 


3X261 


2X366 


14 




U 


2.2460 


2.2566 


2.2673 


2X781 


3X889 


3X998 


3X109 


2X220 


2X833 


3X445 


IS 




«7 


2.3S59 


2J673 


24789 


2X906 


3X023 


3X142 


3X363 


2X383 


2X604 


3X637 


33 




68 


2.4751 


2.4876 


2.6002 


2X129 


3X257 


2X386 


3X617 


2X649 


2X782 


3X916 


31 




6> 


2.6051 


2JI187 


2X325 


2.6464 


3.6605 


2X746 


2.6889 


2.7034 


2.7179 


3.7326 


30* 




IV 


2.7476 


3.7625 


2.7776 


2.7929 


3X083 


2X239 


2X397 


2X556 


2X716 


2X878 


19 




71 


3.9043 


2JO08 


3X376 


2X644 


3X714 


2X887 


3X061 


3X237 


2X416 


3X695 


18 




n 


8J0777 


3X961 


3J146 


3.1334 


3.1634 


2.1716 


8J910 


3X106 


3X806 


3X606 


•17 




n 


8.2709 


3.2914 


3X122 


3X333 


3X544 


3X759 


3X977 


3X197 


3X420 


3X646 


16 




74 


3^74 


3J105 


3X339 


3X576 


3X816 


3X059 


3X305 


3X654 


3.6806 


3.7083 


IS 




75 


8.7321 


3.7583 


3.7848 


3X118 


3X391 


3X667 


3X947 


3.9233 


3.9620 


3.9813 


14 




79 


4.0108 


4.0408 


4X713 


4J022 


4.1335 


4.1663 


4J976 


4X303 


4X686 


4XS72 


It 




77 


4.3315 


4.3662 


4.4016 


4X374 


4.4737 


4X107 


4X483 


4X864 


4X263 


4.6646 


M 




78 


4.7046 


4.7463 


4.7867 


4X288 


4X716 


4X162 


4X694 


6X046 


6X604 


5X970 


11 




7t 


6J446 


5 J 929 


6X422 


6X924 


6X436 


5X965 


6X486 


5X026 


5X578 


6X140 


10° 




80» 


6.6713 


5.7297 


6.7894 


6X502 


6X124 


6X768 


6.0405 


6.1066 


6J742 


6X433 


« 




81 


6J138 


6.3859 


6.4596 


6X350 


6X122 


6X912 


6.7720 


6X548 


6X395 


7X264 


8 




83 


7J154 


7.2066 


7X002 


7X962 


7v4947 


7X958 


7X996 


7X062 


7X168 


8X386 


7 




83 


8.1443 


8.2636 


8X863 


8X126 


8X427 


8.7769 


8X162 


9X679 


9X062 


0X673 


6 




84 


9.5144 


9.677 


9X45 


10X2 


10X0 


10X9 


10X8 


10.78 


10.99 


11X0 


6 




85 


11.43 


11.66 


11.91 


12.16 


12.43 


13.71 


13X0 


13X0 


13.63 


18X6 


4 




86 


14 JO 


14.67 


16X6 


15.46 


16X9 


16.35 


16X3 


17X4 


17 XM 


18.46 


3 




87 


19:08 


19.74 


30.46 


21X0 


32X2 


22.90 


23X6 


24.90 


26X3 


37X7 


3 




88 


38.64 


80 J4 


81X2 


33.69 


35X0 


38.19 


40.92 


44X7 


47.74 


52.08 


1 




8» 


57.39 


68.66 


71X3 


81X5 


95.49 


114X 


143 X 


191 X 


386X 


673 X 


0» 






•1.0 


•0.9 


•0.8 


•0.7 


•0,6 


•0.5 


•0.4 


•0.3 


^0.3 


•0.1 


t>«(. 





yGoogle 



VNIT8, FACTORS, AND TABLBS SeC 1-14{ 

14>. Lofarithms of Humbara 



2 



3 



8 



10 
11 
12 
13 
U 

U 

16 
17 
18 
IS 

20 

21 
22 
23 
24 

25 
20 
27 
28 
28 

30 
31 
32 
33 
34 

35 
3S 
-37 
38 



40 
41 
43 
43 



45 
4ft 
47 
4S 
«» 

80 
SI 
S3 
63 
&4 



0000 

0414 
0702 
1138 
1461 

1761 
2041 
2304 
2553 
2788 

3010 
3222 
3424 
3617 
3802 

3979 
41M 
4314 
4472 
4024 

4771 
4914 
5051 
5185 
6315 

6441 
6S63 

5682 
6798 
5911 

6031 
6138 



6335 
6436 



6S32 



6638 
6721 
6812 
6802 



6890 
7076 
7160 
7343 
7834 



0043 
0468 



1173 
1493 

1790 
2068 
2330 



2577 
2810 



3032 



3444 
3636 



0086 
0492 
0664 
1206 
1523 

1818 
2086 
3355 
2601 
2833 

3054 
3363 
8464 
3666 

3838 



0128 
0531 
0899 
1339 
1563 

1847 
3122 



0170 0212 



3997 
4166 
4330 
4487 
4630 

4786 
4928 
5065 

5186 
6328 

6453 
5575 
6684 
6808 

5822 

6081 
6138 
6243 
0345 

6444 

6543 
6637 
6730 
6821 
6911 



4014 
4183 
4346 
4502 
4654 

4800 
4942 
5078 
5211 
5340 

6465 
5587 
5705 
6821 



2635 
2866 

3075 
3284 
3483 
3674 
3866 

4031 
4200 
4362 
4518 
4668 

4814 
4866 
5002 
6324 
5353 



0042 
6148 
6253 
6356 
6454 

6661 
6646 
6738 



6478 
5580 
6717 
5832 
6944 

6063 
6160 



6306 



7084 
7168 
7251 
7332 



6830 

7007 
7083 
7177 
7250 
7340 



6464 

6561 
6656 
6749 
6830 



7016 
7101 
7185 
7267 
7348 



0569 
0934 
1271 

1584 

1875 
2148 
2405 
2648 

2878 

3096 
3304 
3602 
3682 
3874 

4048 
4216 
4378 
4533 
4683 

4839 
4868 
5106 
5237 
6366 

6490 
5611 
6729 
6843 
5866 

6064 
6170 
6274 
6375 
6474 

6571 
6666 
6758 
6848 
6037 

7024 
7110 
7193 
7275 
7356 



0607 
0968 
1303 
1614 

1903 
2175 
2430 
2672 
2900 

3118 
3324 
3522 
3711 
3802 

4065 
4232 
4393 
4548 
4698 

4843 
4083 
6119 
5250 
5378 

6602 
6623 
5740 
5856 
5966 

6075 
6180 
6284 
6385 
6484 

6680 
6675 
6767 
6857 
6946 

7033 
7118 
7202 
7284 
7364 



0253 
0645 
1004 
1335 
1644 

1631 
2201 
2466 
2606 
2923 

3139 
3346 
3541 
3729 
3909 

4082 
4249 
4409 
4564 

4713 

4867 
4887 
5132 
5263 
5391 

6514 
5635 
5752 
5866 
6977 

6085 
6191 
6294 
6305 
6493 

6690 
6684 
6776 
6866 
69S6 

7042 
7126 
7210 
7292 
7372 



0284 
0682 
1038 
1367 
1673 

1850 
2227 
3480 
2718 
2945 

3160 
3366 
8660 
3747 
3027 

4098 
4265 
4425 
4579 

4728 

4871 
5011 
6145 
5376 
6403 

6627 
6647 
6763 
6877 
6088 

6086 
6201 
6304 
6405 
6503 

6509 
6683 
6785 
6875 

6064 

7060 
7135 
7218 
7300 
7380 



0334 
0719 
1072 
1388 
1703 

1087 
2263 
2604 
2742 
2967 

3181 
3386 
3579 
3766 
3945 

4116 
4281 
4440 
4504 
4742 



4886 
6024 
5159 
6280 
5416 

5539 
5668 
6775 

5888 
5909 

6107 
6712 
6314 
6415 
6513 

6609 
6702 
6794 
6884 
6972 

7059 
7143 
7228 
7308 
7388 



0374 
0756 
1106 
1430 
1732 

2014 
2279 
2529 
2765 
2989 

3201 
3404 
3698 
3784 
3962 

4133 

4288 
4456 
4609 
4767 

4800 
5088 
6172 
6302 
5428 

6551 

5670 
5786 
6899 
6010 

6117 
6222 
6325 
6425 
6622 

6618 
6712 
6803 
6893 
6981 

7067 
7152 
7236 
7316 
7306 



40 



y Google 



Sec 1-149 UNITS, FACTORS. AND TABLES 
Logarithms of Numben. — Concluded 



N 





1 


2 


3 


J_ 


5 


6 


7 • 


8 


9 


55 


7404 


7412 


7410 


7427 


7435 


7443 


74(;i 


74S9 


7466 


7474 


56 


7482 


7490 


7407 


7505 


7613 


7620 


7528 


7538 


7543 


7661 


57 


7559 


7566 


7674 


7682 


7580 


7597 


7604 


7612 


7610 


7627 


58 


7634 


7642 


7649 


7657 


7664 


7672 


7679 


7686 


7694 


7701 


59 


7709 


7716 


7723 


7731 


7738 


7745 


7762 


7760 


7767 


7774 


60 


7782 


7780 


7796 


7803 


7810 


7818 


7826 


7832 


7830 


7846 


61 


7853 


7860 


7868 


7875 


7882 


7889 


7806 


7003 


7010 


7917 


62 


7924 


7931 


7038 


7045 


7052 


7950 


7966 


7073 


7080 


7087 


63 


7993 


8000 


8007 


8014 


8021 


8028 


8035 


8041 


8048 


8066 


64 


8062 


8069 


8075 


8082 


80S9 


8006 


8102 


8109 


8116 


8122 


65 


8129 


8136 


8142 


sue 


8166 


8162 


8169 


8176 


8182 


8189 


66 


8195 


8202 


8200 


8215 


8222 


8228 


8235 


8241 


8248 


8264 


67 


8261 


8367 


8274 


8280 


8287 


8203 


8299 


8306 


8312 


8319 


68 


8325 


8331 


8338 


8344 


8351 


8357 


8363 


8370 


8376 


8383 


60 


8388 


8395 


8401 


8407 


8414 


8420 


8426 


8432 


8439 


8445 


70 


8481 


8457 


8463 


8470 


8476 


8482 


8488 


8494 


8500 


8606 


71 


8513 


8519 


8525 


8531 


8537 


8543 


8549 


R555 


8561 


8667 


72 


8573 


8579 


8586 


8591 


8507 


8603 


8609 


8616 


8621 


8627 


73 


8633 


8630 


8645 


8651 


8657 


8663 


8669 


8675 


8681 


8686 


74 


8692 


8698 


8704 


8710 


8716 


8722 


8727 


8733 


8739 


8746 


75 


8751 


8456 


8762 


8768 


8774 


8770 


8785 


8791 


8797 


8802 


76 


8808 


8814 


8820 


8825 


8831 


8837 


8842 


8848 


8854 


8859 


77 


8865 


8871 


8876 


8882 


8887 


8803 


8899 


8904 


8010 


8015 


78 


8921 


8927 


8032 


8038 


8943 


8049 


8964 


8960 


8965 


8971 


79 


8976 


8982 


8087 


8003 


8998 


9004 


9009 


9015 


9020 


9025 


80 


9031 


9036 


0042 


9047 


0063 


0081 
0112 


9063 


9069 


9074 


9070 


81 


9085 


9000 


0006 


9101 


0106 


0H7 


0122 


9128 


0133 


82 


9138 


0143 


0140 


0154 


0150 


0165 


0170 


0176 


0180 


9186 


83 


9191 


0196 


0201 


0206 


0212 


0217 


0222 


0227 


9232 


0238 


84 


9243 


9248 


0253 


9258 


9263 


9269 


9274 


9279 


9284 


0280 


85 


9204 


0200 


0304 


9309 


9315 


9320 


9325 


0330 


9335 


0340 


86 


9345 


0350 


0355 


9360 


9365 


0370 


9375 


0380 


9385 


0390 


87 


9395 


0400 


0405 


9410 


9415 


0420 


0425 


0430 


0436 


9440 


88 


9445 


0450 


0455 


9460 


9465 


9469 


0474 


0470 


0484 


9489 


8V 


9494 


0409 


0504 


0509 


0513 


9618 


9523 


0528 


9533 


9538 


00 


9542 


9547 


9552 


9557 


9562 


eS6f. 


9571 


0676 


9581 


9586 


91 


9590 


0595 


9600 


9605 


0600 


0614 


9619 


0624 


9628 


9633 


92 


9638 


9843 


9647 


9652 


0657 


0661 


9666 


9671 


0675 


9680 


93 


9685 


0680 


0604 


9699 


0703 


9708 


0713 


0717 


0722 


9727 


94 


9731 


0736 


0741 


0745 


0750 


9764 


0760 


0763 


0768 


9773 


95 


9777 


9782 


0786 


0791 


0795 


9800 


9805 


0800 


9814 


9818 


96 


9823 


0827 


0832 


9836 


0841 


9845 


9850 


0864 


9859 


9863 


97 


9868 


9872 


0877 


9881 


0886 


9890 


9894 


0899 


9903 


9908 


98 


9912 


9917 


0921 


0926 


9930 


9934 


9939 


0943 


9948 


9902 


99 


9956 


9961 


9965 


9989 


0974 


9978 


9983 


9987 


9991 


9996 



yGoogle 



VfflTS, FACTORS, AND TABLES 
IM. HjparboIIo Locarithma 



Sec 1-lSO 



.V 



—000. 
10^2.30262. 
103.90573. 
303.40123. 

403.68893. 
S03. 91203. 
SM. 09434. 

I I 

;W4. 24854. 
8M. 38204. 
904.49984. 

1004. 6052*4. 
1104.70054. 
1204.78754. 
1304.88754. 

I 
1404.94164. 
1M5.01065. 
1605.07S25 

17IU. 13585. 
18015.19305. 
24705. 



29836. 
34715. 
39365. 
43815. 

48065. 
52155. 
56075. 

59845. 
63485 
6099^. 

703S5. 
73665. 
7S835. 
7991J. 

1 
.82895 
85795 
88615 

I 
91355 
94025 
96615 

99155 
01626 
04036 
063»6 



1 J_ 

odboo. 

39793. 
04453. 
43403. 

I 
71363. 
93183. 
11094. 



69311 
484! 
0910'3 
4657|3. 

7377 3-, 
9512 3. 
12714. 



7 I 8 



210i5. 
2205. 
2306 
I 

2405. 
IM.'i. 
2605. 

270ls. 

ao5. 

»05. 

30o!s. 
3105 
3205. 
IMS. 

I 

3M5. 
3505. 
U95 

I 

37«5 
»U 
M45 

«as 

41M 
<»« 
43M 



2«27'4.2767 4. 
39444.40674 
51094. 5218|4. 

61514.625014 
7095I4.7I854, 
7958'4.804a4. 
87524.8828 4. 

948S4.95S8 4. 
01735.0239 5. 
08145. 0S76S. 

I 
14175.1475 5 
19855.2040 5 
25235.2576 5 

3033 5.3083 5 

3519.5.35665 
39825.4027 5 
44^5.44675 

48485.4889 5 
52555.5294 
56455. 6683 5 

60215.6058 5 
63845.04195 
6733,5.6768 5 



oiozls.gisgs. 

042815.0454 5. 
^5. 9713 5. 



««M aH8«.080»6 
«« 10924.11156 
<•» 13126.13346 



«. 99655 
.01866.02106. 
.O42&e.045a6. 
.066116.00846. 



0913 8 



1I37S 
1356 6 



471J! lS27«.1549«.1670te 
I*** 173R6.17S0|6.1779 8 
[jM».l»446.1964p. lOOSfi 



09861.38631.60941.79181.94502.0704 2.1972 
56492.63912.70812.77262.83322.89042.9444 
13553.17813.2189 3.25813.29683.33223.3673 
496^ . 5264 3 . 5553 3 . 58353 . 6109 3 . 6376:3 . 6636 



76123. 
97033. 

1431 k. 

29054. 
41884. 
63264. 

634714. 
72744. 
81224. 
89034, 



78423. 
98904. 

1589H 



B9j4. 
414 



8041. 

43084. 

643314. 

644414 
736214 
82034 
89784 



80673. 
00734. 

1744j4. 

31754. 
44274. 
5539M. 

6540I4. 
74494. 
82834. 
00634. 



82863.8501 

02644.04314 

1897,4.20474 



9e28'4.9698'4.9767 
03045.03706.0434 
0938,6.0999,6.1069 



15336. 
20955. 
26275 

31325 

36135, 
40725, 
451015, 



16915 
21495 
2679,5. 

818lk 
36606. 
4116|5. 
4553I5. 



33074. 
46434, 

56434. 

66344. 

,75364. 
.83634, 
.9127,4, 



3.87123.8918 
06044.0776 
2195^.2341 



343814.35674 
46694.4773I4 
5747^.686014 



67284 



4.6913 

4.7791 

4.8598 

92004.92734.9345 



7622 4 
8442 4 



4.983ff4.9904 4.99726, 
6. 04995. 0662 6. 0626 5. 
5. 11205. 1180 5. 1340 6. 



164S5. 
2204'5, 
27305. 



32305 
370616 
4161 
4596 



.493116.49725. 
.53345.63735. 
.57226.67595. 



17066.1761 
22575.2311 
278115.2832 



.6821 
.7707 
.8520 



3004 
4886 
.6061 



5.18186. 
6.2364:5. 
5.2883,5. 



,3279|5. 3327 5. 33756 
375316.37995.38455 
,4206,5.425016.42935 
,4638'5. 4681 5.4723 5 



60136. 60636. 6094'5 
64136.64525.64916 



0030 
0680 
1209 

1874 
2417 
2933 

3423 
3891 
4337 
4766 



9S6.C 



6797 



5.68365.687215 



,609516.613115. 
64545.64906. 
.6802 5. 6836:5. 



6168 
6525 



6134 5.6176 
55305.5588 
59105.6947 



5.6204 5.624015, 
5.65605.65055, 



68705.6904:5.6937:6 



6276'5.63I2 
66305.6864 
69715.7004 



7071 5. 710415. 7137 6. 717015. 72036. 723816. 7268 5. 7301 6.7333 
7398 5 . 7430 5. 7482l5 . 7494 5 . 7526 5 . 7557 5 . 7689!5 . 762 1 5 . 7652 
77145.7746 5.7777:5.78075.7838:5.78695.7900,5.79305.7961 
8021 5. 8051^. 8081 5. 8111,5.8141 6. 8171|6. 8201 5. 82305. 8260 



83I»'5 . 834815 . 8377'5 . 8406l5. 843516 . 8464!5 . 8493 S . 8522 5 . 8561 
8608 3 . 8636 5 . 86655 . 8693,6 . 872 1 '5 . 8749 S . 877715 . 8805 S . 8833 
,8889:5.8916 5.8944 5.89726.80995.9026,5.90546.90815.9108 



92165.9243,'5 
94806.95065 
6.g764!S 



098918. 00146 
02.348.02596 
0474:8.0497:6 
070716.07306 



02e9!6. 
053215. 
97896. 

0039« 
02836. 

.0621^. 
07336. 



9296l5.9322l5.93496.9378 
96586.95845.96106.9636 
.981416.98395.98655.9890 

,0064le. 008816. 01136. 0137 



03076.0331 
0544,6.0568 



6.03556.0379 
6.060116.0616 



077616 . 0799:6 . 0822 6 . 0846 



.ll.WO 
.1377|i 



.1691 
.18006 
■ 2005|6 



,0958'6.0g816. 
,11818.12036. 
,1 399.6. 1420|6. 

161241. 1633«. 
182ll6.184l'6. 
2025|6!2046|6. 



10036. 10266. 
122.';,6. 124716. 
14426.146316. 

16546.167516. 
18626. 1883|6. 
20666.2086,6. 



104816.1070 
128916.1291 
1485 S. 1506 

16966.1717 
190318.1924 
2106 16. 2126 



i 



61 



i 



Sec 1-150 viriTS, factors, and tablss 
Byp«rboIie LAgailtliiiia. — Condudtd 



N 



SOOlO . 2 U6|6 . 2 leele . 2 186^ . 2206 8 . 2226 6 . 3246 B . 2266 8 . 228fi 5 . 2305|6 
S.2383«.24O36.24226.2442a.2461S.3480 6 
258816.25586.267716.2696 6.26156.2634 6.26636.2672 8 
S30|6 . 2729 6 . 2748 6 . 2766 6 . 278S|6 . 2804{6 . 2823|6 . 2841{« . 2860|6 



5506.3099 



5606.32796.3297 



1 



5406.29166.29346.29536.2971 



6.3117 



6.31356.3164 
6.33156.3333 



5706.34666.34746.3491 
5806.3630,6.36486.3665 
6906.38016.38186.38356.3852 



6006 

6106. 413516.4151 

6206. 
6306.44576.447314.4489 



3 



6. 3509 6. 3526 6. 3544 
6.36826.3699 
6.3869 



3969^.39866.40036.4019 

6.41676.4184 

4297^.4313 6.43296.4346 



640» . 4615 6 . 4630'6. 464A6 
6506 . 4770.8 . 4786 6 . 48U0{6 
6606.4922,6.49386. 



6.29896.30086.30266.3044 
6.3172 



6.3351 



6.40366.40526.4009 6.4086 6.41028.4118 
42008.4216'6. 42326. 42496.42656. 4281 
6.4362^.43786.4394 8.4409 6.44256.4441 
6 . 4562 6 . 4568 6 . 4583 6 . 4509 



6.45056.45206.4636 



6.4677 

6.4831 

49536.49686.4983 



466] 
.4811 



6706. 507316.60886. 5103 6. 51 17 
680 6 . 622 1 i6 . 5236!6 . 5260|6 . 5266 6 
690,6.5367,6.5381,6.5396,6.5410 



7006. 
710fl. 
7206. 
7306. 

7406. 
7506. 
760|6. 

7706. 
780'6. 
790,6. 

SOOV. 
810{e. 
8206. 

8306. 

84o'6. 
8506 
8606 



55116 
56536 
5793,6 
5930» 

60676 
620 IM 
63336 



65256.653916 
56676.5681 
5806,6.6820^ 
59446.59586 

60806. 6093:6 
62146.6227,6 
63466.6359 6 



5564 
5605 



.64646 

.66931 

.67206 

.68466 
.69706 
70936 
72146, 

73346 
74526. 
76696, 



6477|6 
66066 
67336 

68595 
6983>6 
7105.6 
7226,6 

73466 
74646 
75816 



6871 
.60956 
.71176 
.7238,6 



6241 

6373 



6.31906.32088.32266.3244 
^68 6.38868.3404 6.3421 



8.8561 



6.35786.35966.3618 
6 . 87 1 6|6 . 3733 8 . 3750 6 . 8767 8 . 3784 
6. 38866.390216. 39196. S936 6. 395S 



6 

5280 
6 ! 54256. 543916. 6453 



6.5294 



6.56686.5582 
6.6709|e.5723e 
5834 6.58486.6862|6 
6.59856 



8971 

6107 6.612016. 
6.6254'6. 
6.6386,6. 



.50996 



6 



6.63096 



6.30636.8081 
6.3261 



6 . 4693 6 . 4708 6 . 4723« . 4739 8 . 47S4 
6.48466.48626.48776.48926.4907 
6.49986.60136.60286.50436.5088 



5132^.51476.6162^.8177^.81918.6206 

5338,6.5358 

6.6468A.64826.5497 



6.55966 
.57376.5751 
.88766 
60126 



5610^.5624 6.6639 

{6.576516.5779 

58896.69036.5817 

60266.60396.0053 



61344. 61476. 6161 
6267«. 6280^. 629416. 
63996.64126.64356 



6490 6 . 6503« . 65 1 6M . 6529 6 

6619 6 . 6631 6 . 6644 6 . 6657 6 . 6670|6 . 6882 

67466.67586.67716.67838 



6.735816 



6 . 6884 6 . 6896!6 . 6908 6. 6921 6 . 

70076.7020,6.7032 6.70446. 

16.71666. 

6.72866, 



71306.71426.7164 
7350,6.72626.7274 



73581 

74766 
.75936 



870 6 . 7685 6 . 7606 6 . 7708 
8806. 77996. 781l|6. 7822 
890,6. 7912 6 . 7923i6 . 7935 



9006.8024 
9106. 8134 
9206. 8244«. 825516 
930,6.8352 



940ib 
9506 
960,6 



k. 



970 

0806 

990p 



8469 8 
85656 
8669n 

8773I6 
8876|6 

8977P 



8035'6. 
81456. 



7370l6 . 7382 6 . 7393 6 . 7405 6 . 741 7 6 . 742916 
7488 6 . 7499 [e . 751 1 6 . 7523 6 . 7534 6 . 7546 8 
760416.76166.76276.7639 6.76606.76626 



6.77196.7731 
6.7833 6.7845 8 
6.79406.79576 



80466.8057 6. 

816e«. 81676. 

82656.8276,6. 

6.8363|6.83736.83846. 



6.77426.7754 
.78666.7867 
.7968,6.7979 



olo 



.8480 



8469l6 

85756.8586|6 

8680:6 

.8783M 



6.84916 
.86966 
8690|6.8701 

6. 



8794 6.8804 
88966.89066 
8987|6.8997|6.90076 



80686 
81786, 
82876. 
83956. 

850ll6. 
8607 6. 
87116. 

8814 6. 
89166. 
9017 6. 

83 



80796.80908.8101 

81896. 8200!6. 8211 
829816. 8309)6. 8320 
8405 6. 841 6«. 8427 



8512».8622».86336 
8617M. 86286. 8638« 
8721«.8732M.8742|6. 

88246.8835M 
8026«.8037M. 894716 
9027p .9037^.904716 



8 



2324 
280016.8519 
S091 8.2710 
28796.3807 



6.8439 



6174 6 

6307 

64386 



6542 6 . 6554 6 . 6567 6 . 6S80 

6.66956.6708 

6796^.6809 6.68218.6834 



.69468 



68S8 
7056^. 7069to. 7081 
7178l6. 719016.7203 
72986.73106.7323 



7765«.7776l6 

78786.7890(6 

6.79916.80026 



6.81126 
6.8222 
6.8330 
6.84376 



8544I8. 
8648{6. 
87626. 

88556. 
89576. 
90576. 



.6187 
6320 
.6481 



,7441 
7558 
7873 

.7788 
.7901 
.8013 

.8128 

6.8233 

6.8341 

8448 



8584 

8688 
8708 

88««. 

8987: 

9088| 



i.jV^iUDyic 



UNITS, FACTOBS. AND TABLES SeC 1-151 



lU. Couffudon c»f Irfii^arlthina. For converting logarithmB to the 
but a, to another base fr: 

loct X— i 1 

log.i 

log. &Xlogt a— I 



(10) 



(H) 
or Brlcsa loKmrlthmi are computed from the base of 10, 
vU* liTpariioUe lec*ritluna are computed from the baae < or 2.7183. 
Tkenfora 

lo.--'i?^' (12) 

in. Til* OrMk Alphabet 



Nan* 


Larce 


Smalt 


Commonly used to designate 


■IplM 


A 




^"g^«^, coefficients. 


bMa 


B 




angles,' coefficients. 


ssr 


r 




speeifio gravity, 
density, variation. 


ecdai 


E 




base of hyperbolic logarithms. 


MU 


Z 




eo-ordinaies, coefficients. 


eu 


H 




byatereos (Steinmets) coefficient, efficiency 


dwta 


e 




angular phase displacement, time constant. 


iou 


I 






bSds 


K 
A . 




dideetrie constant, susceptibility. 
conductivity. 


aa 


M 




permeability. 


na 


N 




relnctivHy. 


xi 


3 




output coefficient. 


omUrea 


O 






pi 


II 




circumference + diameter. 


So 


P 




resistivity. 


■cma 


z 




(cap.), summation; leakage coefficient. 


taa 


T 




time-phase displacement, time constant. 


r- 


r 
* 




flur. 


da 


X 


X 




pa 


* 


* 


angular velocity in time. 




a 


<# 


(small), angular velocity in space. 



BIBUOOBAFHT 

Ut. BafarsneM to iaaportaat Uterature. 

Hnnro, C. — "Beady Reference Tables." John Wiley and Sons, New 
Tark, IMM. 

Gbat, T. — "Bmlthawiian Physical Tables." Smithsonian Institution, 
VaAiagton. D. C.> 1908; 4th rev. ed. 

EruBTT. J. D.— "Unita and Physical Constants." Macmillan and Co., 
Leadon. 1802; 5tfa ed. 

Gut, a. — "Afaaoluta Measurements in Klectndty and Magnetism." 
u._al.« and Co., Ixindon, 1888. 

BiAetias ol tbe Bateau (rf Standards, Dept. of Commerce, Washington, 
D. C; Vd. 1, I904. to data. 

TUies </ Equivalents; Bureau of Standards, Dept. of Commerce, Waah- 
Maa. D. CrnOlS: **^ '^ 

R«imct to tlae International Committee on Electrical Units and Standards; 
VMkiagtan, D- C, Bnraau of Standards; Jan. 1, 1012. 

Stats i-if Nstiooal I«ws Concerning the Weights and Measures of the 
Caisd State*: Waahincton, D. C, Bureau of Standards; 1912; 2nd ed. 

^VHMefMiu, Anoerican Inatitute of Electrical Engineers, American Elec- 
tmrtiial) al Soeioty, Illuminating Engineering Society. 

TVaawflfsris. Intamstional Electrical Congress; St. Louis, Mo., 1904. 



» 



yGoogle 



► 



^ 



y Google 



( 

4 



SECTION 2 



ELECTRIC AND MAGNETIC CIRCUITS 



Profi 



BY VLADIMIR KARAP£TOFF, 

of EUttricai Bnffineering, Cornell Vnivernlyt Fellow, American 
Institute of Electrical Bngineere 



COHTBHTB 

(.ffttmbere refer to Parafraplu) 

Transient Currenta and Voltages 



Ckctris Potential 1 

Ekctrie Corrsnts 9 

CoBtinuona-Carrent Circuits 19 

ElectroznacBetic Induction 36 

Tka Uacnatic Circuit 43 

ladortanee 67 

HyiterMia and Eddy Currenta 89 

Tka Didaetrie Cireoit 106 



138 

Alternating-Current Cirouita 151 

Non-Sinusoidal or Complex Waves 190 
Polyphase Systems 213 

Uniformly Distributed Resiat- 
anco, Reactance', Cai>aoity and 
Leakage 327 

Bibliography 238 



St 



y Google 



SECTION 2 



ELECTRIC AND MAGNETIC CIRCUITS 
SUCTUO rOTMttTIAl, 

1. The MtUM of ut elaetrle vainat in a dreuit ii termed the alaotro- 
motlT* (oroa or Toltac*. The latter name U derived from the praoUoal 
unit of electromotive force called the volt. The current between two pointa 
in a circuit ia due to a different electric state or "potential" at each point; 
for this reason the electromotive force or voltage is sometimes caUed th« 
dUIarancM of potential. 

t. TIm alaeblo tawgj (IF) developed or absorbed by an electric circuit 
may be considered due to the actual flow of an incompressible something 
which we call electricity. From this ^oiiit of view, the quantity of electricity 
Q which is transferred between two.pomts of the circuit is the quantity factor 
of the energsr, while the difference of potential, or the voltage B between the 
same points, is the intensity factor of the energy ; or 

W = QE. (1) 

When Q ia in coulombs, and S in volts, W is in joules (watt-seconds). 
Hence, electromotive force or voltage may also be defined as electrical energy 
developed or work done per unit quantity of electricity. 

S. Blectrto Power. — Dividing both sides of the preceding equation by 
the time which it takes for the quantity Q to flow through a croes-seotion of 
the circuit, we get 

P-IS, (2) 

where P is the power, and / the rate of flow or the current. The e.m.f . can 
thus be defined as the power developed per unit of current. 

4. The prineliial loureei of electromotiTe toroa or difference of poten- 
tial are the following: 



(a) Electromagnetic induction (see Par. M); 

(b) Contact of dissimilar substances (see Par. 

So) Tharmo-eleotric action (see Par. () ; 
J _. 
e) 
In the 



(d) Chemical action (See. 19): 
I Friction between dissimilar substances (see See. 22). 
ne light of the modem electrical theory, all these phenonema, with the 
exception of (a) ■ appear to be but special cases of the general contact action. 

I. In a clroait made up of leTeral lubitancai, a difference of potential 
(e.m.f.) exists at each junction, of two unlike substances. However, from 
the law of conservation of energy it follows that unless the circuit contain 
a source of energy, the resultant e.m.f. in the circuit must be sero and no 
current can be established. This phenomenon also takes place in circuite 
made up of a single substance whenever the substance is not physically and 
ehemiciuly homogeneous. The following are the principal cases of thermal 
and contact action: 

(a) Seebeck eBaet. Inaoloeedcircuitoonsvtingoftwe different metals, if 
the two junctions are kept at different temperatures, a permanent current 
will low. Thus, if one junction of a copper-iron dreuit De kept in melting 
ice and the other in boiling water, it will be found that a current passes from 
copper to iron across the not junction. If, however, the temperature of the 
hot junction be raised gradually, the e.m.f. in the circuit slowly reaches a 
maximum, then sinks to sero, and finally is reversed. 

(b) Peltier eBeet. When a current is passed aeroas the junction between 
two different metals, an evolution or an absorption of heat takes plaee. 
This effect is different from the evolution of heat (>*r), due to the resistanee 
of the Junction, and is reversible, heat being evolved when the ourrent 

S6 

DigiiizMbjV^iUUyie 



SLBCTKIC AND MAONBTIC CISCUITS S«C 8-6 

paana ona way >eraa the Jonotioii and abaorbed when the oumnt paaaea in 
the othor direction. There ie a definite relation between tlie diieotion of the 
tharmo-«ieotrie eorrent and the aisn of the Peltier effect. If a current be 
fanad acroae a junction in the aame direction aa the thermo-electric current 
Iowa at ttaa hot junction, the junction will be cooled, that ia, heat will be 
abaorbed. Converaely, a ourreat paaain^ in the normal direction aorcaa the 
•aid joBction of a thermo-electric circuit erolTea heat. In general, then, a 
Ibwiiaj uleiliic current abaorbe heat at the hot junction and ^vea up heat at 
the cold junetion. Therefore, a ounent produced in the aame direction by 
•Klanial meana most cool off the junetion which aerrea aa the "hot" junction 
aad warm up the "ecdd" junction, 
(e) Thomaon aSaet. In a copper bar, heat ia carried with the electric 
when it flowa from hot regions to oidd onea; on the other hand. 



wfcrea tlta earrent flowa from eold regiona to hot onea,_theae hot parte of the 
bar an cooled. In iron theae effeete are i 



■B^nti 
I dinen 



r reryeraed. The conductor may be 
of aa eompoaed of a number of littie elementa of volume, at the 
jeaHiona between which occur rereraible heat effects, similar to Peltier 
ifctta at the junetione between different metala. 
(d) Talte aSaet, or eoBtaet alaetiUhMttion. When piecee of varioua 
^t in contact, an e.m.f. is dereloped between them. 
aine and copper, ainc becomea charged poaitivaly and 
atirely. Aeeordins to the electron theory, different subatancea 
lerent tandeneiea to giTe up their negatively charged corpuaelea. 
pvea them up very eaaily; therefore a number of negatively charged 
I pass from it to copper. Measurable e.m.fi. are observed even 
L two pieeea of the aame substance, having different structuree; for 
) between a piece of oast copper and dectrolytic copper, Friotional 
dcetricity ia explained in a similar way, only a more intimate contact ia 
aaataaaty where the eonduetivitiee of the subatancea are small. 

•._ Utarstor* rafaraneaa. _ For a detailed treatment, curves and mathe- 
ai a tiral theory of thermo-electric and contact phenomena see Maxwell, J. C, 
" Bectricity and Macnetism," Vol. I, Arte. Z4S al ««g.; Encyclopedia Bri- 
laaaiea, under "Thermo-electricity"; Whetham, W, C. D., " The Theory of 
Expasimental Eleetriei^/' Chap. 6; Brooka and Poyaer, "Magnetism and 
Bectricity." Chap. 28. For an explanation of thermo-electric effects in the 
Isaguaaa of the deetroa theory see Foumier d'Albee, "The Electron 
ttaosy." Chap. 5; Thomaon, J. J., " The Corpuscular Theory of Matter," 
!». n aad 97; CampbeU, N. R.. " Modem Electrical Theory,'* pp. 118-124. 
T. Th* *aliM of tha a.in.f. at a Junetloa tS imlike tnbatMieaa 
dveada iqxm the kind of subetancaa, and ia approximately proportional to 
the temperature. The e.m.f. generated in tloa way can be utilised aa a 
■HSBra of temperature. For temperature riaea up to 200 dec, cent. 

I'ht+h^, ' (3) 

•al for te mp er a ture riaea above 200 deg. oent. 

Iac««i«Iog<-fi« (4) 

A men general formula ia 

*ma+U+cP (5) 

Tks taastitica b, hu lt», i\, a, h and e are constants. For numerical values 
M8ee.4. 

t. Tkannoeeiiplaa and battarlaa. In order to utilise these contact 
c-mJi., raeana xnuvt be devised to supply energy to the system continuously. 
Tkcre an two ways of doing this, namely, by heat and by chemical reaction. 
Tie theraoooaple is an example of the former, and the battery an example 
of the latter. For farther discussion of thermocouples see Sec. 3. Batteries 
an seated in See. 30. 

XUCTUC CTTWUirTS * 

1 Aa daiililn •luiwt t is daflnad as the rate of flow of electricity, or the 
tmatity al tiliiulildty whieh flows through a croae-eeetion of the circuit per 
Slit tias. If the eurrent / is steady, then 

'-§• (8) 

B Oil the qnaatity of eleetiicity in eonlomba, and 2* the time in seconds, 

67 

DigilizedbyV^jUUyiC 



Sec. 2-10 ELECTRIC AND MAONBTIC CIRCUITS 

the ourreat / is in amperes. When the rate of flow is non-uniform, the in- 

■tantaneouB current is 

for a classification of electric currents see the Standardisation Rules of the 
American Institute of Electrical Engineera, Sec. 24. 

10. 8t«ady and tr&nsleat statai. An electric circuit may be in n 
steady or in a transient state. When a current is continuous, or when it 
varies periodically between the same limits and according to the same law, 
the circuit ia said to be in a steady state. For instance, the circuit of aa 
idternator is steady as long as the load, Bp>eed and field excitation are kept 
constant. The same circuit is in a transient state when the load is switched, 
on or off, or when it ia varied in such a way that the same conditions do not 
repeat themselves periodically. A transient current may be periodic, for 
instance in a rectifier, in which cycles follow in such rapid succession that 
the current is very different from the permanent value which it would grad- 
xiaXiy assume. 

11. A dlreot currant given out by a chemical battery is constant in 
value, or oontlnuouji. when the load is constant. A current delivered under 
the same conditions by an electric generator or a rectifier is pul««tln|r» 
that is, it varies periodically due to a finite number of commutator segments. 

IS. An alternating current may vary according to the simple sine IftW 
(Par. 162), or accoroung to a more complleatea periodic law. In the 
latter case the current may be resolved, for purposes of theory and analysis, 
into a fundamental sine wave, and sine waves of higher frequencies (Par. 
S09). Sometimes a complex alternating current or voltage is replaced for 
practical purposes by an equivalent sine-wave. 

IS. Transient currents may be OBcillatinff or non-oiclUating, ac- 
cording to the conditions in the circuit. Oscillations are due to ^riodic 
transformations of the electrostatic ener^ stored in the dielectric into tho 
electromagnetic energy of the magnetic flux Unking with the current. 
During these transformations part of the energy is converted into the 
Joulean (tV) heat in the conductors and in surrounding metallic objects, 
including the iron of the magnetic circuit. Part of the energy is also con- 
verted into the heat caused oy magnetic and dielectric hysteresis. The 
oscillations are thus damped out, and their amplitude decreases. When the 
conditions are particularly favorable for the conversion into heat (high 
resistance in series, or low rcsistanoe in parallel), both the electrostatic and 
the electromagnetic energy are directly converted into heat, instead of being 
partly converted into one another. This conversion into heat is an irre- 
versible phenomenon, so that in this case the current is non- oscillating, but 
gradually reaches its final value. 'When it is desired to maintain oscilla- 
tions as long as possible (wireless telegraphy) the series resistance must be 
kept down as low as possible. When oscillations are harmful (switching in 
long cables or transmission lines), extra resistance ia temporarily connectod 
in ^e circuit. 

14. Conductora and iniulatori. For practical purposes, materials 
used in electrical engineering are divided into conductora and insulators. A 
conducting material allows a continuous current to pass through it under the 
action of a continuous e.m.f. An insulator (more correctly called a dielec- 
tric) allows only a brief transient current which charges it electrostatically. 
This charge or displacement of electricity produces a counter-e.m.f. OQual 
and opposite to the applied e.m.f., and the flow of current ceases. Tho 
division into conductors and dielectrics is not strictly correct, but convenient 
for practical purposes. A substance may practically stop the flow of current 
when the applied voltage ia sufficiently low, and at the same time be unsuit- 
able as an insulator at high voltages. Some materials which are practically 
non-conducting at ordinary temperatures become good conductors when 
sufficiently heated. For numerical data and tables of conducting and 
insulating properties of the principal materisils used in practice see Sec. 4. 

18. The electronic theory of conduction. According to the modern 
electronic or corpuscular theory of electricity, there ia an indivisible atom of 
negative electricity, called the electron or the corpuscle. Atoms of matter 
consist of one or more electrons and an unknown something which has the 

58 

DigilizedbyV^iUUyie 



ELECTRIC ASD MAGNETIC CIRCUITS SeC. 8-16 

nature of poAitive ettHrtricity. A ne^tively charged particle of matter is 
one ID which there are more elertronfl than necessary to neutralize ita potntive 
electricity, A powtively electrified body is one which has loMt some of the 
electrons it bad in the neutraJ titatc. 

16. XetaU and other solid conductort aupiKM^dly poi»au fro* or 
roamiiif •lectronB* in addition to those aMociat«d with the molecules. 
Tht'^e free electrons are in rapid motion aa if they were the particles of a gas 
dissolved in the metal. When an e.m.f. is applied, each electron gains a 
compnnent velocity which, on account of its negative charge, is in the oppo- 
site direction to the e.m.f. Thin drift of electrons is equivalent to a current. 
In their motion the electrons come in collision with the molecules and give 
up part of their momentum. This loss is supposed to account for the 
Joulean (iV) heat set free in all conductors. Also see Sec. 22. 

IT. XlectrolTtot. In liquids which are chemical compounds (electro- 
lyted) the passage of an electric current is accompanied by a chemical 
decomposition. Atoms of metals and hydrogen travel through the liquid 
in the direction of the positive current, while oxygen and acid radicals 
travel against the positive current. Thus, while in solid conductors elec- 
triritv travels across the matter, in electrolytes it travels with the matter. 
For uet&ils of electrolytic conduction see Sec. 19. 

IS, OaaM in the normal atata conduct electricity only to a ilirht 
degree. A gas may be put in the conducting 8tat« by different means, such 
u nu.-ang ita temperature, drawing it from the neighborhood of flames, arcs, 
or glou'iug metals, or from a space in which an electric discharge is passing, 
etf. This conductivity is due to electrons which form electrified particles 
mixed up with the gas (ions). The process by which a gas in maoe into a 
conductor is called the ionization of the gas. The movement of free 
electrons constitutes the current through the gas. * Also see Sec. 19. 

coHmruouB-cinuuiiT cxecuits 

If. Ohm'i law. When the current in a conductor is stead v and there 
are no electromotive forces within the conductor, the value of the current i 
is proportional to the voltage e between the terminals of the conductor, or 

e-rt (8) 

where the coefficient of proportionality r is called the raatstance of the 
e&oductor. The eame law may be written in the form 

i^oe (9) 

where the coefficient of proporUonality a— 1/r is called the condoctanoe 
of the rooductor. When tue current is measured in amperes and the elec- 
tromotive force in Tolts, the resistance r is in ohms and the conductance q 
in mhos. 

When there is a counter-electromotlTe force ec within the conductor, 
Ohm's law becomes 

«(-ee-n', (10) 

t-.fl(«*-r*). (11) 

where et is the voltage between the terminals of the conductor. 

M. For eylindric&l conductors the resistance is proportional to the 
length I, and inversely proportional to the cross-section A, or 

r-4. (12) 

vbere tlw coefficient of proportionality p (rho) is called the rMiltirity (or 

•periBc resiitsnce) of the material. For numerical values of f for various 
materials kc Sec. 4. , 

Tbe fonductance of a cylindrical conductor is 

a-x-j, (13) 

* For tbe on^nal development of the electronic theory and its application 
to various electric and maenetic phenomena see numerous books ana articles 
^ Sir J. J. Thomson. A popular exposition of the results will be found in 
Fouraier d' Albee's " The Electron Theory " and in a somewhat more advanced 
"Modem Electrioal Theory" by N. R. CampbalL 



at _ DigilizedbyCOOgle 



^ 
> 



Sec. 2-21 BLBCTRIC AND UAONSTIC CIRCUITS 

whete X (lambda) ia ealled the oondoetlTlty of the suterial. Sinee t^l/r,\ 
the relation alao holda, that 

X--- (W)i 

P 

For the oaloulatioa of reaiatanoe of Don-cylindrioal conductors see ths' 
author's "Electric Circuit," Chap. Ill, and the referencea given there. 

tl. T«mp«r»tnr« ooeffleiant. The reaistanoe of a conductor varies 
with the temperature accordins to a rather complicated Ia». The leaiatancs 
of all metala and of praetioally all alloys increases with the temperature. 
The resistance of carbon and of electrolytes decreases with the tamperaturs. 
For numerical values see Sec. i. For many materials the variation of r» 
sistance with the temperature can be represented by the relation 

ri-r.(l+aO (18) 

where r< is the resistance at ( dec cent., r, the resistance at dec.'eent., and 
a (alpha) is called the temperature coefficient of the material. For nnmerieal 
values of <t for various materials see Bee. 4. When the resistance of a material 
increases with the temperature, a is positive; otherwise it is negative. For 
other formula see Sec. 4. 

n. Seiiituieaa and oonduetanoM In wrlM. When two or more 
resistances are coimeoted in series the equivalent resistance of the comfainsr 
tion is equal to the sum of the reaistances of the individual resistors, or 

r«t>«n+r«+etc. (18) 

When conductances are coimected in series, the equivalent conduetanee 
ax is determined from the relation 

i— i+i+eto.. (17) 

a<t n «• 
in other words, when two or more conductors are connected in aeries, the 
reciprocal of the equivalent conductance is equal to the sum of the reciprocals 
of the individual conductances. - 

It, Whan resUtanoei ara oonnaetad In parallel, the equivalent t»- 
sistanoe r<s is determined from the relation 

— --+J- +eto. (18) 

or simply 

»„-»i+«+etc. (19) 

S4. Tha limpls ml* is: Bailitaneea are added when In Mriea; oom- 

duetaneas ara added when In parallel. In the case often met in practice 

when two resistances are connected in 
parallel 

riri ,-^ J. 

'••~;r+ri* ^ ' '^ » VWVWW— ^g-^VWWW- 

M. Barlei-parallel eireulti. In '> k **• 

a combination like the one shown in sro 

Fig. 1, where some of the resistances \ 

are in series, some in parallel, and „ f 

where it ia required to find the equiva- ■'' ii 

lent resistance between A. and B, the 

Eroblem is solved step by step, by com- Fia. 1. — Seriea-parallel circuit, 
ining the resistances in series, con- 
verting them into conductances and 

adding them with other conductances in parallel. For instance, in the case 
shown in Fig. I begin by combining the resistances ri and A into one, and 
determine the oorrespondisg conductance 

1 . 
(«+r«)' 
add this conductance to the conductance 1/rs. This will give the total con- 
ductance between the points tt and N. The reciprocal of it gives the equiva- 
lent resistance between the same pcants. The total resistance between the 
points A and B is found by adding n to this resistance. When a network of 
conductors cannot be reduced to a series-parallel combination, the problem 
is solved as shown in Par. M. 



Digitized by CjOOQIC 



ELBCTSIC SND UXONBTIC CIRCUITS SeC. S-26 

M. Voww knd nurcy. When a steady current t flows through a eon- 
duetor and the ▼oltage acroea the terminals of the conductor is 0, the power, 
or the energy per unit time, delivered to the conductor is 

P-ti. (21) 

If the ennent is ezpieased in amperes and the potential in Tolts, the power 
/* is In watt* Qoolea per second). When the voltage and the current are 
variable, Xhmx instantaneous vaJues bein^ represented by « and t respect- 
inly, the prebeding equation gives the instantaneous power, that is the 
isetantaneoua rate at which energy is being delivered to the conductor. 

The total energy delivered to the conduetor during a time ( is 

W-tU-tQ, (22) 

vbers Q is the total quantity of electricity (coulombs) which passed through 
the eenductor. If Q is in coulombs (ampere-seconds), FT is in joules (watt- 
seeonds). When the voltage and the current are variable the total energy 
tsopnssedby 



W" I tUt, 

Jtl 



(23) 



•ken the time interval is <t— (i. 

iT. Jonto^ IkW. When the conduetor eontains ohmio resistance only 
aad DO eoontar-eleetroinotive forces, we have fri-'i/g, so that the power 

t' s* 

P-i«r--- — -eV. (2<) 

I r 
TUs >ipiMslun is known as Joola'l I»w. 

n. If tha oondnetor oontalna » eouatar-a.iauf., «« for instance, 
that d a motor or of a battery, tb* power is given by 

P-«o-«rt+»>, (28) 

wkcR «i is the voltage across the terminals of the conductor. In this expres- 
■oa fci is the osefuTpower, and tV is the heat loss in the conductor. See 
Par. 1(. 

It. Kirehlua*B l&wi. In an arbitrary network of conductors (Fig. 2) 
with soareea o( eontisuous e.m.f. connected in one or more places, the die- 
triboticB of the eanents is such that two conditions are sati&ed, namely, 

Z» » 0, and Ze — Ztr. (26) 

The Cnt equation refen to any junction point of three or more conductors 

sad states the fact that aa much current flows toward the junction as away 

from it, because electricity behaves like an 

incompressible fluid. In this equation all 

the currents which flow toward the junction 

are taken with the sign plus (+) S all those 

which flow awajr from it with the sign 

minus ( — ), or nee verMa. The second law 

refers to any dosed circuit taken at random 

In the network. The voltages s are the 

local electromotive forces in such a circuit 

and the currents and the resistances refer to 

the individual conductors of the circuit. 

The directions of flow of the currents can 

be assumed arbitrarily to start with, and in 

writing the second equation one follows a 

selected circuit in a certain direction, cloek- 

wise or counter-clockwise, taking as posiUve 

Fh. 2:— Ketwork of eon- the current* which flow in this direction and 

dnetorsi the e.m.fs. which tend to produce currents 

in the same direction. The currents and the 

wihsgM ia tbs opposite direetion are entered in the equation with the sign 

■tnoL For > given network of conductors the total number of equations of 

Ik fast form is equal to the number of junction points less one; tne number 

*f eqestioBS of the second kind is equal to tne number of independtnt 

lirnni paths in the network. Tha total number of equations of both kinds 

■Xqalto tha anmber of nnknown ourrents so that these eurrents can be 

61 DigilizedbyV^iUUyie 




Sec 2-30 BLSCTRIC AND MAGNETIC CIRCUITS 




Fl«. 3. — WhoaUtone Bridge. 



(2S) 



determined by aolnng eimultaneous equations. For an example of each 
equations see Far, SI Delow. 

10. Wheatlton* bridga. The comtnnstion of rix reaistancea shown in 
Fis. 3 is called the Wheatstone bridge. The resistances are denoted by 
a, Ot r, a, 0, y, the currents by 2, 
V, s, t* )t f> , An electric battery 
of e.m.f. J? is connected in the 
branch BC, and the value of a 
includes the internal resistance 
of the battery.^ In practice a 
galvanometer is usually con- 
nected in the branch OA, and a 
indudee its resistance. When 
the four resistances b, c, 0, y, arc 
so adjusted that no current flows 
through OA, the bridge is said 
to be balanced, and the condi- 
tion holds that, 

bp-ey. (27) 

11. Unbalanced bridge.. 
When the Wheatstone bridge is' 
not balanced, Ohm's law and 
Kirehhoff's laws give the follow- 
ing equations: 

ax-'C-B+E, a(-A, t+u — t-0, 

by = A-C, 0V-B, ^+t-x-0, 

CM-B-A, yS-C, t+x-V-0. 

Here E is the battery e.m.f., and A, B, C, denote the potentials of these 

points below that at 0. These mne equations contain nine unknown 

quantities, vii., six currents and three potentials. Solving them as simul- 

toneous equations an^ of the unknown quantities may be determined. For 

instance, the current in the galvanometer circuit is 

t_^(6/»-cr), C29) 

where the "determinant" D is given by 

£)-oi>e + 6ctf-(-7)+M(T + a)+oi(a+«-Ka-f-H-c) (fiy^^a+aff).* 
U. Networks of oonduotort. In a general cose (Fig. 2) as many 
Kirohhoff equations (Par. tS) may be written as there are conductors; the 

unknown quantities may be 
the currents, the resistances 
or the voltages; also any com- 
bination of these, provided 
that the total number of un- 
known quantities is equal to 
the number of equations.^ The 
equations are conveniently 
solved by the method of deter- 
minants, found in most text- 
books on algebra. 

»i. Mazwell't solution. 
In Borne cases it is convenient 
to consider, instead of the ac- 
tual currents, fictitious cur- 
rcnta in each mesh (MaxweU, 
ibid.. Art. 282i). The actual 
current in each conductor is 
equal to the algabraio sum of the fictitious currents. For instance, in 
Fig. 4 the ourrent in conductor /is the difference of the fictitious currents 
X and Y, The Kirchhoff equations are written for the fictitious currents. 

* Maxwell, J. C. "A Treatise on Electricity and Magnetism,*' Vol. 1, 
Art. 347. 

For practical forms of the Wheatstone bridge and its application to tho 
measurement of resistance see Sec. 3. 




Fig. 4. — Method of simplifying networks. 



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ELECTRIC AND MAGNETIC CIRCUITS See. S-34 

An examine of Bueh a solution will be found in Del Mar's "Eleotrie Power 
Conductors," p. 34. 

U. JBquiTUent >tar and maah (d«lta). The ntiniber of meshes, and 

. conaeqoently the aumber of equations, ma^ be reduced, when some of the 

tneeh^a are in the form of s triangle, like ^c in Fig. 4. For tha three retistancea 

furmi^ the trioTigle may be mbstiluted the three retittaneea a, 0, arid y, which 

Taitate from one point. 

The currenta and the voltages in the rest of the network remain the same, 
pcov»ied that 

6c , CO ah 

""(a+t+c)' ''"(a+6+c)' '*'"(o+6 + c) *^^ 

The Qumber of meshes is thus reduced by one. See Kennelly, A. E.. EUc- 
irknl World and Engineer, VoL XXXIV (1809), p. 413. For a discussion of 
frqiiivalent star- and delta- connected impedances for alternating currents 
•ee his "Application of Hyperbolic Functions to Electrical Engineering 
Problems," Appendix E. 

U. In the pTftctieal oaM of distributing networica and feeders, the 
drtennination of the currenta and voltages at the junction points is simpu6ed 
by uidnc the following l«wa of superposition of currents and voltaffes. 
(1) The true current at any point in the network is the algebraie sum of 
the currents which would flow if the consumers' eurrents were taken in 
•ReeeaEion instead of simultaneously. (2) The voltage dr<^ to any point 
in the netwtvk is equal to the suni of the drops to the same point calculated 
Bsder the araumption that the consumers' currents are taken in succession, 
and not simultaneously. Some simplification in the solution <A the Kirchboff 
eqaations ia posnibly due to the fact that the voltage drop along a conductor 
is usually small as compared to the voltage between it and the return con- 
dnrtor. For details of such calculations see Teichmullcr, " Die Elektrinchen 
Icituwen;" F. B. Crocker, " Network of Electrical Conductors," El. World, 
VoL LIX (1912), pp. 799, 847, 901; Alex. Russell. "The Theory of Electric 
Cables and Networks," Chap. 4; Nowak, J., " A Machine for the Calculation 
of Supply Networks." The Electrician, Vol. LXVIII (1912). p. 748; Hersog 
Md Feldmann, "The Distribution of Voltage and Current m Closed Con- 
dufting Networks." Trarnt. Inst. Elec. Congress, 8t. Louis. 1904, Vol. II. p. 
6^: also their book entitled " Die Bereohnung Elektrisoher Leitungsnetxe," 
and lUiha und Seidoner, " Starkstromtechnik, Sec. 8. 

EI.XCTEOHAOinCTIC IKDUCTIOH 

M. Faraday's law of indnetlon. When a mat^netic fl\ix * within a 
loop of wire varies with the time, an e.m.f. is induced in the loop, the instan- 
taneau value e of the e.m.f. being proportional to the rate of change of flux; 

.--t-3;^. (31) 

vbere d*/dt la the rate of change of flux 4 with resiwct to the time t, and h 
iiteoDstant which depends upon the units of voltage, flux, and time. When 
4^ is ia maxwells, e in volts, and time in seconds, k=^ 10~*. If the flux is 
fxpreved in webers, k= 1. The sign minus determines the relative directions 
of the flux and the o.m.f. Namely, when the circuit is closed, the induced 
«-m.f. tends to produce a current in the direction such as to oppose the change 
IB flux. This latter statement follows from Lens't law, which is stated by 
MmwcU* as follows: If a constant current flows in the primary circuit A, 
*odif, by the motion of A, or of the secondary circuit B, a current is induced 
tn B, the direction of this induced current will be such that, by its electro- 
^N9Hic acUon on A, it tends to oppose the relative motion of the circuits. 
See the right-hand screw rule (Par. S6) or Fleming's rule (Par. 67). For 
pPsctieal purposes three particular cases of electromagnetic induction are 
cooadered below. 

n. Stationary conductor and variable flux. This is the case when 
both the cxnting xn.m.f. which produces the flux, and the winding in which 
»n e.m.f. is induced, are stationary, relatively to one another. The voltage 
winducpd by a varying magnetic flux, the chani(cs in the flux being prodncwl 
by rar>'ing either the magnitude of the m.m.f. (stationary transformer) or 

, 'Maxwell. J, C. "A Treatise on Electricity and Magnetism." Vol. U. 
Art M2. ^ •^ 



63 



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Sec. a-38 BLBCTRIC AND MAONETIC CIBCVITS 

tb* raluotaaoe of tbe masnetio oimiit Ondaotor-type alternator). If tb* 
flux k linked with N turns and variea harmonically with the time, at a fre- 
quency of / cycles per second, the znazimam Induced e.m.f. ia 

«.»» - 2x/3V*«..10-» Tolta, (32) 

where *mt* is the maximum instantaneous value of the flux, in maxwelta. 
The efteetlT* value of the induced e.m^f. is 

S - 4.44/if *».>10-i Tolts. (33) 

When the flux rarles according to a lav different ftrom the line lav the 
effective voltace is 

E-ixIN*m«AO-*, (34) 

where x is the form factor (Par. lOT). 

The aTcrase e.m.f. Induced in one turn, no matter what tlie law of 
variation of the flux with the time, is 

where the subscripts 1 and 2 refer to the initial and the final instant* 
respectively. 

M. Stationary flux and movinc conductor. When the exdtins m.mj. 
which produces the flux, and tbe winding in which tbe e.m.f . is induced, movo 
relatively to each other, as in a generator, so that tbe conductors out aoroea 
the lines of flux, the instantaneous induced e.m.f. in a oonduetor ia 

c-MU>,* (38) 

whece (B is the flux density, I the length of tbe conductor, • the relative veloc- 
ity between the flux and tbe conductor, and k a coefficient which depends 
upon the units selected. When « is in volts, (B in maxwells per square centi- 
meter (gaussee), I in centimeters and o in centimetera per second, k " 10~*. 

The three directions, (B, I, and i, are supposed to be at right angles to each 
other; if not, their projections at right angles to each other are to be used in 
the preceding formula. For practical formulas giving the e.m.f. induced in 
direct-current and altemating-cunent mabbinery see Sec. 7 and Sec. 8. 

t>. ▼arlabla Huz and movinc conductor. When coilsor conduetois 
are moving through a pulsating magnetic field, as for instance in single-phase 
motors, the induced e.m.f . is due to a combined transformer and generator 
action (Far. 37 and U), and is equal at any instant to the sum of the e.m.f. 
induced by a constant flux in a moving coil and that induced by a pul- 
sating flux in a stationary coil. Let the frequency of the pulsating fiela be 
/ cycles per second; that of the rotating coil f cycles per second. A pul- 
sating field can be resolved into two revolWng fields, one rotating clock- 
wise, the other counter-clockwise. Therefore, the Induced e.m.f. is a result 
of the superposition of two e.m.fa, one of the frequency /+/'. the other 
f—f. In the particular case of f^f the e.m.f. induced in the rotating coil 
IB of the frequency 2f, the frequency f—f being equal to sero. 

M. Torce on a conductor cairj^nf a current in a macnetlc field. 
Let a conductor carry a current of i amp. and be placed in a magnetic field 
the density of which is ffl maxwells per square centimeter ((B gausses). TheOt 
if the length of the conductor is I cm., the force tending to move the con- 
ductor across the field is 

J'-10.2.(BI10-» (kg.) (37) 

It is presupposed in this formula that the direction of the axis of the conductor 
is at right angles to the direction of the field. If the directions of i and B 
form an angle a, the preceding expression must be multiplied by mn a. 

The force F is perpendicular to both i and B, and its direction is determined 
by the right-hand screw rule (Par. ■•]. Namely, the effect of the magnetic 
field produced by the conductor itself is to increase the original flux density 
((B) on one side of the conductor and to reduce it on the other side. The 
conductor tends to move away from the denser field. 

41. The attraction or repulsion between two parallel straight eon- 
ductor>» carrying currents ii and ti (amp.) and placed in a non-magnetio 
medium, is cslcuTated aocording to the formula 

F-2.04uf«(j^)10-« (kg.) (8q> 

64 

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ELECTRIC AND UAQNETIC CIRCUITS S«C. 2-42 

vken I/l ii tha ratio of the length of euh eonductor to the kzial diatanee 
bMvMn the condueton. The foroe ie an attraction or a repulaion according 
to vliether tlie two cumnta are flotring reepeettrely in the aame or in tlM 
apocate dinctioni. 

MKhanical force exerted between magnetic flux and a current-earnring 
•ondnctor ii alM> preoent iniida the conductor itaelf , and ii called pinch eaiMit. 
TlH force between tike infiniteeimal fiiamenta of the current is an attraction, 
K that a current in a conductor tenda to contract the conductor. Thia 
tlMt k o( importance in «ome type* of electric furnacea where it liraita the 
ranent wUeh can 1m carried by a molten conductor. The same atreaa alao 
tmda to elongate the conductor. 

tt. iBtarlinkac* of eUetrie uid ntafoMe elrealtg. The most general 
nlstioaa b e t ween the electric and tlie magnetic quantities are expressed bv 
two lawi of etrenltaUon. * Stripped of the Teotor^analjraia termain whicn 
tlnas lavs an uaually expressed, they are as follows: Let H be the magnetie 
iatesaty or the m.ni.f . gradient at a pcont in a medium of constant permea* 
fajlity, and let (7 be the electric intensity or the e.m.f. gradient at a point. 
Tie Snt law of eircuitation atatea tliat the line integral of H along a closed 
tvra is propwtional to the Tolume of the total current (conduction current 
ud displacement current) linked with this curve. The second law of 
drmitatioa states that the tine integral of the electric intensity along a closed 
rarre is proportional to the rate of change of the total magnetic flux linked 
«itb this curre. The coefficients of proportionality depend only upon the 
nits and. The theory of propagation of electromagnetic waves is based 
•poB these two lawa. See for instanoe W. B. Franklin's " Electrio Waves," 
Art 57. 

TBI MAaHXTIO OntOVIT 

II. The ilinple magnstle circuit. The simplest magnetic circuit is a 
aaifomly wound torua ring (Fig. 5). The relation between the m.m.f. 7 

and the flux * ia aimilar to Ohm's law 
(1»), vis., 

S-Sl* (39) 

where A is called the ralneteaes of the 
magnetic circuit. The same relation is 
sometimes written in the form 

*-<P9 (40) 

where <?— 1/91 ia called the pannaane* 
of the magnetic circuit. Reluctance is 
analogous to redstanoe and permeance 
is analogoua to conductance of an elec- 
ttie circuit. 

44. The m.m.f. does not depend 
alone on either the current in the wind- 
Pto. 5. — Closed magnetio circuit, lag or on the number of turns, but on 
the product of the two; therefore, tha 
natural unit for tlu m.m.f. li 1 amp-turn, but in the practical system 
1 smp-turn ia 1.257 unite of m.m.f. U the flux in the preceding equations 
isexprsssed in welsers (one weberM 10* maxwells) the permeance is expressed 
in benrys (bein^ of the nature of inductance). It hsia been proposed to call 
the eorreapondinc unit of reluctance the ymeh, this being the word henry 
spelled backward, corresponding to ohm and mho. It has also been pro- 
posed to name the unit of permeance a perm, and the Unit of reluctance a 
rel,t when tha flux is in maxwella and the m.m.f. in ampere-turns, but no 
names have yet been generally accepted. In the C.G.B. electromaxnetic 
■Vitem the unit of m.in.f. is the gilbert, equal to 10/4t — 0.7055 amp-turn. 
Tberefort the in.in.f. in gilberts, expressed as a function of ampere-turns, is 

* Hcaviside, O. "Electromagnetic Theory," Vol. I. 

t Karuetoff, V. "The Magnetic Circuit;" MoOraw-FliD Book Ca Inc.. 
New Yore, 1912, Chap. I, and appendices. 

( 6S 




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SecS-45 SLSCTRIC AND MAONBTIC CIRCUITS 

where nJ is the product of the number of turn* and the currant in ampere*. 
For further information about magnetic unite ace See. 1. 

M. f •rmeabillt^ and relnetlTltjr. The reluctance of a uniform mac- 
netio path (Fig. 6) la proportional to ita length { and inversely proportional 
to its croea-eection At or 

»-'2 (42) 

and 

(f-l'j. (43) 

In theae ezpreariona r ia called the reluctivitv and it the permeability of the 
material of the magnetic path. For air ana all non-inagnetic ■ubatsnoea, 
r and ti are aasumea to be equal to unity per oentimeter-cubo, oorreapondins 
to centimeter measure for I and A in (42) and (43), and the ^bert as the 
unit of m.m.f. This is the conventional aaaumption in the C.O.S. eleo- 
tromagnetio system and ia the one generally employed. See alao Par. IS 
andM. 

The method preferred by the author, and expounded in his " Macoetie 
(Mreuit" (see footnote reference in Par. M), ia to t&loe the ampere-turn aa 
the unit oi nti.m.f. - In such eases, with the maxwelras the unit 6i flax, the 
permeability and the reluctivity of air, respectively, are 

F-0.7e55 per cm.>-0.3132 per in.« 1 ,. .. 

>.-1.2S7 per cm.«-3.193 perin.*/ (**' 

This method has the advantage of ^ater airaplictty in caleulationa, but ia 
not yet in general use (see Sec. 1; Giorgi aystem of units. Par. S(<<a)). 

4>. Macnetio field Inteniity X is defined aa the m.m.f. per unit length 
of path. In any uniform field 

K-f. (45) 

In a non-uniform magnetic circuit 

K.'f. (4«) 

Inversely 

^-XlorS-J'Xal. (47) 

3C is alao known as the nukcnetlaing fore* or as the magnatie potantial 
(radiant. 

If 9 is in ampere-turna, 3C ia in ampere-turns per centimeter (or per inch*) 
of length. If 7 is in gilberts, 3C is in gilberts per centimeter (or per inch). 

4T. Tlux density ((B) is defined aa the flux per unit area perpendicular 
to the direction of the Unea of force. In a uniform field 

In a non-uniform Add 

«-aJ- («) 

Inversely 

*-(B.4, or *-y*(Ba.<l. (50) 

If the flux ia measured in maxwella and areas In square centimeters, 
flux density is expressed in maxwells per square centimeter; one maxwell 
per square centimeter is sometimes called a gauH. In thia country flux 
density is alao expressed in maxwells, or in kilolinee, per square inch. 

It follows at once from (40), (43), (4S) and (48) that 

(B-piK (51) 

which ia the familiar relationship between flux density, permeability and mag- 
netic field intensity. 

4t. Beluctanees and parmeaneas in larlaa and In parallel. Reluct- 
ance* and permeances are added like resistances and conductances (Par. n 

oe 

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Fio. 5. — Typical 6i-X cam. 



ShSCTBIC AND MAOUSTIC CIRCUITS SeC S-40 

toM), respeetn^y. That u, reluctaneea are to he added wfwn in eeriee, and 
fwrneanfM art to b«^idded whrn in paralkl- If several permeance* are given 
roonected in series they are first converted into reluctances by taking the 
redprocsl of each. Similarly if reluctances are given in a parallel oomoina- 
tioB, they are first converted into permeances by taking the reciprocal of 
esch. 

49. ICarnctljifttlon characteristic. The magnetic properties of a 
■smple of steel or iron are represented by a saturation or nuiglisti latlon 
eorra (Fig. 0). Magnetic intensities X in ampere-turns per centimeter 

(or per inch) are plotted as abscissa 

and the corresponding flux densities 

(B in kilolines per square centimeter {or 
per square inch) as ordinates. The 
eiuve IB also known as the (B-K curve. 
The practical iiae of a magnetisa- 
tion curve may be best illustrated by 
« ["f'H jfi l" M ! I i I" t'l t I t" n ~l *° example. Let it be required to find 
Jl»---'-^ 1 — I the number of exciting ampere-turns 

f'-f for magnetising a steel ring so as to 
_-L . produce in it a flux of 168,000 max- 
— Nt l-t t I- H H i t I M M 1 T wells. Let the cross-section of the 

ring be 3 cm. by 4 cm., and the mean 
diameter 46 cm. Let the quality of 
the material be rapreeented by the 
curve in Fig. 6. The flux density is 
168,000/(3X4) -14,000 maxwells per 
square centimeter or 14 kilogausses. 
For this flux density the corresponding 
abscissa from the curve is about 18 
amp^tums per centimeter. The total 
required number of ampere-turns is 
18X1-X46-2.600. 

It may be noted that it is much more convenient to plot curves of <B 
wing as abaoissiB 3C in ampere-turns per unit length, rather than gilbertt per 
ludt length. For '*(B-dC curves oi various grades of steel and iron see 
See. 4. The principal methods for experimentally obtaining magnetisa- 
tioa curves wul be found in 8eo. 3. 

M. Zn a mAffn«tio dreult eonslstinsr partly of Iron and partly of 
sir the ampere-turxu required for establishing a certain flux are calculated 
by adding together the ampere-turns required for each part of the circuit. 
I^ (Bi be the flux density (gausses) in the iron and U the length (centimeters) 
o( the path in the iron, ffl« the flux density in the air and l» the length of the 
sir-Ksp in the direction of the linee of force. Then the total ampere-turns 
rcqaiied for the circuit are 

JV7-3Ci^+3CJ^ (52) 

vhne Xi (amper»-tums) is found from a saturation curve for the known 
nine of (&t (O) and 9C.«0.7g55(B.. If U is in inches, and (B. in maxwells 
per iqaare inch, 3C«>-0.3132(B«. The same method is applied if a ma^etio 
ciremt consists of more than two parts, as for instance tne magnetic circuit 
d an electric generator or motor (Sees. 7 and 8). For numerous practical 
problems and solutions see the author's "Magnetic Circuit,'* pp. 27-31, 
ud Chaps. V and VI. 

11. Anal/ils of marnstisatlon curre. Three parts are distinguished 
iBsmsffnetuationeurve (Fig. 6), the lower or nearly straight part, the middle 
psit ca&d the knoo of the curve and the upper part which is nearly a straight 
luie. As the magnetic intensity 3C increases, the corresponding flux density 
A increases more and more slowly, and the iron is said to approach satura- 
tton. The percentage of saturation of a machine is defined in Art. 47 of 
the Staadvt&sationRnles of the A. I. E. £. (Sec. 24). 
. H Sosesptlblllty and Inducsd magnetisation. A magnetic flux in 
iron or in another magnetic substance mav be thought of as due to two 
caows: (1) the extAmai applied m.m.f., and (2) the internal or molecular 
in.in.fi., induced by the applied m.m.f. Thus, we have 

. X-.3, (53) 

vbcrt X is the mag^netic intensity due to the external m.m.f ., and 3 is the 



( 



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^ 
> 



Sec S-^3 SLBCTRIC AND UAOlfSTIC CIRCUITS 

intuwity of indnced mastietintioa. Tha eoeSoient < is oalled th* nucapti- 
bilitjr of the material. The total flux density in iron also oonsists of two 
parts, vis., that due to 3C and to 3, or, in the C.Q.S. system, 

(B-3C+4t3. (54) 

Dividinc both sides of this equation by X, s>ves 

/.-l+4«, (55) 

where /■ is the permeability of the material (Par. H) . SoaoeptibiUty is equal 
to sero for non-magnetio materials, is positive for paramagnetic and ne(»- 
ti ve for diamagnetic substances. It is seldom used in practice. * 

It. The permeability 0<) and the reluoUTlty (r) of » in>t«i1»l (Par. 
M) are also defined as the ratios 

Their values depend upon the units selected for (S and 3C. In the C.Q.S. 
electromscnetic system S and X are numerically equal for non-masnetio 
materials, consequently it^fl. When (B is expressed in maxwells per 
square centimeter ^or per square inch) and K in ampere-turns per unit 
length, li and r for air and other non-magnetic materials nave values given in 
Par. M, Eq. 44. 

(4. Two dlfler'ent scales of permeability. For steel and iron the per- 
meability fi<^(S/K is frequently calculated from the magnetisation curve 
(Par. 49), and is usually plotted against (B as absoissai (see curves in Sec. 4). 
One must be careful to distinguish between the absolute permeftbUit^ 
and the relative permeability. The former is equal to (B/3C, the latter la 
the ratio of the permeability of a sample to that of the air. In the C.Q.8. 
electromagnetic system both permeabilities are numerically the same, 
because n is assumed to be unity for the air; nevertheless they have diffeient 
physical dimensions in any system of units. 

U. Kagnatle oaloulatioiu. In practice, calculations of macnetio 
circuits with iron are usually arranged so as to avoid the use of permeatauitjr tt 
altogether, using a (B-3C curve directly (Par. 49 and 50). In some spe^uJ 
investigations it is convenient to use the vsJues of permeability and also an 
empirical equation between ii and (&. For small and medium mix densitiee ^ 
may be expressed as a parabolic curve, of the form 

M-o-K(Bo-(B)'10-« (57) 



» : : : •. ■ o,^'' 




Fig. 7a. — Relation between directions Fia. 7b. — Fleming's rules, 

of current and flux. 

For numerical values of the coefficients see Sec. 4. It is also possible to 
represent the relatlomblp between ffi and X tor % magnetle material 
empirically by a hyperbola (FrShlich's formula) 

or also in the form 

reluctivity »-^-a+^"i. (SB) 

The coefficients a and fi must be so determined as to satisfy the saturation 
curve of the particular material used. 

§9. The right-hand screw rule. The direction of the flux produced 
by a given current is determined as shown in Fig. 7a (see also f^. 5). If the 

'Maxwell, J. C. "ATreatise on Electricity and Magnetism," Vol. II., 
Arts.,42e to 428. 

68 

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BLECTSIC AND UAONETIC CJBCVITB SeC 3-57 

cancat Bows in the diraotioii of rotation of % lisht-haod acrew, the flux is in 
tte diraction of the ^rocreaaive movement of the ■crew. If the currant in a 
■tiaight eoadoctor u in the diieetioa of the procreaaive motion of a lii^t- 
haad aerew, then the flux encirelee thia conductor in the direction in which 
the acrew most be rotated in order to produce thia motion. The dots in the 
fiiafe i n di cat e tbe direction of fluz or current toward the reader; the croeses, 
thai away from him. 

tn. Tba ralatire dlraetion of flux, e.m.f. and moUon in a senerator 
mn be determined with the richt hand by plaoinc the thumb, index- and 
lawlrilw fincera ao aa to form the three axee of a coordinate ayatem and then 
f^^iK*i*>^ tAe index-finjier in the direction of the flux (north to south) and 
the thumb in the direction of motion, the middle finder will give the 
iHreetiiin of the generated e.mJ. (Fi^ 76). In the aame wa^ in a motor, 
■■as tile left hand and pointin|t the index-finger in the direction of the flux 
aad tlw ifnAAX^ finger in the direetion of the current in the armature oon- 
dactor, tbe thumb will in^cate the direction of the force, and, therefore, 
<ke laaultina motion. Theae two rules, indicated in Fig. 76, are known 
aa naaalac'a ml**- 

n. taplacia'a tow. In a medigm the permeaUlity of which ia tbe aame 
at an poanta, tbe magnetie field intensity produced at a p<nnt ^ by an 
t of a conducted da (in em.) through which a current (u i amp, is Bow- 

Me- ***jg.° " (gOberteperem.) (60) 

■ r is the diatanoe between the element 9t and the point A, in centimeters 
sad <r is the angle between tbe directions of Aa and r. _ The intensity 9X ia 
pcrpendicfdnr to the plane eompriidng da and r, and ita direction is deter- 
■ijM by the right-hand seiew rule pven above. The field intensity pro- 
daecd at ^ by a closed dreuit ia obtained by integrating the above expression 
far UK over tbe whole circuit. 

W. Tbo macnaUe Held due to an Indeflnita itraicht eonduetor, 
cafrying a eorrent of i amp., consists of concentric circles which lie in planes 
psrpeamenlar to the axis of the conductor and which have their centres on 
Tbe Hold Intanaitj at a distance of r cm. from the axis of the 
is 

3C-^ (gilberts per om.), (61) 

its fieetioa being determined by the right-hand screw rule (Far. M). 

M. Ifacnetisflelddastoaelossd 
drenlar oondnctor. If the conduc- 
tor carrying a current of / amp. ia 
..^ bent in the form of a ring of ramus r 

J ^^^ cm. (Fig. 8), the magnetising force at 

a point along the axis is 

(gilberts per cm.). (6^ 
Wben(-0 

X-2f-' (68) 

and when I is very great in comparison 

Fu. BL — Mvuetie fidd along the axis *° '' 2n-t 

of a evealar eonduetor. JC- ~^ J. (64) 

U. Tha magnoUe Intanaitjr within a solanoid made in the form of 
a tSfSi ttng, and also in ibe middle part of a long atnight lolenold, ia 

3C-jgni» (gilberta per cm.) (6S) 

vlaK ■ ia the current in amperes, and ni is the number of turns per centi- 
■ncrkagtb. 
Tts determination of the field intensity produoed by short coll* ia 

09 

DigiiizMbjV^iUUyiL' 




Sec 8-62 SLBCTRIC AND UAQNBTIC CIRCUITS 



usually a complex matter, and the results are expressed by complicated 
formuls. See references in Par. 74. 

62. The stored maffnetle emerg;; In a single loop of non-magnetic wire, 
when the dimensions of the wire are small compared to those of the loop (so 
that the flux inside the wire is negligible), is 



IF_J,*=},t(J>. 



29 



(joules) 



(66) 



where t is the current in amperes, 4 the flux linking with the loop, in webers, 
and (P the permeance of the magnetic path, in henrys. 

(S. Kflect of leakage. When the flux linking with part of the turns of a 
coil C is not negligible (see Fig. 9), the total stored energy may be expressed 
in the following forms: 

(67) 



ir-Jinn'<Pc+Sn»»A*,l. / 



The last expressioii is identical with 

W-IW (68) 

where L is the inductance of the coil (Par. •?) . The subscripts r in the fore- 
going expresaiona refer to complete Unkagea, that is those which embrace 




Fio. 9. — Magnetic field due to a coil. 



-'<- 



all the tumfl of the coil, the subacripts p to partial llikkafftl. See the 

author's "Magnetic Circuit," Art. 57. 

64. The denidty of magnetic enM^, or the magnetic enersy stored 
per cubic centimeter of a magnetic field is 

<BJC <B' 
*"8» "s — (jouleeper cubic cm.). (69) 

Here 3C la the intensity^ in gilberts per centimeter, (B Is the flux density in 
webers per square centimeter and /< ia the relative permeability; or if 5C is 
in ampere-turns per centimeter, then 

W"- i/*3C*- J<B3C-^ (joules per cubic cm.) (70) 

where ii is the so-called absolute permeability (see Par. M). To find the 
total energy of a field the preceding expressions are multiplied by the element 
of the volume dr and integrated within the desired limits of volume. For 
an interesting comparison of practical possibilities as to the amount of 
energy storea in the ma«netic form per unit volume, compared with other 
forms of energy, see Steinmeti, C. P., General Electric Review, 1913, p. 
636. 



70 



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SLKCTBIC AND UAONETIC CIRCUITS SeC. 3-65 
U. Ibciutlc tnkCtlTa force. * Tha eariTlnc wsight of a lUtinc nukc- 

"*" i^-^ (k«.) (71) 

wben (fi is tbe fiuz dennty in the air-sap, ezpresned in IdloUnes per square 
ecnunwter. and A is the total area of toe contact between the armature and 
the core, in square centimeten. See also Sec. 5. 

M. MacnaUe force or torque. The meehjuileal toree or tha torque 
lirtweeu two parte of a maifnetic circuit may in some cases be conven- 
iently calculated by maldnc use of the prlnofple of vlrtuiU dliplaee- 
BMats. An infinltewmal displacement between the two parts is assumed, 
aad the aammption is made that the work necessary for this displacement 
is equal to the cbange in the stored magnetic energy, plus the electrical 
cnencT added during the ehange from the sotirce of the ezoitinc current. For 
details see the author's " Magnetic Circuit," Art. 71. 

DrDUCTANCK 

ST. The eleetromarnetlc Inductance, or the coeffldant of salf-tn- 
I L, is defined from any of the following three fundamental equations: 



"V 



(72) 



W-\i^L: (73) 

L-n.»ff'.+ I n,H<fr- (74) 



^X"' 



These ezpresaions are true only when the permeability of the medium is con- 
scant. The first equation expresses the fact that the self-induced voltage 
is pro|)ortional to the^rate of change of ^the current in the cireuit, and L is the 
eoefident of proportionality. ^ According to the second equation, the mag- 
Betie ettei gy stored in a eiremt is proportional to the square of the current 
fPar. U), and L is the eoefficient of proportionality. In the third formula 
L is expressed through the permeances <? of the magnetic paths linking with 
the eimiit (Fig. 9), and the number of turns with which these paths are 
Eaked. The snbacnpta e and p refer to complete and partial linkages respec- 
tiveiy (Par. M). For practical purposes both inductance and permeance 
are e xpus ecd in henry* (Par. 44). The first expression is convenient for 
nrseamnenta of inductance, the third one for calculations in ttiose cases 
where the shape of the magnetic paths is known or can be estimated. 

M. Cloaed magnetic circuit. For a torua rlnc (Fig. 5) uniformly 
vsand with one uurer of thin wire the partial linkages may be neglected, 
so that fly — 0, and Ve^uA/l, where for non-magnetic materials /i« 1.000; 
A is tlie eroas iretion of the Sox within the ring, and I is the average length of 
tb* flex. Consequently 

£_L?*^f!i^^,10-«-1.267n«iM10-» (henrys) (75) 

la this cxprrsaion ne is the total number of turns, and m ■■ nc/l is the number 
el turns per eentimeter length of the magnetic path; I and A are in square 
reBtinetefB; bt is the relative i>ermeability of the core with respect to the air 
(Pu. M). 

M. For a toma rlnc of reetanynlar eroH-iectlon wound with MTeral 
lajan of wire the indoetanee is 

JE,-0.4^'li»+|«(6+»+0110-« (henrys) (76) 

la tUs cipreBaion h and h are the dimensions of the non-magnetic core on 
wts^ the wire is wound, D is the mean diameter of the ring, n is the total 
aujab ei of tarns, and t the thirlcness of the winding (all in centimeters). 
If the core is magnetic, the product bh must l>e multiplied by the relative 

* Maxwdl, i. C. "Treatise on Electricity and Magnetism;" Cambridge 
I'avmaly Pnaa; \<A. II. Art. 043. 






Sec 2-70 BLECTBtC AND UAONBTIC CIRCUITS 

permeability of the steel. If the macnetio core occupiea only a part a of 
the croae-eection bh, yue the expreeaioa bA[eg<r + (l— a)], in place of Uk. 

TO. For other raleulatioiu of induotanee uainc formula (S8) eee the 
author's " Magnetic Circuit," Chapa. X to XII. 

Tl. Thin aolenoida. For a straight coil imiformly wound vith m turns 
per centimeter length, provided that the lengUi of the coil is large com- 
pared to its transverve dimensions, and that the winding consists of one layer 
of comparatively thin wire, tba induetane* is 

£-1.2fi7ni>iAI0-« (heniys) (77) 

the notation being the same as ifi Par. 68. 

Tt. The InduetanM of a Ions itraif ht eoll wound with several layers 
of wire, and with an iron core of radius a inside, 

i-4n.«««r«[H-0>,-l)^'+^+|^]lO-? (henrys) (78) 

where r is the inside radius of the winding, and 
d its radial thickness; m is the number of turns 
per centimeter length, and all the dimensions 
are in centimeter*. If there is no iron core, 
put a»0. 

T>. ttat. Morfui Brooks has derived s 
universal semi-empiiioal formula for the in- 
doeteneo of ihort and lonr eoila without 
Iron oorM. His formula is given below in 
two forms, one (79) for dimensions in centi- 
meters, the other ^80) for dimensions in En- 
glish units. Both give results in henrys. The 
notation is explained in Fig. 10. 



Cm* 



F'F" 

'b+c+B 10« 



(heniys) 



(78) 



XPV" (henrys) (80) 



ln£q.(80) the conductor length is in thousands 
of feet, and the coil dimensions in inches; 0.366 
is the conversion factor. P' and F" are em- 
pirical ooU-sha^ factors dependent upon the 
relative, and independent of the absolute 
dimensions of the winding. Values of F^ and 
F' are as follows: 

10fc+12c+2S 



T' 


hnnt 


1 


1 


-I 


1, 










r. 


— 


D 


i:. 


4 


■ 





k 



-Axis 



Fio. 10. — See Par. 73. 

UR \ 



'"- m+i^+ilR - ^'-o-' '°'"^'^+mk) 



Cm indicates the length of the conductor in centimeters; 

Ft indicates the length of the conductor in feet, and A/ 1000 — thousands of 

feet; 
AT is the total nuQtber of turns in the winding, whence 
Cm — 2waN, when a is in centimeters, and 
Ft 2nN . .... 

looo" Ilooor "'"""' "•° ""'•"*• 



(82) 
(83) 

Numerous tables, curves, and charts which simplify the use of this formula 
for practical design will be found in the Bulletin No, 53 of the Univerrity 
of Illinois, by Morgan Brooks and H. M. Turner, entitled "Inductance of 
Coils." For another empirical formula see Doggett, L. A., **The Induotanoo 
of AiKsored Solenoids," EUc. World, Vol. LXIII (1814), p. 260. 

T4. Buroau of Standard!, fonnulaa for inductaneo. For a thorough 
analysis and comparison of various formulas for the inductance of coils the 
reader is referred to the following excellent series of articles published in the 
Bulletin of the Bureau of Standards: 

" Formula and Tables for the Calculation of Mutual and Self-inductance " 
(Revised), E. B. Rosa and L. Cohen, Vol. VIII, p. 1; 1012; "Calculation of 

72 J ' a 



SLSCTBIC AHD UAOSBTIC CIRCUITS SeC. 2-75 

tb Sdf-imloetaiioe of Sincle-Uyer Coib," Edward B. Rom. VoL II, p. 181; 
IWt; "The 8«lf'4nductance of > Coil of any Length Wound with anjr Number 
dLMcn of Wire," Edward B. Koaa. Vol. IV, p. 369; 1B07: " Self-Inductance 
efaSolnuad of any Number of Layers," Louis Cohen. Vol. IV, p. 383; 1907; 
**CoiiBtraction and Calculation of Absolute Standards of Inductance,'* 
J. G. Coffin. VoL II, p. 37; 1906. 

" BcriaioB of the Formulas of Weinstein and Stefan for Mutual Inductance 
e< Caudal Coils." Edward B. Rosa. Vol. IL p. 331; 1906; "The Mutual 
ladactaaee ot Two Circular Coaxial C<uls of Reotangular Section," Edward 
B. Baaa and Louia Cohen. Vol. II, p. 359; 1906. See also E. Orlich, 
"Kuaiititund InductivitAt " (Vieweg),p. 74. and Louis Cohen, " Formulie 
sod Tables for the Calculation of AltematinK-current Problems," Chap. 2, 

n. Thi indaeteaea of a eoncentrlo aabto is (Fig. II) 

Z-0.4006 logio(^Wo.05+i:'' (miUihenrys per km.) (84) 

^'-Tii['-1^(f)'+4-o(f)'+- • • • ] ^««> 

The faracoins e x pr e ssion for L is true at low freqneneisi onljr. At high 
fraqaeacies an unequal distribution of currents reduces the partial linkages 

L-0.4605 1<«>«(^ +HO.OS+L'). (86) 

HcR t— I at naoal industrial frequeneiea, and gradually approaches sero 
as the frequency increases to infinity. 

n. H-eoadaetor oabloa. For the flald 
distribution in and the indnetanee o( non- 
eoneontrlc o»bles see Alex. Russell, "Alter- 
nating eurrents," VoL I; for the indnotanea 
of armorad ««bl*t see J. B. Whitehead, 
"The Reaistanoe and Reactance of Armored 
Cable*," Trans. A. 1. E. E., Vol. XXVIII 
(1909),-p. 737. 

TT. Tha indaetane* of a aiiicla-phaaa 
tranamladon lino is given by 

L - 0.4605 logi«-+ 0.06, in miUihenrys per 

a 

kilometer of one conductor, (87) 

where a is the radius of the conductors, and 6 

rM. 11.— Croaa-seetion of is the distance between their centres. To find 

eoDcentrie cable. the inductance per mile multiply by 1.609. 

To find the inauetanoe per thousand feet 

<STids by 3.2SI. For tables of reactance (Par. IM) at usual frequendee 

Md ipaeuigB see Sec. 1 1. 

n. For iroiL eondaeton use O.OSjir instead of 0.05 in the above formula, 
■hoc ^r is die relative permeability of the iron with respect to the air. The 
Tilas of It, varies with the current, and also depends upon the quality of the 
irsa. For good telMraph wire ^r is equal approximately to 150. 
. 19. Far gtrandod eondaeton the actual radios is too large to be used 
m tim fonnula for inductance. For ail practical purpooes, the equivalent 
n£ai of a stranded conductor majr be assumed the same as that of a solid 
■vsad eoodnctor of the same sectional area. For an accurate calculation 
tf_ the iadoctanee of stranded conductors see Dwight, H. B., EltctriaU 
'wR 1913, VoL LXI, p. 828. 

W._Th « inductance of a three-phaia line with irnunatrieal ipaolng, 
PV Vka, is the aame as the inductance of a single-phase line per wire, with 
tar 'eiae siaa of wire and the same spacing. It is expressed by the formula 
W la Par. TT. This formula holds true lor balanced as well as unbalanced 
>"», tat faalaneed and unbalanced line voltages, for a three-wire two-phase 
•fxm, three^wire single-pbaae system, monocyeUc system, etc. 

n. For a iemi-iTnunetrteal tpaoing of a threa-phMe line, that is 
•in two spaongs are eqtal, sod the third is different, formula (87) in 

73 

DigiiizMbyV^jOUyiC 




Sec. 2-82 ELECTRIC AND UAONBTIC CIBCOITS 

Par. 77 holds true oi^ for the eonduetor situated symmertricaUf iritti refpaot 
to the other two. The inductance of the other two wires cannot be cal.- 
culatcd in a simple manner. For practical purposes it is sufficient to take 
the inductance of all three wires as equal to that of a line symmetrically 
spaced, the equivalent apadng being equal to the geometric mean of the three 
actual Bpacings, or 

b^'-^bibtbi. (88) 

81. Vor the •quiTalant reiistanee and raaetuuM of » three-phua 
Una with onaqual ipadngi of wirai see the writer's " MagneUc Circuit", 
Art. 63. In this case the e.m.f. induced in a conductor by the varying mag- 
netic fluxes consists of two components, one being in quadrature, the other 
in phase with the current in the conductor. The first component oorreeponda 
to the inductance of the conductor, the other represents transfer of power 
from one phase to the others.^ In general, those components are different 
for the three conductors, and in order to equalise them for the whole line 
conductors are transposed after a certain number of spans. This tranfpoBl-^ 
tton of conductors is used on power lines (Sec. 11) as well as on telegraph 
and telephone lines (Sec. 21) to reduce the unbalancing effect of mutual m^ 
duction. See also Par. 87 below. The inductance of two or more parallel 
cylinders of any cross-section can be expressed through the so-called geo* 
metric mean distance introduced by Maxwell.* For details also see Oruch» 
" Kapazatit tmd Inductivit&t," pp. 63-74. 

83. Mutual Inductancs. When two independent electric dreuits, 
(1) and (2), are in proximity to each other, their electromagnetic energy may 
be said to consist of three parts: the part due to the linkages of the flux pro- 
duced b^ the circuit (1) with the current in (1); that due to the flux produced 
by the circuit (2) with the current in (2) ; and that due to the current in each 
circuit linking with the flux produced by the other circuit. Employing the 
notation in Par. 87, the total energy of the system is expressed by 

W-iu'L, + iU'Li+<,itLm (joules) (89) 

where Lt and Lt are the coefficients of self-induction of the two circuits, and 
Lm is called the coefficlant of mutual induetanea of the two circuits. 
All three coefficients are measured in henrys. 

84. The ooeffloient of mutual Inductance is also defined from the 
relations: 

■• <f«» •. dii ,«._ 

«i - -^"-Jf , or e» - -i«jj-, (80) 

that is, Lm determines the voltage <i induced in the drcuit ( 1) when the current 
it in circuit (2) varies with the time, and vice 9er$a. 

88. The coefficient of mutual Inductance of two long eoudal 
(ingla-layar colli of the same length I and cross-section A, is 

Z.»,-1.267niniM10-«, (henrys), (91) 

where ni and m are the numbers of turns per centimeter length of the two 
coils respectively; I and A are measured in centimeters. 

85. Tor two long coaxial colli wound in MTarU layers the coefficient 
of mutual inductance is 

I,«-4nitn.>Widiri«(l-(-^-|-|^,) (henrys) (92) 

and if an iron core is present 

I,«-4ni'ni«Wid»-i«[n-(Mr-l)o«+*-(-5^J] (henrys) (93)" 

For explanation of notation see Par. 7t above. See also .the references 
in Par. 74. 

87. Tlia coefficient of mutual inductance of two parallel line 
circuits (Fig. Ila) is given by 

£»> 0.4605 logi>(^^ (millibenrysperkm.) (94) 

where ai and bi are the distances from one of the wires of circuit 1 to the 

* Maxwell,J.C. "Treatise on Electricity and Magnetism," Vol. II, p. 324. 

74 

DigiiizMbjV^iUUyiC 



BLBCTRJC AND MAONBTIC CIRCUITS See. 2-^8 




eonducton of the other circuit, and at ftnd bt 
are the corresponding diatances of the other 
wire of drctiit 1 from the conductors of the 
other circuit. For interference between 
tr&nsmisalon and telephone linei due to 
mutual inductance see Sec. 21. TranBposition 
of telephone lines ia alao explained in Sec. 21. 
tS. Aetoal meMurement must be em- 
ployed in most eases to determine the ooeffi- 
dent of mutual Inductance. See Sec. 3. 



BTBTXE1SI8 AHD XBBT GXrUUHTS 

it. Tike li^steresis loop. When a sample of iron or steel is subjected 
to an altematins macxketisation, the relation between CB and 3C (Par. 49) is 
diffc t en t for increasing and decreasing values of the magnetic intensity (Fig. 
12). This phenomenon may be thought of as due to some kind of friction 
b e tween the molecoles of the magnetic material. Each time the current 
ware eompletee a cycle, the magnetic flux wave must also complete a cycle 
ai^ each molecular magnet be turned through one revolution. This loss 
appcaxa wm heat. The figure AefBcdA in Fig. 12 is called the bystereais loops. 

M. Kete n t t T itj . If the coil shown in ¥lg. 5 be excited with alternating 
cmest, the ampere-tunu and consequently the m.m.f. will, at any instant, 
bepg op Dc ti oiial to the inatantancous value of the exciting current. Plotting 
a O-X or a 4— 7 curve (FSjc- 12) for one cycle, the dosed loop, cdAefB, is 
obcaised. The first time the ut>n ia magnetized the Tirgln or neutral currep 
OA^ win be produced; but it cannot be produced in the reverse direction, 
JO, b e taue e when the mnif. drops to sero there will always be some mag- 
■etism (+0« or — Oc) left. This ia called residual magnetism and in 
onfer to reduce this to aero, an m.m.f. i—Of at +0d) of opposite polarity 
BMMi be i^qiUed. This m.m.f. is called the coerdre force. 

91. Wave dlatortlon. If the instantaneous values of the exdting current 
I (which are directly proportional to the m.m.f.) and ^ are plotted with 
time (Fig. 12) it ia seen that if the coil is connected across a alne-wave e.m.f., 
the cwrent wave will be badly distorted and displaced from the e.m.f. 
wvfe, which ia in time quadrature with the flux wave, as shown at the left 
ia Fig. 12. On the other hand, if the coil is connected in series and the cur- 
rent forced to foUow the sine curve, the flux wave is distorted and displaced 
from tbe enncitt wave, as shown at the right in Fig. 12. 




Fia 12. — Periodic waves of current, flux and e.m.f.; hysteresis loop. 

tl. CompcMienta of axel ting current. The alternating current which 
6e«a IB the exciting coil (Fig. 12) may be considered to consist of two com- 
pcaeato. one exciting magnetiam in the iron, and the other supplying the 
aj *e»g ai a loee^ For practical purpoees both components miur be replaced 
^cqaitraleot sine- waves, and finally by vectors (Fig. 13). We have 

/r ^1 COS tfv power component of the current; 
Fh^IB eo9 0''IrB- hysteresis loss in watte, 
Im^I an tf^mikgDetiaing current. 



75 



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Sec. 2-93 BLBCTtaC AND UAONBTIC CIRCUITS 



£.. 




Flo. 13. — Components 
of exoitinc oun«nt; hy»- 
tentic angle. 



■ Macnetie Cirouit," 



wherein / U the total exciting ourrent and 9 the angle of time-phase diaplaee- 
ment. 

The nutgj lost par orele can be represented by the area, A/Bd, of ths 
loop ; see Par. M below. 

M. Hyftwatle ansla. Without hysteresis, 
the ouirent / would be in phase quadrature with 
B. For this reason the angle a -90— # is called 
th* angla c^ hyitaraUo adranee dl phaia. 
_. I, I,B watts loss , . 

I IB apparent watts 
In praetioe, the measured loss usually includes 
•ddjr currents (Far. M) so that the name "hys- 
teretio" is somewhat of a misnomer. 

•4. Th* anarnr lost par hyataraiU ejd* 
(Ilg. 12) is proportional to the area of the loop, or 

+(B 

Energy -er^SCAO (Joules) (96) 

-» 
wherein V is the volume of the iron, (B and K 
being the coordinates of the loop instead of * and 
S as shown in Fig. 12; and e a constant depend- 
ing upon the scale used. For details see the author's ' 
Art. 18. 

•(. BtsiniiMta'i formtlla. According to exhaustive expeiimenta by 
Dr. C. P. Steinmets, the heat energy, released per cycle per cubio eentimeter 
of iron is approximately 

Jr-lS'«-« (ergs) (97) 

The exponent of (B varies between 1.4 and 1.8 but is generally taken as 
1.6. Values of i; are given in Sec. 4 (see index^. 

96. Power loss par unit wsight. The most oonvenient way to express 
the hystarsais lois is 

' loov 1000 ; 

wherein / is the froqueney in cycles per second; S the maximum 6ux density 
in lines or maxwells per square centimeter, and kk a constant; see Bee. 4. 

9T, Two-tarm fonnuto. Another empirical formula for the hyataraaia 
loiais 

Pt-/(.v'B+^"B') (watU per unit weight) (09) 

where n' and 17" are empirical coefficients. This formula 
is more accurate at medium and high flux densities tbmn 
the preceding one. 

•S. Iddy-oturamt loisat are IVt losses (Par. 27) due 
to secondary currents (Foucault currents) established in 
those parts of the circuit which are interlinked with alter- 
nating or pulsating Suz. Referring to Fig. , 14, a bar- 
shaped conductor is just entering a non-uniform field. 
The advancing side, A, is cutting more lines than the 
trailing side, S, so that there is a difference in potential 
between these two sides and electricity will flow as shown 
by the arrows. The value of the currents, aoeording to 
Ohm's law, is directly proportional to the e.m.f. and in- 
versely proportional to the resistance of the path. The 
e.m.f. is directly proportional to the thickness, (, of the 
bar, but the length of the path, and therefore its resist' 
ance, is but slightly altered by varying the thickness, I. 
Referring to Fig. IS, which shows a cross s e ction of a transformer core, the 
primary current, /, produces the alternating flux, •, which by its change 
generates an «.m.f., «, in the core; thia e.m.f. then seta iq> the leeondaiy 



Pk-ki 



(watts i>er unit weight) (9S) 




Fio. 14. 
Eddy currents. 



76 



dbyv^iuuyie 




BLBCTBIC AND UAQNBTIC CIBCVITS SeC. 2-99 

Now, if the core be divided into two (&), four (e), or n p«it«, 

I total e-inJ. will be ^nersted but the e.m.f. in each ciicuit mil be 

e/2, e/4t e/n respectively, whatever the 

len^h of the circuit, and therefore the 

neutance will not be materially ^tered. 

M. Uaet of lamination. From the 
two examples given above it ia seen that 
the eddy currents can be greatly, reduced 
by laminating the circuit, t,«., by making 
it up of thin sEeets each insulated from tha 
others. The same purpose is aoeompliahed 
by using stranded eonduetors or bundles 
Vta. IS. — Section of trans- of wires. Tha addy-emreBt lou in s 
former core. lunla»t«d iron oor« la 

'•"*"C^^)' (watts per unit waght) (100) 

1 1 ifl the thiekiMss of the laminations in mils; / the frequency in cycles 
per ■eeood, and t, a factor including the specific weight and reristivity of 
tht material. 

Tke determinatioD of valnee of the constant, kn for different materials ia 
treated in Bee. 4 (see index). 

A formula for the loai In eondueton of dreujar Motion, such as wire, ia 

P'-^^^^ (watts per ou. cm.) (101) 

wiieivbi r ia tlie radius of the wire in oentimeten ; / the f reqnenoy in eyelea par 
as e o n d ; a_a ia the maximom flux denai^ in lines per square centimeter 
aad p tha apeeifie reaatanee of the win, i,t., the resistaooe in ohms per 
aisiiliiiM Uii cube. 

A iarmnia for the loaa in slieati is 

wi i a s e ia I ia Uie tidoknsas in oentimetera ; / the frequency in cycles per second ; 
If II is tbe maximnm flux density in lines per square centimeter, and p the 
i U a tific. resiataiice. 

Tbe apeeifie reaistanea of various materials is given in Sec. 4 (see index). 

IM. Baal or obmie raailtenea is the resistance offered by the conductor 
to the paaaage of electricity. Although the specific resistance ia the same for 
eilfaer alternating or continuous current, the total resistance of a wire is 
graater for alternating than for continuous current. This is due to the fact 
that ia a oondaetor which is continuously cut by flux, there are generated 
C-mJa; these e.m.fs. are greater at the centre than at the circumference 
t the potential difference tends to satablish currents which oppose tha 
I eaireut at the centre and assist it at the circumference. The result is, 
tte main eo/rent is forced to the outside thus redudng the effective area 
sf tha oondttctor. This phenomenon is called skin effect (Par. 101). 

Ml. A thaoratieal formnla tor tha ealeulatlon of ikin eSaet is* 

afcsron r is the raaistanee offered to an alternating current; R that offered 
to a eootiBaooB current; / tiie frequency in cycles per second, m the relative 
psnasaMity of the eondnctor and ( the length of the conductor in centimeters. 
It win be noted that 1/5 is proportional to the area of cross se ction of the 
eoodactor; therefore, the skin effect depends upon the area of cross-section 
sf the conductor and the frequency of the current. These should be kept as 
ssasU as poasible, although skin effect seldom cuts any great figure where 
■sderste siaed eonduetors are used to carry current at ordinary frequencies. 
it is ia iron or other magnetio materials, where skin effect becomes really 
iBportant. It must be conadered in riiil returns for alternatingHiurrent 
^Meiu. Skin eifeot tables are given in See. 4 (see index). For a detailed 

■ Msxwdl, J. C. " A Treatise on Electricity and Magnetism," Vol. II, 

" r,,- r.-ii-vA i()( )Ull' 



Sec. 2-102 BLBCTRIC AND MAGNBTIC CHtCUITB 

treatment of resistance to alternating currents and eddy current loeeea tn 
metallic conductors see Louis Cohen, " Formuls and Tables for the Calcu- 
lation of Alternating-current Problems," Chap. I. Numerous tables and 
formuln will be found there, relating to the resistance to alternating currents 
and eddy current losses in solid, hollow and concentric cylindrical conductors^ 
flat conductors, coils and conductors in slots of laminated iron armatures. 

lot. IffectiTe reiiatanee and reactance. When an alternating-current 
<urcuit has appreciable hysteresis, eddy currents and skin effect, it can be 
replaced by an equivalent circuit, without these losses, by using aquiT&lent 
realstancai and aqulTalent reactances (Par. 1S4) in place of the real ones. 
These equivalent or effective quantities are so chosen that the energy rela- 
tions are the same in the equivalent circuit as in the actual one. In a series 
oirouit let the true power lost in ohmio resistance, hysteresis, and eddy 
currents be P, and the reactive (wattless) volt-amperes F^. Then the effec- 
tive, resistance and reactance are determined from the relations 

i*r^/f^P; i*x,ff^P', (104) 

In a parallel drcuSt, with a given voltage, the eauivalent eonductance and 
susoeptance (Par. 16S} are calculated from the r^ations 

eV.//-P; ««fr-//-P'. (106) 

Such equivalent electric quantities which replace the core loss are used in 
the analytical theory of transformers and induction motors, 

101. Core loas. In practical calculations of electrical machinery the 
total core loss is of interest rather than the hyteresis and the eddy currents 
separately. For such computations empirical curves are used, obtained 
from tests on various grades of steel and iron (see Sec. 4). 

104. The uparation of hTitereala from eddy currents. For a 
given sami^le of laminations, the total core lossP, at a constant flux density 
and at variable frequency /, can be represented in the form 

P-a/-f-V» (106) 

where of represents the hysteresis loas and bf* the eddy or Foucault-current 
loss, a and 6 b^n^ two constants. If we write this equation for two known 
frequencies, two simultaneous equations are obtained from which a and 6 
are determined. 

100. Determination of constants. It is convenient to divide the fore> 
going equation by /, because in the form 

^-a+6/ (107) 

it represents the equation of a straight line between {P/f) and /. Havins 
plotted the known values of {P/f) against / as abscissn, the most probable 
Btrai||;ht line is drawn through the points thus obtained. The intersection 
of this line with the axis of ordinates gives a; h is calculated from the pre- 
ceding equation. Knowing a and b, the separate losses are calculated at any 
desired frequency from the expressions of and £/* respectively. 

THX DIXLKCTBIC CIRCXnT 

106. Dielectric flux. When a source of continuous voltage E (Fi^. 16) 
is applied at the terminals of a condenser AB, a quantity of electricity Q 
flows through the connecting wires and the same quantity of electricity 
may be saia to be displaced through the dielectric between the condenaer 
terminals, because electricity behaves like an incompressible fluid. Thia 
displaced electricity in a dielectric is called the dielectric flux and is measured 
in the same units as a quantity of electricity in a conducting circuit; that 
is, in coulombs or in microcoulombs. 

107. The dielectric flux density and the iK>tentiftl gradient. The 
flux density D or the dielectric flux per unit area is D^Q/A when the flux 
distribution is uniform, or D^dQ/dA when the flux distribution is non- 
uniform. In these expressions Q is the dielectric flux and A is the area 
perpendicular to the electrostatic lines of force. Flux density is measured 
in microcoulomba per square centimeter or per square inch. 

The voltage B applied at the terminals of the condenser acts upon the 
whole thickness I of tne dielectric, and the dlalactrlo stress O is characterised 
as the voltage per unit thickness (unit length) of the dielectric in the direction 



SLSCTRIC AND MAONBTIC CIRCUITS Se«. 2-108 



o( the BnM of force. Thoa, in a uniform field, O — S/l, and in a non-uniform 
fMd. 0=-9S/»l. The dielectric itreaa O ta also called the TOltan gntdlmt 
' the el*etne force. It la meuured in volta per inch, IdlovoTts per mm. 



or in other such oonrenient unite. 



m 



"•THHk 



in»= — I 

Kej^ 1 









A- \ 



Oendenaer 



^f^:r. 



—-Q 







Flo. 16. — Circuit oontainins a 
condeiuer. 



In a homogeneous dielectric, the flux 
density D at any point ia proportional 
to the voltage gradient at that point, 
and the ratio of the two characterises 
the material; or. D^^kO, where c is 
called the absolute permittiTlty of 
the dielectric. See Far. Ill and IM. 

IN. Kl^etrofltatie caMdtj (or 
permlttanea). The dispUcement Q 
of electricity through a dielectric is 
proportional to the voltage S applied 
between the terminals (Fig. 16) as long 
as the safe limit of insulation is not 
exceeded; or 

Q~CS (108) 

where the coefficient of proportionality 
C is <»Ued the electrostatic capacity or 

rrmittanoe of the condenser. When 
is in volts and Q in coulombs. C is 
in farads. If Q is in microcoulombs, 
C is in microfarads. 

When the applied voltage is vari- 
able, the precwling equation is writ- 
ten in the form 

" at ^ 31' 

where Q and B are differentiated with respect to time t, and u ia called the 
eharfliis or diiplaeamant current. Either thit equation or the relation 
Q^CB may be considered as the fundamental one denning capacity C. 

IM. Baatanco. The same proportionality between the applied Toltafe 
and the displaoement of eieotricity is sometimes written in the form 

S-SQ, (110) 

where 8 — l/C is called the •lastancc of the rondenser. When £ is in volts 
and Q in coulombs, S is measured in units which the author has termed 
"darafs" (farad spelled backward). When Q Is in microcoulombs, 5 is in 
"megadarafs." 

110. Oondanaan in urlcs and In parallel. When condensers are 
cosneeted in parallel, the equivalent capacity is equal to the sum of all the 
cafiaeities of tne component condensers, or 

C^-ZC. (Ill) 

When two or more condensers are connected in aeries, the equivalent 
capacity is determined from the relation 

J— si- 

Ck C 
Analccoody, for a MrlM connection of clattanoac (Par. 

&,-Z5; 
and for parallel conncotlon of clartanoos 



(1«0) 



IM) 



(112) 



(113) 



,-4 



(114) 



111. For azampla, let two permittances CioO.2 mf. and Ci-0.3 mf. 
be connected in parallel with each other, and in series with a third condenser 
for which Ci — 0.4 mf. To find the total capacity of the combination we not* 
that the combined capacity of the two condensers in parallel is Ci + Ct^O.i 
mf., or the elastance of the combination is two megaaarafs. The elastance 
of the third condenser is I/Ci— 2.5 megadarafs, so that the total elastance 
of the oombination is 2+2.5-4.5 megadarafs. Consequently the equivalent 
capacity is 1/4.5-0.222 mf. This example shows the oonvenience of uainc 
ilastanccs wboi oondenaeis an oonnected in aeries. 



79 



V^iUUVlC 



,y, 



Sec. 2-112 ELBCTRIC AND MAONSTIC CIRCUITS 

lit. The ipadfleindaetlTeoapMttrof »dl*lMtrte(t) iaiha nrtio be- 
tween the capacity of a eondeoaer made entirely of this meleetrie and of u 
identical oondenaer using air for dielectric. It ii also termed tlie dlalaeld* 
eonitant. Another name for spedfio inductive capacity ia relattr* p«r- 
xalttiTltr. For numerical values for varioua dielectrics see See. 4. 

lit. Capacity (parmlttanM) batwean parallel plates. When a 
condenser consists of two parallel plates the distance between which is small 
compared to the dimensions of the platest the lines of electrostatic 'displace- 
ment are nearly straight lioea normal to the adjacent surfaces of the plates. 
The capacity of such a condenser is 



C-(^)j (abstatfarads) (US) 



where A is the area of one of the plates in sq. cm., I the normal distance 
between tliem, in cm. and k/tw tixe JjwnoMmtj ol the dielectric; it is the 
dieleetric constant, which for air is unity. If C is to be in mierofarada. then 
in the preceding formula in place of k/Ar use 

A^J^_0.08842XtX10-« (mf. per centimeter-oube). (118) 

where • is the relooity of light, or the factor required to change from deetro- 
statio to electromagnetic units. 

If instead of talung k/ir as the permittivity, a term kt called the absolute 
permittivity is introduced, then 

C-kA (microfarads) (117) 

I* 
And for air, instead of unity (the relative permittivity), the abaoluta per- 
mittivity is 

«.- 0.08842 X 10-* (mf- per centimeter-eube) (118) 

antf for any other substance the absolute permittivity would be 0.08842 X 
10~*Jb, where k is the specific inductive capacity or the relative permittivity 
of the dielectric; see Par. 111. See also the author's "Electric Circuit, 
Article 51, for further elaboration of this theory of absolute versus relative 
permittivities. At present the accepted method of calculation is baaed on 
the use of formula (US) and (116). 

114. Tha el aata n ea of a dieleetric between two parallel plates a 
short distance apart is 5»r (l/A) where the coefficient # (sigma) is called 
the alastlvlty.of the dlaleetno. If 5 is in megadarafs (1 daraf ia the recip- 
rocal of 1 farad) and the dimensions in centimeters, # is in megadsrafs per 
centimeter cube. Elastance is the reciprocal of permittance, or 8^ 1/C, 
and, likewise, elastivity is the reciprocal of permittivity, or r — 4v/l; 
Therefore 

^-(T)-i-'X "») 

For air, in practical units, 

r - 11.31 X 10* mgd- per centimeter eube. (120) 

Example; to calculate the capacity of a plate condenser (Fig. 16) built ac- 
cording to the following specifications: The metal plates are 60 em. by 70 
cm. each, placed at a normal distance of 0.3 cm. The dielectric consists of 
tliree consecutive layers of insulation, which are 0.12 om., 0.07 cm. and 0.11 
cm. thick. The relative permittivities of the materiab are 2, 3 and 6 raapeist- 
ivelv. Since elaatances are added in series (Far. 110), tha total elaatanoe 
of the condenser is 

S - I11.3X 10«/(S0X70)1I0. 12/2 -fO.07/3 -1-0.11/81 
-0.34X10> mgd. 

Hence the capacity C-5'>-2.B4X10~* mf. 

lis. Capaoity of concantrie cablai. For a single-oonduetor eabla 
with a grounded metal sheath (Fig. 17) the capacity 



„ 0.03882* , , ,, , 

C-, vT-r-, (mf. per mile) or 

logi«(6/a) 

„ 0.02413* , , . . 



(121) 



logi>(Va) 
80 



h, V^3' 



oogle 



BLBCTRtC AND MAONSTIC CIRCUITS SeC. 2-116 

wiMn 1 is the rdative permittivity ot the dielectric (Par. lU). The ume 
formula applies for the capacity or permittance betweea any two concentric 
eylindcra. provided that their axial length ie considerable aa compared to 
thai radii ao that the effect of the enda may be neglected. 

111. Graded inaulmtion. When the insulation between two concentric 
qrlindeii consists of several concentric layer* (Fig. 17), the elaatanc* ot the 



S-<^i-l5.7Sr*i-' loBio(fci/a) +*!-• lo«io(V*i) 

+*>~> locu(i>>/h) +etc.l (megadarafs per mile) (122) 





-^ch 



lEa'r 



Fu. 17. — Concentric cable. Fio. 18. — Concentric cable and lead sheath. 



ti, kt • . • are the relative permittivities of the layers (Par. lU). 
Ths capacity in microfarads per mile is the reciprocal of this expression. 
1%s capacity of a cable is directly proportional to its length, while the elas- 
taaee is inversely proportional to the length. 

IIT. For » liiicle-phaM concentrio cable with a grounded sheath 
(Fig. 18). the capacity between two conductors. Cm, and that between the 

outer conductor and the sheathing, Cw, 
is calculated according to the formula 
given above. Then, if the voltage be- 

f^ \ I >, \ tween the two conductors is £■« and the 

/ Ni j -♦4'*k-\ voltage between the outer conductor and 

/ ^^ ^1 j^^ \ _^^_^ ^^ sheathing is Eu, the charging current 
~\^R 1 ^Wi ^^ at a frequency of / cycles per second is 
\ !*-«*[/ J-2v/(«rtCrt+«rtCw)10-«(amp.),{123) 

if Cat and C>« are expressed in micro- 
farads. 

118. Twin-oonduotor obla with 
grounded sheath. In this case the 
sheath may be replaced by a pair of con- 
ductors located outside, as shown in 
Fif . 10. The spacing, b, of these im- 







aginary conductors being given by the 
relal ' 



Pio. IS. — Twin conductor cable 
•koving electrical image due to the 
Cniuided sheath. 

ilation* 
ba-d* 
and the eapkelti' of s aincl* eonduetor 1* 
0.0 388 2* 
logior2a (d' — at) i 
L r(d«+a«) J 
The capacity per mile of the circuit (two miles of conductor) is one-half 



(mf. per mile). 



(124) 



(12S) 



*I«o Uehtenatein. BUk. Znt. Vol. XXV, pp. 100 and 124 (1904). 



81 



Jgk 






Sec. 2-119 ELECTRIC AND UAONBTIC CIRCUITS 

of the preceding value. The tranavene dimenaions may be either in inchaa 
or in centimeterB because only their ratio enters in the formula. 

llf . A three-conductor cable may I>e treated in a aimilar vay (Fig. 20>- 
The sheath ie replaced by three equally spaced conductors of the same diam- 
eter and spaced according to the relation ba — d'. The eapaeltr of a alncle 
oonduotor is 

^0.07764* 

, r3a«(d»-a«l»i (mf. per mile) C128> 

where the transverse dimensions are injnchee or in centimeters. 

110. The espadtr of a dnsle-phasa tranunlision Iln* per wire, or 
the permittance between one of the wires and the plane of symmetry is 

_ 0.03882 , , ... ,.„_. 

log»(o/a) 
where a is the radius of the wire, and i (he spadns between the oentraa. 
The rapacity between tb^ two conductors is equal to one-half of that given 
by the formula above. For values of charging current atfttandard frequencies 
see tables in Sec. II. 




^ 



£urth 

Fio. 20. — Three-conductor cable; Flo. 21. — Overhead conductor, 

showing electrical images due to the 
grounded aheath. 

ISl. Th« cftpadty of a single orerhead conductor with ground 
return (Fig. 21) U 

0.03882 , , ,, ^ ,,,^^ 

lir. Whan a tingl«-phaM line with metalUe return ii stupondml 
lufflciently near the ground its capacity is somewhat increased. Let 
the wires be suspended at'the heights h\ and At above the |[round; then cal- 
culate the capacity according to formula in Par. ISO, using the corrected 
spacing (see tue author's "Electric Circuit," Art. 61) 

t." ■ - * - -^= (120) 

VI +(0.256) VAi»« 
When the heights of suspension Ai and At are greater than 3.S times the 
spacing b, the difference between 6 and the corrected spacing be is less than 
1 per cent. The correction in formula (117) is still smaller, because 
logarithms of numbers vary more slowly than the numbers themselves. 

In formuUe (128) and (12Q) a perfectly conducting ground is assumed. 
With dry non-conducting earth the increase in capacity is somewhat less. 

US. Capacity of a three-phase line with i^nunetrieal ipaetiiff. 
The concept of the capacity of a three-phase line is not definite without 
further qualificationB. In practice a three-phase line is calculated by re- 
ducing it to an equivalent single-phase line consisting of one of the conductors 
of the three-phase line and a ground return. This equivalent single-phase 
line carries one-third of the total iwwer transmitted by the thrae-phaee Une 

82 

DigilizedbyV^iUUyiL' 



MLBCTBIC AND MAONBTIC CIRCUITS SeC 2-124 ^ 

It t Toitaca S/a/s eonespoDdins to the star voltage of the three-phaae line. A 

For astfa an eqidTaleiit line the capacity ia ezpreaaed by the formula given 
in Par. IM above, where a ia the t^uliua of each wire and b the spacing be- 
tween the wires. This expreaaton for capacity meana that the charging cux^ ^ 
rent per wire calculated from the formula / * 2rfCS/'\/3 checks with that 
actoJly obaerred in each wire of a three-phaae hne when a pure sine-wave 
vokaff B is applied between the wires. For values of charging current see 
■aUniaSeclfr 

IM. With Hk oaayinjiMtTicml ipaolnv let the actual distances between 
th« three pairs of wires be bu bt^ and bi. The capacity can be calculated 
from the above given formula using the MialTklsnt spacing 

b^- ^/SSh! (1301 

(qid to the geometric mean of the actual apacings. For a more detailed 
trcstsient of capacity of three-phase lines with unsymmetrical spacing, 
uBiTmBietrical voltages and the effect of the ground, see the author's " Elec- 
tric Cimrit," Art. 65. For other formule for the capacity of linear oon- 
tetois and eaUea see Cohen, L., "Formula and Tables for the Calcu- 
IstioB rf AltcmatiiiJC Current Problems," Chap. 3. See also Fowle, F. F., 
"The Csleulationot Capacity Coefficients for Parallel Suspended Wires," 
B. World, VoL 58 (1911), pp. 386, 443, and 493. 

lU. A Iiaydan Jar (Fig. 22) may be considered as 
-ijtU- Ur-J '^ co,nbiiUktion of plate condensers. Thus, using the 

' A general formula Par. Ill, iu capacity, 



C-.j-. "'"^^"' (microfarads) (131) 



Irtiff 

I ' Hi where the dimeiuions are in oentimetere and k*- 
l^^l ? 0.08842X10-«i; see Par. 111. 

^^P^l i_ ISft. Permittance of Irrectilar paths. In some 

I cases it is necessary to calculate toe capacity of a 

condenser the dielectric of which ia limited by irregu- 

Fm. 22. — Leyden jar. lar boundaries. The problem is solved either by ex- 

^>eriment or by calculations. In performing the ex- 

tKriment the dielectric is sometimes conveniently replaced by a (>iece of 

■^ of identical shape and with identical terminals. Let the resistance 

of the metal paths be a, the unknown capacity C. the absolute permittivity 

of tbe dielectric Jb« (Par. lU) and the resistivity of the metal p (Par, SO). 

Tkea 

C-^P (132) 

la order to calculate the permittance without any experiment, various 
■msptioBS are made as to the most probable paths of the electroat^tio 
^Bu of force, and of the various assumptions one is selected which fdyea the 
■szinam permittance. For details see the author's "Electric Circuit,'* 
Ana5i-Si 

, Iff. The tomrgf stored in & eondaaser. The potential energy stored 
a s eeadeaaer is 

CS^ Q^ SO 
W - -s" " ^ " 2 * ^^ iowl«« (watt-seconds) (133) 

*^keit the voltace f ia in volts, the electrostatic 6uz (Par. 106) or charge 
9 i^.Melomfaa. and the capacity C in farads. If C is in microfarads and Q 
If is in microjoules. 



Itt. Tha dend^ of electrostatic energy, or the energy stored per unit 
"•■Jat ei the dielectric, is 

yfcgf W is expreesed in microjoules per centimeter cube, ka is the absolute 
ftviOnity oithe dielectric in microooulombs per centimeter cube, and O 
Mtkevolti^ gradient in volts per centimeter length of path; D is the di- 
t^Ktiie ftox density (Par. lOT) in microcoulombs per square centimeter. 
^ total energy of an tiectroetatio field is found by multiplying W* by 

83 LijiizGdbyV^iUuyie 




Sec 2-129 VLBCTRIC AND MAONBTIC CIRCUITS 

an elemeDt of volume dv and inteRratin^ within the desired limita. For an 
interesting comparison of practical pooubilitiea as to the amount of energy 
stored in the dielectric form per unit volume, compared with other fornu of 
energy, see Steinmeti, C. P., General Electric Review, 1013, p. 536. 

Itfl. A uatam of eh&rved bodlea (Fig. 23). The total charvas on 
the Individual conductors are expressed by the equations 

fli-Ciri+Cii(ri-w)+Cii(n-w)+ etc.. 1 (185) 

tfi-Cjtt+Cn(ri — pj)-fC«Cn — »i)4 etc.,/ 
where vi, «i. «t» etc.. are the potentials of these conductors above the ground. 
The coefficients Ci, Ctt Ca, etc., are called the partial eapacltiai of the con- 
ductors; Cis, Cu, etc., are called mutual eapad* 
tlei. Their computation is possible in a few 
simple oases only, but having deterisdned them 
experimentally, it is possible to calculate from the 
preceding equations the resultant or equivalent 
capacity of the system under various operating 
conditions. 

150. Maxwell*! equatlona of a eharved sy»- 
tezn. The same equation may be written in 
Maxweirs form 

fli-iCuti + Jr««+Jri»fi+etc.,l (136) 

tf«— ifiin+#r««+iC«w»+etc., J 
where the coefficients Kn, Xts, etc., are called the 
capacities of the individual conductors, and the 
negative quantities Kn, Kn, etc., are called coeffl- 
olenti of mutual induction. Pi^, 23. System of 

151. Coefflclenta in BCazwell's equations. eharted bodice. 
The following relations bold between the coeffi- 
cients K and C: 

iiTn -Ci+Cit+Cii+eto. ) 

iC«-Cf+Cn+CM+etc. [ (137) 

JCn- -Cu; Kw-Cn, etc. J 

Its. The eleotrottatio energy stored in the field Is 

W~iKiivi* + ^Knvi*-^9to,-\-Kimvi-\-Kainn-\-KtsnH-^eto, (138) 
W is expressed in joules (watt-seconds) if the potentials are in volts and the 
capacities in farads. 

ISS. The dielectric strength of Insulating materials, or the ruptur- 
ing voltage gradient, is the maximum voltage per unit thickness which a 
dielectric can stand in a uniform field, before it breaks down electrically. 
The dielectric strength is usually measured in kilovolts per millimeter or 
per inch. Theonly correct way is to refer the dielectric strength to a uni- 
form field, for instance, between large parallel plates placed at a short die- 
tsnco apart. If the striking voltage is determined between two spheres or 
electroaes of some other shape, the fact should be distinctly stated. In 
designing insulation a factor of safety is assumed depending upon the con* 
ditions of operation. For numeriocU. values of the rupturing voltage gradi- 
ents of various materials see Sec. 4. 

134. The critical dielectric flux density is the density at which the 
material breaks down. It is determined from the relation 

DmMM - 0.08842iW7«4. X lO"*, (139) 

where i>iii«« is the critical density in microcoulombs per square centimetere 
Gm^m is the rupturing voltage gradient in kilovoita per millimeter, and 
Jbis the relative perniittivity of the material (Far. 111). 

ISB. llectrottatic corona. When the electrostatic flux density in the 
ur exceeds a certaiir value, a pale violet light appears near the adjacent 
metal surfaces; this silent discharge is called the electrostatic corona. In 
the regions where the corona appears, the air is electrically broken down, and 
Ionised so that it becomes a conductor of electririt;^. When the voltage is 
raised still higher a brush discharge takes place, until the whole thickness of 
the dielectric is broken down and a disruptive discharge, or spark, jumps 
from one electrode to the other. 

The fonnation of corona leads to power loss which may be serious in some 

84 Dgii.olhy'^iUDyie 



SUtCTRIC AND UAONBTIC CIRCUITS SeC. S-136 

tarn Case See. 11). Moraorer, eorona facilitatm the formation of nitrio 
Mid near the eoadaetor*, and may lead to ooiToaion. When corona ia allowed 
to play OD insulation other than air, thia ioaulation may in time be charred 
aod deteriorated. For these reaaona it ia of importance to know the critical 
▼oltagea of corona formation and the power Ices under varioua confiitione 
of mrfaxea, barometric preaaure, humidity, ete. The problem is atill in a 
research atate. For numerical data in application to tranamiaaion lines aee 
9«e. 1 1; in connection with the design of other hish-tenaion apparatoa, See.IO. 
U(. ■nMrimenti. on enrona. A large amount of experimental and 
titeoretioal information conoermng corona and other allied topics will be found 
in Vola. XXIX, XXX, and XXXT of the Tran$. A. I. E. £. See in particular 
the TsluaUe papers by F. W. Peek, Jr., H. J. Ryan, and J. B. Whitehead, 
snth the accompanying diacuaaion. 

IIT. DiaUetzle hyrtereils and aondnotaaee. When an alternating 
▼nlta^ is applied at the terminals of a condenser, the dielectric is subjected 
to penodie streasea and displacements. If the material were perfectly elastic, 
no energy would be lost duringone complete cycle, because the energy stored 
dming toe periods of increase in voltage would be given up to the circuit 
when the voltage decreased. In reality, the electric elasticity of solid and 
hqnid dielectrics ia not perfect, so that the applied voltage has to overcome 
aonie kind of molecular friction, in addition to the elastic forces. The work 
done against friction ia converted into heat, and is lost, as far as the circuit 
is concerned. Thia phenomenon is similar to magnetic hysteresis (Par. 9t), 
and is therefore called dieUetric hytteremU. The energy lost per cycle is 
proportiona] to the square of the applied voltage, because both the displace 
ment and the stress are proportional to the volta^. 

An imperfect condenser cioes not give out on discharge the full amount of 
ensigy put into it. After having been discharged and stood some time, 
an additional diacharge may be obtained; this is known as absorption in 
tlw dislaetrio. 

An imperfect condenser, that is, one which shows a loss of power from one 
cause or another, can be replaced for pnrpoaes of calculation by a perfect 
ecmienser with an ohnrio conductance shunted around it. This conductance, 
or "leakance," as some authors call it, is selected of such a value that the 
l*R loai in it is equal to the loss of power from all causes in the given imi>erfect 
eondenser. The actual current through the imperfect condenser is considered 
then as consisting of two components — the leadin|C reactive component 
through the ideal condenser, and the loss component, in phase with the volt- 
age, through the shunted conductance. In this way, imperfect condenser* 
can be treated graphically or analytically, according to the ordinary laws of 
the electric dreuit. 

nuiTBixKT cimsnTS ahs toltaoks 

us. Trangient electric phenoniMUt are such as occur between two 
permanent conditions; for instance, when a load is suddenly changed, an 
appreciable time elapses before the generators and the line adapt themselvea 
to the new conditiona, and the currents and the voltages dunng the inter- 
Mediate time are called transient. Some electric phenomena are transient 
m time (for instance, the ahort-<^reuiting of a large alternator) , others are 
transient in space (tlie distribution of altemating current in solid conduo- 
ton), and some are transient both in time and in space (surges and traveling 
waves in long transmission lines). 

in. TI10017 of tranilent phenomena. The subject is too large and 
advanced to Se treated here in detail. An elementary treatment of the 
sabjeet will be' found in W. S. Franklin's "Electric Waves" and in C. P. 
Stemmeta'a "Electric Discharges, Waves and Impulses." Numerous 
formulB and results will be found in Cohen's "Formuln and Tables for the 
Calculation of Alternating-current Problems,** Chaps. 5 and 6. For a more ad- 
vaaeed treatment see J. A. Fleming, "The Propagation of Electric CurrenU;'* 
A. E. Kennelly, '*The Application of Hyperbolic Functions to Electrical 
EngiBeeiing Problems," Cnap. 6 and foil.; C. P. Steinmets, "Transient 
Beetrie Phenomena and Oscillations.*' Numerous articles on the subject 
will be found in the recent volume* of the A. I. E. E., SlektroUckniacha 
ZtUmJiri/t aad Ardutftr BltktnUclmik. 

lit. Oloainf a drcnlt eontaining a reiistance r (ohms) and an indnc^ 
aaee^ (Iwnrj^ in series with a continuous e.m.f. When the de^nergised 






Sec. a-141 BLBCTRIC AND MAONBTIC CIRCUITS 

oirauit u suddenly connected to a source of continuous voltage «, tha ourrent 
gradually rises to the final value to — e/r according to the law 

i-V,(l-.-"'/^. (140) 

where ( U time, and « is the baae of natural (or hyperbolic) logarithms' 
Thi« expression is known as HalnUlolts'fl law. When the source of e.in.f. 
is short- oircuited the current in the remaining circuit decreases to lero ae* 
cording to a similar law 

141. Periodic a.m.f. When a de-energised circuit containing r and L 
is suddenly connected at the instant t»0, to a source of alternating 
Toltage fEm sin (2r/t+ot), the current in the circuit varies according to 
the law 

i-?=! Bin (2»/(+o-*)-^ sin (a-*)."'''/^ <142) 

In this equation s — v r' + (2W/*) » is the impedance of the circuit and ^ is 
the phase displacement between the current and the voltage, determined by 
Um ^»%wfL/T. The angle a is the phase displacement between the volta^ 
and the reference wave which passes through sero at the time t — 0;/ la 
the frequency. The first term in the expression for t is the current corro- 
■ponding to the permanent condition, the second term is a transient which 
rapidly approaches sero with the time. (See also Eq. 14fi.) 

14S. Closing a droiilt containing araslstancs r (ohms) anda capacity 

C (farads) in series. The charging current is theoretically expressed by 

,._,.^"i/(rC)^ • <1*3) 

where u is the ourrent at the first instant. This equation is not api^cable 
to the beginning of the charge because it presupposes a sudden jump of the 
current from sero to ia. In reality, the unavoidable inductance m. the circuit 
smoothes down the initial change in current. 

When a condenser, charged at a voltage Pa, is discharged through resist- 
ance r, the discharge current at the first instant is theoretically equal to 
t* ■" fff/r, and then vanes accordlog to the law 

.■„.-^-</(rO (144) 

The voltage across the condenser terminals decreases according to a similar 
law 

,-«-'/('C) (145) 

When a de-energised circuit containing r and C is suddenly connected at 
the instant /°>0 to a source of alternating voltage e«*£mflin(2iryi-l-a)i the 
ourrent in the circuit will vary according to the law 

i- — «n(2ir/t-|-a+*)-— flin(a+*)«"'^^'^ (146) 

In this equation 2» "N/r* + [1/ (2t/C) 1 ■ is theimpedance of the circuit, and ^ 
is the phase displacement between the current and the voltage, determined 
by cot — 2«-/Cr. The angle a is the phase displacement between the voltage 
e and the reference wave which posses through sero at the time f*=0; / ia 
the frequency. The first term in the expression for i is the current corre- 
sponding to the permanent condition, the second term is a transient which 
rapidly approaches sero with the time. Compare Par. 141. 

14S. Single-energy and double-energy transients. The two pre- 
oeding cases are examples of single-energy transients, because the energy 
is stored in one form only (electromagnetic or electrostatic), and the energy 
change consists in an increase or a decrease of the stored energy. In the 
case of inductance the energy is that of the magnetic field and in the case of 
capacity it is the energy of the electrostatic field. When both inductance 
and capacity are present, the energy of the circuit is stored in two forms, 
and there is a possibility of periodic transformation of the magnetic energy 
into the dielectric energy, and vice vevBa, which constitutes electric oscilu- 
tions, surges* and waves. There is also a possibility of a triple-encrsy 
transient, when for instance a synchronous motor is hunting at the end oxa 
long transmission line which possesses inductance and capacity. In the last 



86 



hy'^TUUyiC 



SLMCTBIC Afro MAONETIC CIRCUITS SeC. 3-144 

cue the total energy of the system U atonid not only in the magnetic and the 
dielectric forms, but in mechanioal form as well. 

IM. Tils gvnaral dlllarential aquktion of % drenit eontalnlnc a 
iwiitaoe* r obau, InduetuiGa L hanrr* uid eapaeity O farads In 
Mrlti, is 

vbere < ia the vcdtage applied to the circuit, and i U time. 

When the impreaaea e.m.f. « is constant (de/cU^O}t two conditions 
may ariw: t*>AL/C and r*<4L/C. The intermediate or critical case 
T*''iL/C 18 of academic interest only. 

lU. Hon-oseillafotT ease. In the fint case ir*>4L/C) the current 
in iht circuit ia non-asciUatory. It rises from sero, reaches a maximum* 
snd fslb axain to lero when the condenser is fully charged; the current never 
reveneg. The voltage across the condenser gradually rises from sero to its 
fall Talue, equal to the applied e.m.f., but never exceeding the latter. During 
the (hseharge both the current and the voltage across the condenser gradually 
decxeaae to zero according to a logarithmic (exponential) law. In practice, 
these conditions are usually harmless, and therefore desirable in cases where 
OKfllationa muat be suppressed. Thia ia usuaily done by increasing the 
Raistanoe of the circuit until the condition r*>^/C is fulfilled. 

IM. OlcUlAtory 0«8«. In the second case, when r*< 4L/C, the charge 
ud also the discharge are oscillatory. The oscillations are of decreasing 
imikKtude, because of the damping caused by the energy consumption in 
Uk tesiatance. When the condenser is charging, the current is 

•sd the Tollase acroee the condenser termlnsb is 

^-cll-.-^/^Ccos^r+J-rfn^*)}. o«) 

For condenser discharge 

,__2^-r'/2L^^ (ISO) 

»d. ' ^ 

-Tt/2Lt q,,T . « 



4 



{'»4« + 5-"4'}- ""' 



!• these eipreesiona q — y/J,AL/C) — r'; < is the applied voltage, and e, ia the 
Tdtsce acroas the condenser at the beginning of the discharge; t ia the base 
of nstuzal logarithms. 

UT. Tha trtaamnef of oaclllatioii and the lofarithmlo doeramant. 
Tk« frequency ol owrillations in the preceding case is 

/— jfV- (cycles per sec.) (152) 

When the xesstance ia negligible, that is, r* small compared with 4L/C, the 
Inqueucy of oecillationa is approximately equal to 

/. ~. (183) 

2tVLC 
I^mithinio doorament. Succesaive half waves of osdllationa de- 
tnssa the more in amplitude, the greater the resistance. The ratio of 
the amplitudes of successive half waves, or the decrement of the oscilla- 
ricB, is ,-'*'/2i' ^here d - !/(?/) is the duration of one-half cycle. 

Mi. Continttotu bteh-l^aqnsney oieiUatlona are conveniently pro- 
teced by mo of n duact-eurrant are (Duddell). In the Poulsen arc, 
tiM soode is c<q>per and the cathode carbon, while the arc is formed in an 
Mooiphere of hydrogen, which appeals to increase considerably the in- 
''■sity of the oaollatlona. Oscillationa have been produced of frequencies 
nugiiig as high as one million per second and of considerable power; they are 

87 

Digili.od by COOgle 






(185) 



Sec. 8-149 SLSCTRic and maonbtic circuits 

■ucoeasfully lued for virelesa telegraphy. See Foulsen, V., "Syitem for 
Producing Continuoua Electric Oxollatioiu," Trant. Int. Eleo. Ck>P«rHW, Ek. 
Louis, 1904, Vol. II, p. 863. Also Austin, L. W., "The Produetioo of Hisb- 
frequenoy Oscillations from the Electric Arc," Bulletin of the Bureau of 
Standards, Vol. Ill (1907), p. 32S. 

149. Stored energy. When a considerable amount of energy is liberated 
at some point on a transmission line, for instance due to an indirect lightning 
stroke, a wave starts along the line carrying this energy to the ends of the 
line. Part of it enters the apparatus at the ends, part is reflected and the 
rest is converted into heat. Generally speaking, tne total energy stonxl ia 
the line, or in some part of it, at an instant is 

W-iU*+iCe', qoules) (1S4) 

where L is the inductance of the line in henrys, t an instantaneous current, C 
the capacity of the line in farads, and < an instantaneous voltage. The term 
}I>t°' represents the electromagnetic energy, the term iCe' the electrostatio 
energy. At certain instants the current is equal to sero, at others the voltage 
is sero, so that the two energies must be equal. Therefore 

?=^-\/?. (ohms) 

Thus, knowing the maximum voltage tm^r, the largest instantaneous eurrent 
i^oM can be calculated, and vice wraa. For instance, in the case of a Ughtning 
stroke, the maximum voltage is limited by the disruptive stren^h of the 
insulation to instantaneous voltages, and the mayimnm eurrent disturbance 
may be calculated from the preceding equation. 

IM. Surge imiradanoe. With oonoentrated indaetanee Mnd 
eapaoity, the (raquenoy of oaolllatloiu Is (Par. 14T) 

With uniformly diatrlbuted tnduetance and capacity, the ftaquaneyla 

The expression s/L/C is called the natural impodanea or the anrn 
Impedance of the line, andats reciprocal the natural admittance or tba 
surge admittance. For further information consult the references in Par. 
in above. 

ALTIRHATINGh-CUUUHT CIECUIT8 

111. Sina-wavM. In this treatment of alternating-current circuita, a 
sine-wave is arbitrarily assumed. For non-sinusoidal currents and v<Mt- 

ages see Par. 190 and follow- 

ing. Beginnini; with non- "I /" "\ „ 

inductive circuits, »'.«., cir- il / \''» 

cuits which contain only .1^ 

resistance, the eurrent at 

any instant is proportional 

to the instantaneous value , , 

of the impressed e.m.f. Plot- 1 i 

ting the i natantaneous values 

of the e.m.f. and the current, 

it is seen. Fig. 24, that the 

waves pass through sero and 

reach their maximum values 

at the same instant. They 

ate said to be In phaM. 

in. Initantaneout 
values. Let the amplitude 
or the instantaneous maxi- 
mum value of the voltage be 
£>ui, then the instantaneous 
value is 




Fia. 



24. — Simple sine-waves; 
circuit. 



non-inductive 



£«u sin 2r/I (158) 

where / is the frequency in cycles per second, and ( is time in seconds. The 



angle 2rft is in radians. 
f-i/T. 



If the time of one complete cycle is T (Fig. 24), 



88 



i.jv^iuuyic 



4 

SLSCTBIC AND UAOlfXTIC CIRCUITS SeC S-153 \ 

111. BuetiT* e.m.f. In a oinnit which containa indnotene* only -^ 

(P>r. IT) the enrrent wave lass by 90 electrical decreea, or a quarter of a 
cjele, beUDd the applied e.mj. Numerically ^ 

E.-2rffJ (159) > 

«hgi> & and / are the root-mean-equare or the effective values (IM) of 
Uk Tottace and the current respectively, L is the inductance in henrys, 
ud/is the frequency in cycles per seoond. A similar relation holds true for 
ti» unpiitodea of voltage and current, or for the average valuea. 

IM. IndaetiT* raaetanee. For the saVe of abbreviation, the expression 
itfii. is denoted by * and is called inductive reactance, so that 

x-2w/L-~ (oiuns) (160) 

If^isin beniya and /in cycles per second, « is in ohms, being equal to the 
ratio of the reactive voltage to the current. If the voltage is expres se d sa 
is ftt. lit, the inatantaneous current is 

• =^ cos 2»/it, (181) 

is othar worda, the cumnt wave lags 90 deg. in phase behind the voltage 

IH. I.iii.f. eomponanti. In a drenit which oontaina raalstuuM 

•ad hidnctaneo in aarlM, one portion of the impressed e.m.f. may be 

_ eonaiaered as consumed in 

^^^^^ __^__„^^ resistance drop and another 

y^^ ^^V ' /Ow «• 1 ^"^ ^^^ counter-e.m.f. of in- 

/VT>^ ^vV^V ' / Jyv\^ I *^"*^^® reactance. The Dux 

// l^? rjiO \\ rTTCrW J interlinked with the circuit is 

// /^^ /hO( \\ !/^>^*V^ y! '" Pi><>** *'*'> ^B current 

44 — I ^^»r?^ ] — L] fy iX \X — y i which prodttoes it. Thee.m.f. 

\\ \ jn J J I y ^^\ir f S^oerated in the reactance is 

W v.C^^ /J I 'VaS*-'^' proportional to the rate of 

\\ IP // I I \ \ //^ chaiage of the flux, and since 

^^i>~-^^ ! -rf^W.^^*^ 1 the rate of change of the flux 

^ -^ lii^l. — ia greatest when the value 

^ passes through sero, the 

^ Flo. 25. — E.m.f. and current wavce in a e.m.f. is in time-quadrati)re 
csremi containing resistance and reactance in with the flux ancl therefore 
series. also in time-quadrature with 

the current (Fig. 26). 
IN. Ssanltant e.in.f. The current is always in phase with the e.m.f. 
vidsfa is oonsumed'in resistaaoe, and the impressed e.m.f. is the resultant of 
the instantaneous values of the components consumed in resistance and in 
the inductive reactance. Referring to Fig. 25, Br is consumed in resistance, 
i% is consumed in overcoming the counter-e.m.f. of Inductive reactance, 
sad £ is the resultant or impressed e.m.f. 

IIT. Phaw ancle. The current is in phase with Sr but lags behind 
the impressed e.ni.f. £ by the phaaa angto ^ determined from the relation 

tan*-?^-.?. (162) 

If the tnstantaDeous applied voltage is expressed as in Par. lit, the in- 
•tantaasons current ia 

»■-/«» stn(2x/il-«) (163) 

when both 2r/l and ^ are expressed either in radians or in degrees. For 
the numerical relation between E and J see Far. lU below. 

IW. Craael^ raaetanaa or oandanauiea. In a circuit which contains 
cleetrcstatie capacity or permittance only. Far. lOS, the current wave 
leads tbs amlied Tcdtase by 90 electrical degrees, or is in leading quadrature 
with it. Numerically 

n.msd (164) 

—^ (ohms) (le.'S) 



89 



DigilizedbyV^iOUyiL' 



> 

> 



Sec 2-159 BLBCTRIC AND MAGNETIC CIRCUITS 

is called cfUMUuty reactance, or condenmve reactance. When inductive 
reactance z (Par. 104) and condenaive reactance x» enter in the same circuit, 
x% i% considered negative. When C ia in farads, xe is in ohms. 

ISf . I.xa.f. components. In a circuit containing resiitance »nd 
condensiT* raaotanco in Mries, the applied e.m.f. may be divided into 
two components; one con- i^, 

Bumed in resistance drop and ^„— i^-t^^-c ' >^ •* 

the other in the condensive /'^(^^'^^^ ' .^^Cir*^ ' 

reactance. The current //A ^ '* r\\ '//?^\ ' 

taken by the condenaive re- // ^c;~^J W ''>/'">OrVv * 

aetance 18 proportional to the // X^A'f'Sl \\ 1 Ex^^ik\\ A 

rate of chan^ of the e.m.f., [ j . P v-\L^j j 1 / f^[ \\ \ ■ Jw 
which is impressed across Jta 1 \ \ J 77 'y^ V\ \I yf h 

terminals, therefore the V\ X..^^/ // r ' v\^^^^/' 

counter-e.m.f, of ^the con- \\ // \ ' XV/^/^ 

densive reactance is in time- ^^''-'--^^l^^^^ ' ■*i0''^\-^ / ' 

quadrature with the current. ^'^ _^^^ J •_• \i/ ' 

Referring to Fig. 28, / is the ^ 

total current in phase with Et 

which is the e.m.f. consumed Fxo. 26. — ^E.m.f. and current waves in a 
in resistance; E% is the volt- circuit contuning renstance and capacity 
age necessary to balance the reactance in series, 
counter-e.m.f. of the con- 
denaive reactance, and E is the total e.m.f. impressed upon the circuit. 
It will be seen that in this case the current is leading. 

If the inatantaneoua applied voltage is expressed as in (1S9), the Instanta- 
neous current is 

i-7»» sin (2x/t+*). (166) 

In this expression, the phftsc angle ^ between the current and the voltage 
is determined from the relation 

160. Termi&oloff7< The following termicology used ia appUcatioD of 
■liie-waT* altamating-eorrant olrcuitt ia recapitulated here for the rake 
of convenience. An lnstant»n«oul Tklu* of alternating current or voltage 
(Fig. 24) is connected with the inaziinum value or the amplitude by 
the relation given in Par. lU. The mean effective value, also called the 
root-mean-iquare value, or simply the effective value of an alternaUns 
current or voltage is defined in Far. IM. For a sine-wave quantity the 
effective value is equal to the amplitude divided by \/2; or 

B.„ -— "---0.7071B.... (168) 

V2 
The mean or averace value of a sinusoidal alternating current or voltage 
ia equal to the maximum value divided by t/2, or 

E.^ - "^"-0.63662Fm«. (169) 

The ratio' between the effective and the average value ia called the form 
factor (Par. SOT) and Is equal to 1.11 for sine-waves. 

161. Periodic time. The interval of time T in Fig. 24. corresponds to 
one complete cycle. The interval of time Tf2 correaponding to one-hsif 
wave ia called an alternation, and for every cycle there are two alternations. 
The frequency or the periodicity of an alternating current may be expressed 
either in cycles per second or in alternations per minute. However, the 
latter method is not common. 

16S. The phase displacement between two currents or two voltages. 
or between a current and a voltage, is commonly meuured in electrical 
degrees. One electrical degree is l/360th part of a complete cycle. 

163. Vector representation. ^ Alternating currents and voltages which 
vary according to the sine or conne law ran be represented graphically by 
directed straight lines railed Tectors (Fig. 27). The length of a vector 
represents, to son^ arbitrary scale, the effective value of the altematiog ' 

90 DigilizedbyV^iUU^ie j 



SLSCTRIC AND UAONBTIC CIRCUITS SeC i-164 



qvantaty, while the position of the vector with respect to s selected refeienoa 
»»etor giTCS the phase displacement. Countrr-clockmM dirtction of rotation 
w almym caiuidtrtd ponlin: so that for instance in the diagram (fc) the volt- 
age leads the current by 90 dcg. By means of vectors the relative phase 
peaition and value of either currents or e.m.fs. can be represented in the 
aame manner as forces in mechanics. 

t«4. Tsctor diagrami for limpla mtIu elreuiti. Referring to Fig. 
Z7, diagnims are shown for circuits containing (o) resistance; (6) inductive 

reactance; (c) condensive re- 
actanoe; Id) resistance and 
inductive reactance; (i) re- 
sistance and condensive ze- 
actance; (/) resistance, in- 
ductive reactance and con- 
densive reactance. 

IM. Obm't law for 
altwnatliic-etirrant dr- 
ouits. The Impedanee (in 
ohms) is the ratio of an 
alternating voltage E across 
a part of a circuit to the 
current I through the circuit. 
Denoting the, impedance by t, 
B-mI, (170) 

where B and / are the effec- 
tive values. This eouation expresses only the numerical relations; it must 
be remembered that B and / are not in phase with one another. 

IH. Iinpsdanca eoluUtInc of resistance and raaotano* in MriM. 
In a circuit containing an ohmic resistance r in series with an inductive 
resctanee x (Par. IM) the impedance is numerically 

s-VTJ-)-T». (171) 

•o that oumerically, 

I- r- (172) 

The phaae aiiKl*> by which the current lags behind the voltage, is found 
from the relatioD 




Fio. 27. — Vector diagram of eunent and 
e.mX; series eireuits. 



tan # — -, or cos ♦ — - 



(173) 



1ST. ImpodaDM eonsiatinc of reaistane* and eondeniane* in lariM. 
In a circuit coDtaining an ohmic resistance r in series with a condensive 
lesetaaee xm (Par. IM), simitar relations hold, in which x* is substituted 
for z. The current leads the voltage and the angle ^ is to be considered as 
negative. 

IH. Impedanea oonsistlnf of resistance, reaetanc* and eondans- 
aaee in swies. If a circuit contain both inductive and condensive reactance 
(Fig. 27/), the impressed e.m.f. is 

«- VjB,« -(-(«.-£.)»- V(/r)»-K/x-/i.)i. (174) 

Dividing ff by J, tlie impedance is 



when 



«-Vr»-)-(»-i.)«. 



(ohms) 
(see Par. IM) 
(see Par. IM) 



(178) 
(176) 
(177) 



IM. Current eomponanti ; parallel eireulti of resistance and react- 
ance. The current, like the e.m.f., can be split into two components, 
one in phase and the other in quadrature with the e.m.f. It is convenient 
to employ the e.m.f. diagram with series circuits and the current diagram 
with parallel circuits. A current diagram is presented in Fig. 28. It pre- 
•uppcees a non-inductive resistance r connected in parallel with a pure 
iadactiva rsaetaoee s. The total ourrsnt 



91 



(wnp.) 



(178) 



dbyV^iUUyiL' 






Sec. a-170 BLBCTRZC AND MAONBTIC CIRCUITS 



If £ is the voltage acron the drooit, then 

I-V(Bg)'+(.Eb)'-B~-Bv 



(amp.) 
(amp.) 
(amp.) 



(ITO) 
(180) 
(181) 



In these expreosiona 



- -^ - oondnotene* 



y_ - >i MllIlittanM 

Ir a ^ I y 
ITO. ftacUtanM and condensuiM In parallel. 



''i^: 



.^- 




*-E 



(mho) (182) 

(mho) (183) 

(mho) (184) 

(186) 

In a circtxit conaatinx 
of a resutance and a capacity in paraller the same relations hold except 
that the current is leading, ana x« is used in place 
of z (Par. IM) . If there is any doubt whether the 
quadrature current is caused Dy an inductance or 
a capacity, use the expresaioDS inductive sus- 
oeptanoe and capacity (or condensive) suscep- 
tanoe. The latter is sometimes called capacl- 
tenee. Fig. 28 also shows, in dotted lines, the 
resultant current when a pure resistance and a 
pure condensance are connected in parallel; in 
such case the phase angle ^ becomes an angle of 
lead. 

ITl, ImpeduxOM In Mriat. In a circuit eon- 
taining several resistances and reactances in series, 
the resistances should be added together and the 
reactances added together, so that 
r^-Zr; 
X n - Sx,- 

«,-V'(Zr)« + (Sl)>. 
The subscript eq stands for equivalent. 

ITS. Impadaaoet cannot be mddad alfabrateaUr, but mnat always 
b« added ceooMttleally, or vectorially. Sinoa 

r—s cos ^, and s—s sin ^, (188) 

the preceding equation gives 

t^ = \/(Zx eoa «)<+(Z« ain ^)<. (189) 

ITS. Admittances In parallel. In a circuit consisting of several parallel 
branches the conductances should be added together and the susoeptanoea 
added together (Par. ItS) so that, 

and 

«"«-V(r«)«+(Z6)«. <191> 

1T4. Admittances cannot be added alcebraleallT, but most alwars 
be added geomatrioally, or vectorially. Since 

ir-v COS ^, and 6 — V sin 0, (182) 

the preceding equation gives 

Vn = Viiu cos ^)'+(Zv sin ♦)'. (193) 

ITS. Squlvalant leriea and parallel eomUnattona. IM r. and x, 

be a resistance and. a reactance connected in series and let r, and Xy be a 



U) 



(186) 
(187) 



Fio. 28. — Vector dia- 
gram of currents; pure 
resistance in parallel 
with pure inductive re- 
actance. 



92 



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BLBCTBIC AND MAONBTIC CIRCUITS SeC 2-176 

leaistanee tad a raaetanoe conneeted in ]>arftllel. The two combin&tioiM are 
ailed equiTalent when a civea impreesed alternatinK voltage produces the 
tuat total eurrent through both, in magnitude and in phase. In other 
vonb, both eombinationa must have the same impedance g (or admittanoe y), 
tad the eame phase angle ^. The two reaistanoes and the two reactancea 



> pbi 
I by 



m coaoeeted by the idatioiu 



rjr. 



-^, 



•Bdalw 



**»-*'-ji: 






C194) 



6 

r.--;, It--;- 

in. OaleolAttoB of ■arlaa-pkrallal dreiiita. The {oracoing relstiona 
■n oieful in detenxdiiing the voltage and current relations obtaining in com- 

plexseriee-paraUeJoircuitfl. For 
_ example, in the circuit shown 

in Fig. 20 the reststanoe r> in 
series with leactance xi is re- 
^t *> _^ plaoed by a conductance^ v 

WW 'WW .B n/n« in parallel with* euaoept- 

ance bi ^ zi/si', where 

»i»-n»+»i«. (195) 
A afanilar substitution is made 
lor the branch 2, then the 
branches 1 and 2 are replaced 
by one equivalent branch o{ 
eondaetance tfgi+m in parallel with the ausceptance fc< — bi+^s. Now 
tke branch g4, &i» ia replaced bjr an equivalent seriee combination consisting 
of a resistance r«—«i/y«* in serie» with a reactano* n — Wv«'> where 

y4«-»4»+k4>. (196) 

Tke original aerim-jparallel combination is thus reduoed to • aimple series 
oiciiit, and we finally have 

Knowing r., and x^t the total eurrent may be found for a given voltage or tic* 
acno, inm the iel*tions given in Par. IM. 

' r ' 



Pio. 29. — Seriee-parallel combination. 





4 
\ 

4 



Fn>. 30. — Circle ^i^F-*"* tor seriee Fio. 31. — Circle diagram for parallel 
dreuita. eircuita. 

ITT. Cinle dUgrun; mtIm dretilti. Drs. F. Bedell and A. C. Crehore 
developed a eirde diacram which shows the interrelation of the various 
constanU ia an altamati&gHnirrent circuit when one or more quantities are 
varied. 



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Sec. 8-178 SLSCTRIC AND MAONBTIC CIRCUITS 

S 

Conridering the series circuit shown in Fig. 30, let it be required to study 
the current when the resistance and reactance are varied, the e.in.f. being 
kept constant. With £ as a diameter draw the circle. 06c, then Obc is the 
e.m.f . or inmedance triangle and 9 is the angte of phase displaoement between 
/ and E. Dividing the current, /, into ima^naiy comiwnents, B/r is laid off 
along OC in phase with E, and E/x is laid on along OA in quadrature with B. 
Drawing the line AC, and the circles, OB A and OBC, the hne, OB, represent* 
the_ current, /, both as to value and phase position. If x is constant ttnd r 
variable, the point. B, will travel along the circle, OBA^ while if r is con- 
stant and X variable, the point, B, will travel along the circle, OBC. 

ITS. Circle dlagrazn; parallel circuits. Referring to the parallel 
circuit in Fig. 31, let it be required to study the e.m.f. when the conductance 
and susceDtance are varied, the current remaining constant. With I aa 
diameter draw the circle Obc, then Obc is the current or admittance tri&nsle 
and d is the angle of phase displacement between E and 7. Dividing the 
e.m.f. into components, I/b is laid off along OA in quadrature with/; then 
drawing the line, AC, and the circles, OB A and OBC, the line, OB, repreaenta 
the e.m.f., B, both as to value and phase position. The circle, OBA, ia the 
locus of the point, B, when b is constant and g variable, while the circle, OBC, 
is the locus of the point, B, when g is constant and b variable. 




FiQ. 32.-^ondensance in parallel 
with inductive impedance. 



Oener- 



Fig. 




33.— Load connected to 
inductive line. 



179. Phase compensation. CondensiTe reactance connected tn 
thunt with an induotlTc impedance can ho so adjusted as to brins the 
total current more or leas in phase with the impressed e.m.f. Referring to 
Fig. 32, Xe and the impedance t, are in parallel, where 



Taking the admittances, 

r 



fa»-r»+x,« 



and 5i= — 



In order that / be in phase vith £, ti -fbi must be equal to lero, or 



(188) 
(109) 

(200) 



ThuSp it is seen that the value of x« depends upon the resistanoet r, aa 
well as upon i.: 

1. - si - Ebv n-gyj(^I-y + (^y-Ey/iJ+bJ, (201) 

^-N(^.)'+ { C4^.)4} '-^^^^'^•"•""'- ^*°^> 

180. Leading current through an Inductive line will ruse the e.m.f. 
at the receiving end of the circuit. Referring to Fig. 33, let B be the voltage 
at the generator end of a circuit, e the voltage at the receiver end, and i the 
line current. Let the load be of such a nature that the current is leading 
with respect to the voltage e. Adding to e the ohmic drop ir in the line 
(Fie. 34a) in phase with i, and the reactive drop I'x in leading quadrature 
with i, the impressed voltage E is obtained. It will be seen thJat £< e; but 
with a lagging current, E>e (Fig. 346). 

181. Series resonance. In a cons tan t^potcntial circuit which contains 
hiductive reactance and also condensive reactance in aeries, it is possibla 



M 



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BLBCTRIC AND UAONBTIC CIBCUITS S«C 8-182 



to obtain an enormous rise in e.m.f. by adjusting the reactances or the 
bequney. Thua, socordins to Par. IM, 

JJ-/»-lVr' + (!.-».)>, (volts) (203) 

Tbe e.in-f. aemas tbe eondenare reactance is 



•Dtkat 



«-/ift 



B Vr«+(«,-a;,y> » 



(804) 





Tm. Ma. — ^Effect of induetaaoe with Flo. 34b. — Effect of inductance with 
leadinc current. lagging current. 

Xov. s (the total impedance) may be less than xm, and in this case e (the 
dinpacroas the condenser terminals) will be greater than E (the total impressed 
Twf ). U the frequency ia 

^~o_ ,-^ (cycle* per second) (205) 



■• shall haTS 

vfculi eooditiona giTes the highest rise in voltage, 
aaee of tbe circuit) is assumed to be xero, 



(206) 
If moreover r (the resist- 



■d we have an extreme case of voltaca raionanM. 
ns* is purely an ideal case, but in any event 



g 



(207) 



(208) 



■ L is the ooeffieient of self-induction in beniys and Cthe capacity in 
fsfl»da of the apparatus connected in series. Sometimes the constants of 
the eirevt arc such that a resonance of one of the higher harmonics of the 
roltage taka place. 

IM. Pandlal rewmanea. When an inductive reactance and a condensive 
rcActaaec an joined together in parallel, they can be so adjusted or the fre- 
r|ii>a ry can be so eboaen that eairent monanee will take place. 

Let the total eonduetanoe of the combination be a, the inductive sus- 
i»Wsiir| b, and the condensive susoeptance b,. Then, the total current 

I<-Bv-Vg*+(.h.-hc)' (209) 

Tht taiieat through the condensive susceptance is 

i.-£j>., (210) 

■>ttat * 

^- ^-•- -»? (211) 



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Sec a-183 BLBCTStC AND UAONETIC CIRCUITS 



But the total admittanoe y may be amaller than &«, and in thia eaaa tiw total 
line current / ia leaa than one of ite component* i«. A ■i*wtUr relation nu^ 
be proved for ti. When the frequency ia 

/"«. .Ai-:? (oyclee per aeoond) (313> 



[U;fonoin that 
and' 



ZwVlC 
6.-i* (213) 

I -Eg, ».--».. (214) 

The line current is comparatively small, but there ia a large intarali«iis« 
'of current between the inductance and the capacity, in parallel. 
h BMonanee can oocur at only on* fr«qaanc7. Sometimes, in the eaas 
of a complex wave, it occurs at the frequency of one of the componant 
harmonics instead of the fundamental frequency. In such case, either for 

voltage or current (series or parallel 
resonance), the macnituda of the reso- 
nant harmonic component is much ezec- 
gerated, as compared with its aormal 
magnitude in a non-resonant oireuit. 
The condition of resonance, except in 
tuned circuits where it is specially de- 
sired (m in radio-telegraphy), is one to 
be avoided. 

IBS. Conaonanee. Reaonanoe in 

the primary circuit of a transformer, 

caused by the proper combination of 

inductance and capacity in the asoond- 

k ary circuit, is called consonance. 

„ _. „ , 184. Alternating curranti »ad 

Fia. 35. — Complex quantities; axes Toltagei treatad b7 meana of oom- 

of reals and imaginariea. pi,x (imaginary) qnantltiea. If « 

and f' (Fig. 36) are the projectiona or 

the components of a vector B along two perpendioular axes, tnsn the veotor 

£ may be represented symbolically aa 

£-«+/«', (216) 

where ___ 

y-V-1, (216) 

and the dot under S signifies that the magnitude as well as the directioa 
of E is meant. 

Let two veoton of Tolt- 




18(. Addition and aubtraetlon of Taoton. 

age be represented as 

JTi-si-H/s't, 

Then the sum or the difFerence of these two veetota ia 
Si - El ± ffj - (ei ± «) +;(e'i ± s't). 
IBS. Botation of a Vector. Multiplying a veetor by / 
00 deg. in the poritive direction (counter-clookwisq). Thus, 

y*-;(«+/«0--«'+*ii 



(217) 
(218) 

(21») 
it by 

(220) 

because j'— —1. Multiplying a veotor by— j rotates the veotor by 90 deg. 
in the negative direction — that is, clockwise. 

A vector S may be also represented symbolically (fig. 35) as 

£-£(coe«+; sin*), (221) 

where E without the dot, on the right^and side of the equation, standa 
for the magnitude only. 
The operator 

c>> - cos ^ +) sin «, (232) 

where • is the base of natural logarithms, turns a veetoc, by the an^ ^ 

in the positive direction. Thus, 

£(cos«+/sin «)-£(cos l+j sin «) (cos t+j sin «)«£[oo* («+*)-(- 

J sin (»+♦). (223) 



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XLECTUC AffD UAONgTIC CIBCVITS SeC S-187 

TfceoptntoT 

W^ -eo* 4 -y iin « (324) 

tanu a vector by the angle ^ in the negative direction, that ia, clockwise. 

UT. Impaduiea and admlttaae* oparaton. Tha ImpadanM 
Qarator 

Z-r+jz (225) 

eoorerta the rector ot a oiimnt into that of a potential difference aeroas an 
impedaoce (conaiating of a reaistance r in setiea rith a reactance *). Tha 
■dnittanea oparator 

r-ff-iJ (226) 

ocaTerla the vector of a voltage applied acroaa the terminals of a conduct- 
BBoe ff in parallel with a susceptance b, into the vector of the total currenl 
through tnia combination. Thus, if a current I^i+ji' flowa through tha 
impedance Z — r+jz, the required voltage is 

«-Z/-(r+>*)(t+i.'), (237) 

«c, separating' the real and the imaginary quantities, 

B-(ir-i'x)+)(,i'T+ix). (228) 

la othar words, £ is a vector such that its horisontal projection e (Fig. 36) 
isMoal to iir~i'x), and the vertical projection is (i'r+iz). 

Tm angle 9 which the vector B forms with the horisontal aiis is detar- 
aoasdhy 

*»»»~7-: — V^' (229) 

(ir-.'i) 

in. Vatworks of oonduetors. The method pven In Par. M to 38 is 
pneraliied in the case of alternating e.m.fB.* by writmglCirohhoff*! equations 
IOC the vectors of the currents and of the voltages. With the notation used 
shove, we have 

Z/-0; ZS-ZIZ. (230) 

EQnatiiia the vertical and the horisontal projections of the vectors to sero 
npsrately (Fig. 35), and using expression (228), equations (230) become 

Zt-0; Zt'-O; 1 

2(»r-»'x)-S«: [ (231) 

2(i'r+»*)-2«'. J 

It thsn an n unknown onrrenta or voltagea, 2n independent aquations of tha 
form (231) may be written, and from theee equations 2n projections of n 
nlmcwn vectors can be determined. The problem is thus similar to that 
vith ^reet currenta, and the references given in Par. Si ma^ be consulted for 
din|>lifieationa which may be taken advantage of in practical cases. * 

_ W. Tha azpraaaloiii for power and powar factor. The avarar* 

power expressed through the projections of the vectors is 

P - n +«'»'- BJ cos «, (232) 

whets ( and e' are the projections of the voltage B (Fig. 85), and i and t' are 
U>cse of the current /. Note that the power is not a vector quantity. 
Xhe power f aotor is found from the relation 

oos « - eos (««- 9i), (233) 



».-tan-« t'/t and *t-tan-> ♦'/». (234) 

Or dse, the angle 4 is found directly from the relation 

tan «-[(«'/«)-«'/0Vll+(«'f7«01 (235) 

If taa # is positive, the current is lagging; otherwise it is leading— with re- 
•Pwtto the f.m.f. See also Par. ISt. 

_*Sm also Campbell, O. A. "Cisoidal OsoilUtions;" IVaiu. A. I. E. E., Vol. 
UX, Mil, pp. 873 to 913. 






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Sec. 2-190 ELECTRIC AND MAGNETIC CIRCUITS 

ifON-8nnr80ioAL or gomplsx watxs 

190. Sxaznples of complex warei. The ouryea ehown in Fis. 36 
illustrate the effect of the inductance aod the capacity in a circuit to which 
ia applied an alternating e.ni.f., differing from the simple sine-waTe. The 
ourres were taken simultaneou^y with an oacillograph. E is the impreased 
e.m.f.; L the current taken by an inductance coil, and /« that taken- by a 
condenser. Fig. 37 shows the circuit. 

191. WftTe of raftctire e.m.f. due to tnductlTe re«ctftnoe. Aseuxnins 

the reluctance of the iron core in 
the inductance coil to be const&nt, 
which ia approximately true below 
the saturation point, the value of 





E 


<— 


N-f« 


,/„ 








/ 


N, 


z1 




kr 




^■^>. 


\ 


\ 


—I^ 


A 




1 V 


\ 


sA W 


J 


^ 




tt^y^ 






r- 


\c 


W V / 


/ 


f 


\ 






/ 




\ 




/' 


/ 


r 






/ 














Fio. 36. — Complex atternatins-ctirreiit 
waves. 



Flo. 37. — Circuit in which the 
waves of Fig. 36 were observed. 



the flux is proportional to the current /.. The instantaneous value of the 
e.m.f. £ (see Par. 67) is 

di .di 

'-"ir-^di 



(236) 



that is, the curve £ will have its maximum amplitude when the curve /. 
passes through sero. This is not exactly true in this case, because of a 
small loss in the resistance and the iron; the current to supply this loas 
being in phase with the e.m.f. E. 

191. Wave of currant through eondanilTa rakCtanoe. The condenser 
current is proportional to the rate of change of the e.m.f. (see Par. lOS) ; 
the instantaneous value is 

. ^« (237) 

" ^df 
that is, the curve, /«, has its maximum when the rate of change of the curve, 
E, is a maximum. Were E a sine curve, / would be also a sine curve and 
would be in quadrature with E, but when the curve of e.m.f. is not a sine 
curve, as in Fig. 36. the maximum amplitude of the current will occur at the 
point where the slope of the e.m.f. curve is a maximum. 

19S. Xflecti of Inductive and condenslve reactance on wave form* 
These curves show the effect upon the current wave form of inductive 
reactance and condenaive reactance. The curve, B, is the wave form 
produced by the generator; it contains several harmonics (see Par. S09). The 
inductive reactance tends to damp out the higher harmonics, while the 
condensive reactance emphasises them. 

19i. Determination of total complex current wave. When the 
applied voltage contains higher harmonics (Par. 809) the total cur- 
rent through an impedance is found by summing the harmonic currents 
due to each harmonic of the voltage acting alone. Thus, the reactance 
at the fundamental frequency ^ is xi — 2t/L, the reactance to the nth 
harmonic is Xi.»2]m/L, and the impedance to the nth harmonic is 

,««Vr«4.(2Tn/£*)*. (238) 

199. Power and energy. The general expression for the energy deliv- 
ered to an alternating-current circuit with any wave form of current and 
voltage is 



\V= I eidt (j 
Jh 



(joules or watt-seconds), (239) 



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ELECTRIC AND MAONETtC CIRCUITS SeC. S-196 

vheia e is aa inst&ntaneoaa valae of the vclitige in rolta, t is the eorra- 
•poiuiiiig instantaneous cumat in amperes undlt — ti'-Tit the interval of 
time, in seconds, for which the energy is to be determined. The average 
power deliTered during the same interval is 

(watts) (240) 

IM. Towwr ttetar, itan-m-m. When the current and the voltage 
vary according to tlie sine law, the power P — IE cos ^, where B and / 
are the effective values of the voltage and the current respectively, and ^ 
is the phase angle hetween the two, cos ^ being known as the power factor 
ot the circuit. See also Far. IW. 

UT. Power factor, eomplaz wavM. When e and i are irrecnlar curves, 
the average poorer is found as the average ordinate of a curve, the ordinates 
of which are proDortional to the product n. If a and i are resolved into their 
barmonJcs, each harmonic contributes its own share of power as If It 
wete acting alone, so that the average power is 

P-*iIi oos^i+ftJi COB «i+eto., (241) 

where 7i, 7i, etc.. and B\,Ei, etc., are the effective values o( the harmonic 
currents and vintages respectively, and the angles ^ are the respective phase 
^splacementa. 

IM. The •nar(T component and the rsaetiTS component of Tolt- 
ace or eurreixt. In a simple harmonic circuit with the voltage £, current 
I, and the pfaas6 displacement < between the two, B cos <p is called the energy 
component of the voltage and £ sin the reactive component of the voltage. 
Analogously. 7 cos 4 is the energy component of the current and 7 sin ^ is 
the reactive component of the current. Similar components are used in 
cireuits with non-einusoidal currents and voltages, provided that these are 
first replaced by equivalent sine-waves. 

199. BTeettro Talae of any ware. The effective value of a variable 
cnrrent or voltage is defined as that continuous value which gives the same 
total iV loss. Or, if / be the effective value of a variable current 1, 

T 

7vr- I ««rd« (joules) 

from which 




(amp.) 



(242) 



TUs may be expressed by saying that the tfftcUtt talue 0/ a eumnt «r tottoffe 
ts^egvof to the uguare root of tht mean aquare (r.m^.) 0/ the variable yaluee. Hot- 
vire instruments and electrod3mamometer-ty]>e instruments indicate directly 
the effective values of alternating currents and voltages. 

100. BfeetiTO Talue of a ilne-waTe. For sine-waves the effective values 
sn given in Par IM. In terms of the maximum value, the effective value 

is JI,/; -0.7071 EmtM. 

Ml. Computation of affecttro valuo of a eomplox wave ; llrtt mothod. 
For irregular waves the following four mothods are used in order to 
obtain the effective value of the ordinates of a curve, y •• /(z). Under the 
first method, plot a curve the ordinates of which are equal to v*- Deter- 
niioe the average ordinate of this curve either by a planimcter or by weigh- 
ing the paper on which it is drawn, and take the square root of the value 
of this onhnate. 

MS. loeond mothod. According to Bitapion'trtllo,* divide the curve 

* Simpson's Rule is a formula for computing the area comprised between 
a ^ven curve, y » /(x) . the axis of abscissv ana two given ordinates. Divide 
the distance between the given ordinates into n equal parts, where n is an 
even aumber, and erect ibe corresponding ordinates. Let these ordinatast 

99 

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Sec. 2-203 ELECTRIC AND MAONSTIC CIRCUITS 

into k equal p»rta by Jb+ 1 equidutsnt ordiiuttM y«, vi> «to., yt, where t ia an 
even number. Then the effeotive value is 

v.// - -T=[v.'+i(]n'+y*+ete.+vt.i')+2(i,'+y,'+ete+»\j+u^]*. 

(243) 
SOS. Third mathod. If the irregular wave » given in terma of ita 

harmonics, then the effective value is 

».//-0.7071V'Ai«+4i«+eto., (2M) 

where Ai, At, etc., are the amplitudes of the separate harmonies. 

S04. Tourth method. Replot the given irregular curve (Fig. 38) in 
polar coordinates (Fig. 39), ana determine the area A^, of the polar curve, 
with a planimeter, or Dy plottinf; on homogeneous paper of known area and 
weight, then cutting out and weighing again; the areas are then proportional 





"l^T- 






3 X 






- ?- t 






i-'tl^' 








\ 






L 


/ 




\ 








n- 




\ 


'\ 








4 S 

180^ — 


10 11 




Flo. 38. — Complex wave in rec- 
tangular coordinates. 



Fio. 391 — Complex wave of Fig. 
38 in polar coordinates. 



to the weights. This area must be expressed in units, v'mun as taken from 
Fig. 38. This is done by multiplying the area, A„ of the polar curve by 

the ratiof — ^m-\ ; y,„ andpxu are meastued in terms of the same units. 

\ Pm.. / 

The mean effective ordinate is 



»•//■ 






intermsof v« 



(245) 



lot. Oeneraliution of fourth method. The latter method has been 
generalised by Mr. C. O. Mailloux for determining the effective value of 
direct current taken by an electric car or a train during a run. For a 
detailed treatment ana numerous practical applications see his paper 
**Methode de Determination du Courant Constant Produisant le M£me 
Echauffement qu'un Courant Variable," in the Transactions of the Intei^ 
national Electrical Congress held at Turin (Italy), 1911. 

S06. The amplitude factor is the ratio of the maximum ordinate to tho 
mean effective ordinate, thus 



Vttf 

tOT. The form factor is the ratio of the mean effective ordinate to the 
mean ordinate, thus 



■amplitude factor. 



- — form factor. 



(246) 



(247) 



including the two given ones, be denoted yo, yi, yi, etc., yn. Then the area of 
tho curve is 

A - }A[yo+4(yi+y«+yi+etc. +y,-i) +2(yi-|-y«-(-y«+etc. +y.-j) -|-y.l, 
where h is the distance between any two adjacent ordinates. The greater 
the number of strips (n), the more nearly the foregoing formula represents 
the area of the given curve. 



100 



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ELECTRIC AND MAONKTIC CIRCUITS SeC. 3-208 



Tlie table in Par. 106 gives the form factor and the amplitude factor 
for Taiioua mathematical curves. 
IM. Table of Tona Tacton and Amplitude Faetori. 



Name. 



Trace. 



Form "??P'~^ Amplitude K«3°«';}. 



factor. 



ReetacKle 




1.00 


1.00 


1.00 


1.00 


Senn-eOipae 


1.04 


0.96 


1.22 


0.82 


Bnunaicte 


1.04 


0.96 


1.22 


0.82 


Semi-eUipm 


J^ ^\ 


1.04 


0.98 


1.22 


0.82 


Sue 


r\ 


1.111 


0.900 


1.414 


0.707 


Tiiaacte 

Inrerae circle or 
utrerae ellipse 


A 


1.15 

1.31 
1.44 


0.87 

0.78 
0.69 


1.73 

2.10 
3.23 


0.68 

0.48 
0.31 



M*. Wam italrtlMi rooiler'i lerlea. In the mathematical treatment 
«( alteniatiiic waves, it is most convenient to work with those having sine 
lona: therefore, thou vatet difffring from th* tint /orm art gtnercUly rffobxd 
%Bfe hdk a funJtnmenlal sine-mve and il> harmonia. The general equation of 
any altematisg wave, as given by Fourier's series, is 
f-risin(«+»i) + riain(2«+»i)+ .... H-r. sin(n<j+«,)+ etc., (248) 

wherein v is the ordinate of the resultant wave; Fi, Y Fm, etc., are 

^c maximiim ordinates of the first, second, . . nth, etc., harmonics; 
#1, fc, . . - f K, the constant angles which determine the relative time- 
phase poation of the corresponding harmonies, and u — 2t/ the angular 
velocity of the generating vector of the fundamental wave. 

tlO. W>T« analyaU; Fiacher-Hinnan'i method. By inspection it 
cmn be said that waves having like loops above and below the time axis 
eontain only odd harmonics, while waves havihg unlike loops above and 
below the axis contain both even and odd harmonics. A direct method of 
wave aaalyais given by J. Fischer-Hinnen* is baaed on the following 
eqnataoDs; 

4m— — (iit+yt+mt +. . . ytn-t—vi—v—vu— ■ ■ ■ in«-«) (249) 



and 



B.--— (»!+»«+»•+ 



. lB».i — H — »i — int — 



in..i) (250) 



wtaeiciB in, n - ■ ■ V* ore ordinates at punts along the base of the half 
wave. wUeb is divided into 2a e><]ual parts, and A, and Bn are the ordinates 
of the ntii harmonics lyin g 90 time-d egrees apart. The maximum ordinate 
of the nth harmonic is VjIu'+B*', and its time phase displacement from 
the resultant wave ia 



tn—itfi' 



•(rk). 



(251) 



'EUl.ZeU., Vol. XXII.p. 396(1901).- Also P. M. Lincoln, Bfec. /our., 
ToL V, p. 286 (1908). 



101 



DigilizedbyV^iOUyiC 



Sec. 2-211 BLSCTRIC AND MAQNETIC CIRCUITS 

9n being measured in terms of the nth harmonic. Assuming time measured to 
the right and ordinates measured up as positive, and quantities tueasured 
in opposite directions as negative, positive values of 0% indicate that the 
nearest intersection of the nth harmonic with the axis is to the right of the 
intersection of the resultant wave with the axis, and positive values of Bm 
indicate that the nth harmonic is rising at its nearest intersection with the 
time axis. The values obtained with the above equations for the nth 
harmonic are afTccted by the harmonics which arc multiples thereof, that is 
2n, 3n, etc. This correction is practically negligible for all harmonics, except 
the first or fundamental, and a correction rarely needs to be carried beyond 
the ninth harmonic. Since wave forms in practice almost never contain 
even harmonics, they do not enter into the correction, and denoting the 
corrected values by prime, we have: 



A'«">X» — A'l« — A'lB — X'Tn- 



(2.52) 



and 

B'.-B,+B'«.-B't.+B'7,- . . . (253) 

When applying this to the first harmonic, Am iB the ordinate of the re> 
Bultant wave at i/o (Fig. 406), and S, is the ordinate 00 time-degrees there- 
from at yt. 





Pio. 40a. — Wave analysis, Par. 211. Fia. 40b. Wave analysis. Par. 211. 

til. Kzunple of w»Te ftiutlTtli. As an example, * assume the wave 
given m Fig. 40a, which is split into three harmomcs; the first or funda- 
mental, the third and the fifth. Fig. 406 shows the method of determining 
a given harmonic, in ttijs case the third. The base of the wave is divided 
into 2n or six equal parts and ordinates erected. Assume the ordinatea to 
measure as follows: 



then, 



and 



tn-676; tn-660; vt-940; v<-1004; Vi-554; w.-0. 



At-Hi/t-jn) 



BfUvi+i/t — v) 



1004-« 



-- 114.7, 



676-I-S54-940 



99.7. 



The maximum ordinate is 



and the phase angle is 



v'(114.7)>-(-(96.7)'-150 



«>' 



. .,/'-114.7\ 



-50deg.t 



(254) 
(25S) 



(256) 



(257) 
(258) 



In a similar manner it is found that Ai— —92.8, and £t — 37.4. In thia 
example the wave contains only the third and the fifth harmonics; therefore, 
the fundamental is determined as follows: 

yll-»»-A'.-A'i-0-114.7-t-92.8--21.9; 

Bi-»«-|-B'i-B'. = 9404-96.7-37.4-998.3; 

»i-tan-"(21.9/999.3) = l deg. 15 min. (approx.) 

• EUc. Jour., Vol. V, p. 386 (1908). 

t Fifty deg. in the terms of the third harmonic, or SO/3 deg. in terms of 
the resultant 



102 



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ELECTRIC AND MAGNETIC CIRCUITS SeC. 2-212 



til. W*!9% maAlysia tablet are available (Publiahed by John Wiley and 
Boca. Inc..') by means of which an irregular wave may be easily analyied 
iaio its h&rmomcfl by taking a sufficient number of ordinatea. For the 
aw of these tablea see the author's "Experimental Electrical EngiiiMiingt*' 
Voiume II, Chapter 31; John Wiley and Sena, New York, 1011. 

POLTPHASI STBTEMB 
SIS. A polypliaae aystem is an alternating-current circuit or network 
to which are applied two or more e.m.fa. of the eame frequency, but dia- 
plaeed in phase by a fixed amount relatively to one another. 



(Wh~^ 






&-1 


^t 






Fia. 41. Fni. 42. Fio. 43. 

Fio. 41. — Symmetrical polyphase e.m.rs. (three-phase system). 
Fia. 42. — Symmetrical polyphase e.in.f'a. (quartei^phase system). 
Tia. 43. — Unsymmetricai polyphase e.m.f's. (two-phase system). 

tl4. S^nunatry of xralypham Byitomi. A polyphase system is called 
eymmetncAl if the applied voltages are eoual and displaced in phase by 
equal amounta. The three-phase system (Fig. 41) and the quarter-phase 
qratem (Fig. 42) are symmetrical systems; the two-phase system (Fig. 43) 
is an ujwymmcirieal system. 

tU. A balanced i>ol7phaaa lyitoin is one in which the sum total of 
the instantaneous power in all the phases is constant (non-pulsatiD^). 
Thai, in a symmetncal three-phase system in which an equal load is applied 
to all the tltfee phases, the power is constant, notwithstanding the fact that 
the power in each phase is puUatin.*:. 





Fio. 44a. — Polyphase star connec- Fzo. 44b. — Polyphase ring connec- 
tion, (ion. 

AM, Balaoea factor. If the total power in a imlyphaae system is pul- 
ating, the system is railed unbalanced; the ratio of the instantaneous 
saiBimum value of power to the maximum value of power is called the 
Vslanee factor of the system. „, . j . , .,^ j , 

tl7. Star and Tiag conneetlona. The two principal methods of 
(Donectinc the separate phases of a polyphase system are the star coo- 
wrtfoo (Tig. 44a), and the ring or mesh connection (Fig. 44b). In a 
irmmetrieal lUpbaae system, with the phases equally loaded, the relation 
btween the star voltases B, and the mesh (or ring) voltages £. (Fig. 4Sa) 
b 

£.-2£.sin— (2S») 



103 



yGoOgk 



SecS-217 JtLBCTRIC AND MAONKTIC CIRCUITS 

I, 




Flo. 45a. — Symmetrical star and Flo. 45b. — Symmetrical star 
hug o.m.fa. and ring currents. 




Fia. 46a. — ^Thiee;-phai!e Y conneo- Fia. 46b. — Three-phase delta oon- 



tion, 




Flo. 48. — Two-phase system; star and ring oonnectiona. 



BLSCTJUC AND MAQlfBTlC CIRCUITS Sec. 2-218 



The reimtion between the star eunents /• uid the mesh cunents Im (Fig, 
4a) U 



Ia-27aaill - 



(260) 



tU. Thr o pli«— T and A eonneetloni. In a thne-phaae ■ystem 
tka star eonneetion is also called the Y-connection (Fie- 46a), and the mesh 
is called the delta ccnneetion (Fif. 4S6). The relations of the currents 
sad the T(dts«ea are (Figs. 47a and 476). 

«. -«rv^ - 1.733«„ and /^ - 7^ - Y.^^2 (261) 




ta. 



Fio. 49. — Two-phase e.m.fs. and currents. 

Tvo-plUM* >tar and rinc eonneetloni. In a two-phasa 
(Us. 48) the relations of the currents and the voltages are (Fig. 49) 

Bm-B. Vi-IAIAB.: '--:;;|=-Y7i4-0"'71Z. (262) 

vhsf* the aabaciipts m and « refer to the mesh and the star respectively • 
(Par. HI) 




Fio. 50. — ^Two-phase three-wire system. 

)Bt. Tw»-plULaa thrae-wlre iritem- ^ith a two-phsse three-wire 

rem (Flc. 60) the current in the common or ratnm wire is v^ times 
eurent in each phase (FSg. fil), and the voltage between the phases is 
Vs timra the Toltace between each phase and the common return. 



105 



i.jv^juuy 



le 



Sec 2-221 ELECTRIC AND MAQNETIC CIRCUITS 

111. PoI]pph>M power. The total power in a syounetrloal n-phmse 
■Titam is given by the formula 

P =• nIS, cos ^ - n7«£. cos 0. (203) 

In an uniymmetrical or unbalanced system the total power is found 
by summing up the power in the separate phases. 

lU. Three-phase power. In a threivphase sjrstem (Us- 46), the power 
i>-3/^i,eos^-3J^£^cos^-7^^V^3 COS « (watts) (2ei> 
if the currents are in amperes and the voltages in volts. 

ISS. Two-phase power. In a quarter-phwe lyttem (Fig. 47) the 
power 

P = iI^,coa4.'=*ImEmcoa*-2V2I^meo»* (watts) (2ft5) 

>M. An equivalent slngle-phue circuit is a circuit which is used in 
computations relating to polyphase transmission lines and macliinery. 
For three-phase circuits some engineers 
use a sinKlo-phaae circuit with a vol- 
tage equal to the Y-voltageof the three- 
phase system, and the power equal to 
that in one phase. _ Others use a single- 
phase circuit having a voltage equal 
to the delta voltage of the three-phase 
circuit, and transmitting the power 
equal to the total power in the three 
phases. Both methods lead to the 
same result, provided that the assump- 
tions are consistently carried out. 

US. Unbalanced polyphase elr- 
oulta are treated as separate single- 
phase. circuits and then combined into 
one. Assuming a three-phase system 
with a line voltage triangle as shown 
in Fig. 52 and an unbalanced load, £i, 
£i and £i, are given. (They form the 



triangle obc.) Constructing semicir- 
cles on Bu Etf and Bt as diameters. 
the e.m.f. triangle for each branch is 
constructed (Par. IBS). We have 
El 




Fio. 51. — E.m.fs. and currents in 
two-phase three-wire system. 



(266) 




Fto. 52. — Unbalanced three-phase system. 

The currents, ti, I'l and u, are in phase with the ir drops in their respective 
branches. These can be conveniently combined by prolonging the ir lines 
until they intersect, and laying off the currents, i, from the inteniectiork. 
The main currents, /i. It and /i. are found by taking the vector sum of ^ho 
branch ciurents, is and tL. is and is, is and ii, respectively. 



106 



, Google 



SLSCTRJC AND UAONETIC CIBCVITS See. 8-226 

tH. Tor fttrthar trsatmmt of the euirent and Toltafa relktioni 
with nnbalanead IomU and unaTmmatrloal TOltac** ooe the last few 
tkaptera, in Dr. Steinmets's " Alternatini^-cuiTent phenomena"; also the 
aaibor's "Experimental Electrical Engineering/' Vol. II, Chapter 25, and 
!us*'Ueber tnehrphaaige Btromsystenie bei ungleichm&ssiger Belastung" 
(Enke, StirttKart, 1900). For the "V" and "T" conneotiona of trana- 
lormers, and for aix-phase eonncctions, see Sec. 6, on transformera. Also see 
See. 11, on Power Transmission, for further treatment of the calculation of 
polyphaae ayatema, and Sec. 12, on Distribution Systems. 

mnFoaxLT dutkibutxd bibistamci, bxactamci, catac- 

ITT AHD LXAKAQK 
SIT. Vnlformljr distributed propartiai. In a truumluion line the 

raristaaee, tbe raactanea, and the eapaelty are uniformly dlitributad. 
- -- .... ^£^, • 



there may be appreciable leakage to the ground or between the 
wiles, which leakage for the purpoeea of computation may also be assumed 
to be uniformly distributed. Under such conditions the current along the 
hne at any certain instant ia di terent in different places; in other words, the 
current ia a function not only .f time ( but also of the distance a from the 
receiver end. 

tU. Continuona impressed e.m.t. For a direet-enrrent line 
paoBcaainc a resistance of r ohms per unit length and a leakage conductance 
of g mhos per unit lenRth, the current and the voltage relations at a distance 
I from tbe receiver end are expressed by the differential equations, 

d*i , dV 

— -rj.. and~-rB.. (2fl7) 

The solution of tbeae equations ia of the form 

»"-^,«-~+il,.~, (208) 

• -«,«-— +Bj.~; (289) 

wher^ m ,> \/rp, and Ai, At, Bi and Bt, are the constants of integration which 
are determined by tbe electrical conditiona at some one point of the line. 

nt. Solntton of eontlnuous-eiUTent ease. The solution of the fore- 
coinc differential equationa is preferably expressed through hnxrbolio 
f tmctiona, * in the form 

i-Ci Cosh ms+Cj Sinh nu; (270) 

e-Di Cosh m*+Dt Sinh nu; (271) 

vbere Cu Ct, Dt, and Ih are the constants of integration which depend upon 
the given conditions at some one point on the line. For example, if the 
raeciver current 7i and the receiver voltage £i are given, the constants have 
the following valuea: 

Ci-/.; C,-Et^; Di-St; Dt-Ii~- (272) 

fn Q 

Tha»» kDowiaic i and < at tbe reeeiver end, th^r values may be calculated for 
tbe adhdiiig end or for any pcriot on the line. For further details see tbe first 
few chapters of A. £. KenneUy's "The Application of Hyperbolic Functions 
to Electrical Engineering Problems." 

AnoitheT form of solution, eznplosring tbe exponential method instead 
of tbe hyperbolic, will be found in the Transttcliona of the A. I. E. E.f for 
1911. where the problem discussed is one of telegraphic transmission over 
looit aerial- wir« circuita by means of the closed-circwt Morse system widely 
■•ed in America. 

* For a simple theory of hyperbolic functions see SeaTcr's "Mathematical 
Backdbook," Sec III; also somewhat more advanced, "Hyperbolic Funo- 
lion«," by McMahcm. The beat tables of hyperbolic functions of real 
hypt-irholic ani^ea are probably those by Becker and van Orstrand, published 
t^ the Smitbaonian Institution. Tables of hyperbolic functions of com- 
plex ancles over a limited range will be found in the above-mentioned book 
Of McMabon, and also in the Otnetal BUctrie Review, Supplement, Mav, 
1010, and in tbe Harvard Bnginterxno Journal, Vol. X, No. 4 and Vol. 11, 



No. 2, A separate reprint of the latter taoles is available. _ ^ *.. „ . 

t F owie, F: F. ••Telegraph Transmission;" Trant. A. I. E. E., 1011. Vol. 

XXX. Fart II, p. 1083. 



Fowie, 

II. p. 1083. 

^^ D,g,l,zedby^^lUUyle 



I 

Sec. S-230 SLBCTRIC ktfD MAONSTie CIRCVITS \ 

no. Altamatlng Imprened e.m.f. Let Bsinc-rnvvalteniatiiisroltaps 
be applied to an equivalent single-phaM line (Far. ISi) with uniformly du. 
tributed characteristics. Let the resistance and the inductive reactance^of 
the line be r ohms and x ohms per unit length, respectively, so that the seiiea 
i mpedance is Z^r+jx ohms per unit length. Let the conaonsive susceptanoe 
ana the leakage conductance be h and g mhos, i)er unit length reepectively,* 
so that the shunted admittance is Y — ^—jb mhos per unit length. The cur> 
rent and the voltage relations at a distance • from the receiver end of the 
Une Are expressed by the differential equaUons 
d'l d'B 

-r^i - an/, and 3-r - WB (273) 

as os» • 

whrre M—-\/YZ. In those expressions /, B and Bf are bomplez Quantities, 
(Far. IM) , and the magnitude and the phase of the current and the voltage 
vary from point to point, remaining at the same time sine functions. In 
other words, the current and the voltage are sine functions of time <, and such 
functions of a as to satisfy the above-given e<iuations. The parameter M 
characterises the line and is independent of either ( or s. The solution ol 
these equations is of the form 

I-/Lji~*^*+A^* (274) 

B-B^t~^'+B^"'• (276) 

where the constants of integration Ai, At, Bi and Bi are complex quantitiea 

These constants are determined by the electrical conditions at some one point 
of the line, for instance, when the current and the voltage at one point are 
given in magnitude and in relative phase position. 
Ml. Solution of altematinc-otiTrent cau. The solution of tho fore- 

foing differential equations is preferably expressed through hjparboUe 
onetioni (Far. 129) of the complex angle M: Namely, 

I-Ci Cosh Af«+C« Sinh Mi; (276) 

S'-Di Cosh Mt+Dt Binh Uf, (277) 

where the complex quantities Ci, Ci, Di, and Dt are the constants of integn^ 
tion which depend upon the given conditions at some one point of the line. 
For example, if the receiver voltage Ei and the receiver current It are given 
in magnitude and in phase (at 8^0) the constants of integration have the 
following values: 

Ci-Iii Ci-Ei -^; Di-Et; Dt-U ^' (278) 

Thus, knowing / and E at the receiver end, their values may be calculated 
for the sending end or a^ any other point on the line. 

131. Heterences to other Utaraturo, For further details and api>Iic»> 
tion of the foregoing equations to power-transmission lines and to the prtip- 
agation of currents in telephone and telegraph lines see C. F. Steinmets. 
**Theory and Calculation of Transient Electric Phenomena and Oscillationa; 
J. A. Fleming, "The Propagation of Electric Currents in Telephone and 
Telegraph Conductors." 

BIBLIOORifHT 

tM. Ovneral rafsrenee llterkton. 

Abnold, E. — "Die Wechselstromteohnik;" S Volumes, Berlin, JuUua 
Springer, 1910-1912. 

Babnstt, S. J. — " Elements of Electromagnetic Theory;" New York, The 
Macmillan Company, 1003. 

Bedelx., F., and Cbehobe, A. — "Alternating Currents;" New York, 
McGraw-Hill Book Co., Inc., 1909. 

Bbnibchke, a. — " Die Wissenschaftlichen Qrundlagen der Blektrt^ 
technik;" Berlin, Julius Springer, 1907. 

Campbell, A. — "The Electron Theory;" Cambridge, University Preoa, 
England, 1913. 

Child, C. D. — "Electric Arcs;" New York, D. Van Noetrand Company, 
1913. 

Cbbistie, C. V. — "Electrical Engineering;" New York, McQraw-HiQ 
Book Company, Inc.; 1913. 

108 L),g,l,zedby^^,UUyHJ 



SLBCTSIC AND UAQNSTIC CIRCUITS SeC 3-233 

CoRur, L. — " tanaxim mad Tsblm for the Caloulation ol Altemating-oui^ 
lant Probleins;" Nov York, McQraw-Hill Book Company, Inc., 1913. 

CaAicr, W. AKD Shith, C. F. — "Vectors and Veotor Diacrami;" New 
York, Loncmans, Green i Company, 1909. 

DmnmoiLiM, C. V. — "The Foundationa of Altemating-ourreat Theory;" 
London, Edward Arnold, 1910. 

Dwiear, H. B. — "Tranamiaaion Una Formulas;" New York, D. Van 
Noatrand Company, 1913. 

EwiNO, J. A. — "The Magnetie Induction in Iron and Other Metals; " Lon- 
don. Elactrieiaa Printing & Pub. Co., Ltd., 1900. 

FLbkiko, J. A. — "The Propagation of Electric Currents;" New York, 
D. Van Noetrand Company, 1911. 

FoaTKB, G. C. AifD PoBTSH, A. W. — " Joubert's Elementary Treatise on 
Beetriei^and Magnetism;" London; Longmans, QreenA Company, New 
York, 1909. 

Fbaitku:;, W. & — ^"Eleotrio Waves;" New York, The MaomiUan Com- 
pav. 1909. 

rnufiasK, W. S., txa WtLUUiaoH, R. B. — " The Elements of Alternating 
Cnrrsnta:" New York, The Maomillan Company, 1904. 

r%t3t*xxs, W. S. xso EsTT, W. — "The Elements of Electrical Engineer- 
■aci" New York. The Macmillan Company, 1906-1907. 

GaBABS, E. — "Electricity and Magnetism;" New York, McGraw-Hill 
Book Company, Inc., 1897. 

Hkatbisb. O. — ^"Electromagnetic Theory," 2 Volumes; London, Elec- 
trician Piinting A Publishing Co, Ltd., 1899. 

Haasoo, J.. Airo Fblsm amh, C. P. — " Die Bereehnung Elektrischer Leit- 
nngsnetaa in Theoiie imd Praxis;" Berlin, Julius Springer, 1905. 

jBAim, J. H. — ^"Mathematical Theory of Electricity and Magnetism;" 
Cambridge, UniTeiaity Press, Endand, 1908. 

Joirae. H. C. — "The Electrical Nature of Matter and Radioactivity;" 
New York, D. Van Noetrand Co., 1911. 

KAMjkrwvorw, V. — " The Eleotrio Circoit; " New York, MeGraw-HUl Book 
Co., Inc., 1912. 

KaaArBTOvr, V^ — "The Magnetic Cirooit;" New York, McGraw-Hill 
BookCo..Ine..l91L 

KsmcBUiT. A. E.— " The Application of Hyperlxdio Functions to Eleo- 
Irical Engineering Problems; " London, University Press, 1912. 

La CooB AND Bbaostad. — "Alternating Currents;" New York, Long- 
mans. Green & Company, 1913. 

Lams, C. G. — ^"Alternating Currents;" London, Edward Amdd, 1906. 

LoDOB, O. — "Modem Views of Electricity;" London, The Macmillan 
Company, 1907. 

Mabcabt, M. E. ars Jocbbbt, J. A.— "A Treatise on Electricity and 
Uagnetiam," 2 Volumes; London, Thoa. De La Rue & Co., 1888. 

1Iazwbu„ J. Clbbk. — "A Treatise on Electricity and Magnetism," 2 
Vdunea; LMidon, Clarendon Press, 1904. 

NiTBBB, F. E. — "Electricity and Magnetism;" St. Louis, Mo., J. L. 
Bolaad Book A Stationery Company, 1895. 

Obucb, E. — ^"KapasitAt und Induktivitftt: " Berlin, C. Viewea, 1909. 

PAITBBaOK, O. W. — ^"Revolving Vectors;'* New York, The Macmillan 
Co.. 1912. 

navBB, H. — ^"Pnaeiplea of Electrical Engineering;" New York, Mc- 
Graw-HiU Book Co.. Inc., 1910-11. 

RsacB, E. — " The Electric Are: " New York, D. V>n Nostrand Co., 1913. 

RoBsBLBB, G. — "Die Femlaitiing von Wechselstrfimen;" Berlin, Julius 
Sprincsr, 1905. 

BrconiBTS, C. P. — "Theoretical Elements of Electrical Engineering:" 
Mew York, McGraw-Hill Book Company, Inc., 1909. 

BiBiBMBn, C. P. — " Theory and Calculation of Alternating-current Phe- 
aomeBa;" New York, McGraw-EDU Book Company, Inc., 1908. 

STBBMBn, C. P. — " Theory and Calculation of Transient Electric Phe- 
aamana and OkcOIations;" New York, McGraw-HiU Book Co.. Inc.. 1911. 

TBOHlutir, A.—" Elaetrieal Engineering ; " New York, Longmans, Green & 

TaoMaoB.J. J. — ^"ElemenU of the Mathematical Theory of Electricity 
sad Magnetism;" New York, D. Van Nostrand Co., 1904. 

TaoaiaoB, J. J. — " Notes on Recent Researohea in Electricity and Mag- 
aMiam;" London. Olanndon Press, 1893. .. , ., u 

WiwiBB. A. O.— " Theory of Electricity and Magnetism;" London, Mao- 
aaaa * Company, 1897. L:,!,.Mb-V,ae)yiC 



I 



yGoogle 



SECTION 3 



MEASXTREMENTS AND MEASURING 
APPARATUS 

BT F. MALCOLM PARMER, M.B. 

Ckuf Bnaineer, Electrical Ttstinff LahoratoriM; FeUmo, American In*tUut4 

of SUetrical Bngineera; Member American Society of Mechanical 

Engineer* 

GEORGE K. BURGESS, SC.D., 

Ciief of the DiwiMion of MetaUurgy, U. S. Bureau of Standards; Member, 

Am. PhjfM. Soc., Fr. Phya. Soc.j Washijigton Acad. Set., Washington 

PhiL Soc, Fellov A. A. A. S.; Author "Meaturement of High 

Temperatitre*,** Etc 

PAUL D. FOOTE, A.M., 

AuiUarU Phj/ticut. U. S. Bureau of Standards; Member Am. Phut. Soe., 
Wathinftm Phil. Soc., Pr. Phj/i. Soc. 



3 



REGINALD J. S. PIGOTT 

Hon Engineer, Tnterborough Rapid T 
American Inttitute of Electrical Engineers 

AND WILLIAM J. DRISKO 



litchanieal CoTiMtruction Bnffineer, Tnterborough Rapid Traruit Co., Member 
I Ini' 



ProfeaMor of Phytice, Mataaehusetia Irtatitute of Technology 

CONTENTS 

{yvmbera refer to Paraoraphs) 

SLBOTUO AHD MAONITIO MXA8UBKHBNT8 

Gcaeral 1 Curve-drawing Instruments 235 

GilTanometcTB 8 Inductance Measurements 240 

CoBtiaaoufl £.in.f. Measurements 42 Capacity Measurements 254 

Alternating £,in.f. Measurements 63 Wave-form Measurements 267 

Continaoua-curront Measurements 82 Frequency Measurements 278 

Altematiog-cnrrent Moasurementa 07 Slip Measurements 283 

Re«stance Meaaurcments 110 Magnetic Meaaureipenta 292 

Power Measurements 149 Bibliography 322 

Energy Measurements 186 

MSOBARICAL POWIR MXASimiMXlTTS 
Torque Meamirements 323 Speed Measurements 333 

TEIBIIOXXTKT, PTBOHXTBT AND HXAT CONDTTCTIVITT 

Thermometry 336 Heat Conductivity 381 

Pynmietry 345 Bibliography 383 

rum. AND OAS ANALYSIS , S8S 
WATER QAB AND STSAM METIBB 
AIB n.OW MEASUBEMENTS 
Vater Ueter* 399 Gas Meters and Air Meters 413 

ntXCUIOR Or^OtASUBBMENTS. 41S 
111 



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SECTION 3 



I 



MEASUREMENTS AND MEASURING APPARATUS 

lUOTUO AMD WAOHZnC MSASTnUHnTTS 
BT r. MALCOLM rABMZB, M.I. 

QBirXBAL 

1. Th« mauuramsnt ot any glv«n qiuntitr ia the eomparisoii of 
that quantity with another quantity of the same kind which hae been choaen 
as a unit. The unit mur be a purely arbitrary quantity with no rational 
significance, such as the foot and the pound, or it majr hare a very definita 
meaning, as the centimeter and the gram. The units used in electrical 
measurements belong to the latter class because they are based on the eanti- 
metar-gram-sacond or C.Q.B. system. The C.G.8. system (Sec. 1) 
is the fundamental system upon which all physical measurements have been 
based, on the theory that all physical phenomena are the result of matter 
and motion, that is, space (centuneteis), mass (grams) and time (seconds). 

t. Mauuremanti clauifled see«rdlnc to pradilon. — Electrical 
measurement may be divided, in a very general way, into three claasea. 
(a) Hlch-praeUion meajurementa, such as those made at the various 
national standardizing laboratories in connection with the establishment 
and maintenance of standards. Every precaution is observed to obtain 
the highest possible degree of accuracy. Expense is a secondary con^dera- 
tion. (b) Commercial Ikborstory meaauramenti, where the object 
is to secure results which are reliable and accurate, but only to the degree 
justified by commercial and engineering requirements. The cost must be 
a minimum, (c) Commercial maaiuramenta are thoee involved in the 
production, distribution and sale of energy. The scope of the subject in 
this section is limited to the last two classes. 

S. A standard is a concrete representation of a unit. The fundamental 
C.Q.S. units are difficult to represent and early-in the development ot the art 
the need for a system of units which could be used in electrical measurement* 
was recognised, and resulted in the establishment of tiie ** practical*' unite 
(see Sec. 1). These units are derived from the fundamental C.G.8. unita 
and can be represented by definite, concrete and reproducible standards. 

The distinction drawn between primary and secondary standards is 
largely a matter of viewpoint. In general, however, primarv standards may 
be considered as thoee which represent directly by definition tne unit involvea, 
such as the mercury ohm, the silver voltameter and the saturated cadmium 
cell, made according to certain specifications. Secondary standards are the 
more practicable working standards which are standardised by comparison 
with primary standards and used as the basis of all ordinary measurements. 
They include, for example, the manganin standard resistances and the ordi- 
nary Weston-type standard cell. Primary standards are, in general, main- 
tained only by the government custodians of the standards in the various 
countries; whereas secondary or working standards, based on these primatv- 
standards. serve as the fundamental basis of practical measurements in engi- 
neering and commercial fields. 

4. The pradalon obtainable in an electrical measurement depends 
upon the various factora which enter into the determination; among these 
are the correctness of the principle employed and the method used, accuracy 
of the standards, number and magnitude of possible erron, correctneaa of 
calculations and so forth. In precision measurements, as classified above, 
a precision of one part in 100,000 in certain classes of measurements is regu- 
larly attained. In commercial measurements, the cost of suoh a high degree 

113 

Digitized by CjOOQIC 



MKA8UR1N0 APPARATUa SeC.S-5 

af preoBon ia not iuatified. The limits, however, an being (radnally niaed 
*■ the ut dSTelopa and Krestar re&nementa are introduced. The table 
aim in Par. • indiestea the precision which may be reasonably expected 
in Tariona elaaaee of measniements made by average obaervera, under onli* 
nary eonditiona, and with standard commercial instruments. 

■. Tabto of Avarac* PraoUlon to be Kzpactad in ▼arlons filititi of 
ComiiMreial Meksurenunta 

Probable 

Qaaa of Measarements and Method precision, 

per cent. 
CDefleetions of two-third scale assumed in indieating instruments) 

Cvrrcnt 

Potentiometer, liich-grade tjrpes 0.03 

Portable ammeter, eontinuons-curtent 0.4 

Portable ammeter, altematingHnirrent 0.5 -1.0* 

Switchboard ammeter, continuous-current 1.5 

Switchboard ammeter, alternating-current 1.0-2.5* 

Raeordinc instruments 1,5 -3,0 

Ptitnlial 

Potentiometer, high-grade type 0.02 

Portable voltmeter, continuous-current 0.26 

Portable voltmeter, alternating-current 0.5-1.5* 

Switchboard voltmeter, continuous-current 1,0 

Switchboard voltmeter, altemating-euTient 1.0-2.5* 

Bceoidins instruments 1,5 -3,0 

ffigh potentials Cin testing of insulators, etc.) 5.0 

P»wer 

Portable wattmeters 1,0 

Labocatory wattmeters (non-portable or semi-portable) 0. 25 

Switchboard wattmeters 2.0 

Becording instruments 2.0 -4 

Kntrty (watt-hour meters) 

Continuous-current 2.5 

AUematinK-eurrent, single-phase, no transformers 2.0 

Altemating-eurrent, single-phase with transformers 2.5 

AJtamatinc-current, polyphase with transformen 3.0 

frmuHcj/ 

rortable instruments 0.5 

Switchboard instruments 1.5 

PMBcr-/ac<or 

Portable instruments (ammeter, voltmeter, wattmeter) 2,0 

Switchboard instruments (above SO per cent.) 1.0 

Switchboard instruments (below 90 percent.) 2.0-4.0 



Mediom: Wheatstone bridge, hi^-giade, 1.0 to 10,000 ohms. 0. 1 
Wheatstone bridge, higb-prade, leas than 1 ohm, 

over 10,000 ohms 0.2-1.0 

Portable bridges 0.5 -2.0 

Low: Fall-of-potential method 0.5 

Thomson double bridge 0.05 

SBgh: (Insulation) 5.0 

CrmdmcHwaw 0.25 

ItagneKe sMosarssMnto 2.5 

t. Olaaaai of erron. There are two general classes of errors in any 
kind of messniements, a, systematic and b, accidental. The former dass 
afltets each result in a series of similar obaervations in the same manner, 
as for example, an error in the standard used. The latter class includes those 
ever wfaieh the obaarver has no control, saeh as observational errors in reading 
aa hidieating instmment. Aoeidental erron, unlike systematic errors, an 
as Skaly to be positive as negative and therefore tend to eliminate tbemselvea 

* Depends upon oapaoity and whether used with instmment transformers. 

S 113 



Sec. 8-7 MEASURING APPARATUS 

from the mean value aa the number of readings is inoreased. Where the 
necessary degree of reliability is not obtained in a single measurement, a 
number of observations are made, from which the most probable true v^ue 
may be obtained, together with its probable error. These latter quantitiea 
may be derived in different degrees of precision by various mathematical 
methods involving the theory of probabilities and the method of least squares. 
In all ordinary electrical measurements it will usually be sufficiently correct 
to assume that the true value is equal to the average of the various values 
obtained (eliminating systematic errors^ plus or minus the average error. 
The average error is the average of the differences between the averaee value 
and each individual value. It should be noted, however, that according to 
the theory of probability, the precision of the result does not increase directly 
but only as tfa^ square root of the number of observations made (see Par. 4M 
toiSS). 

T. Certain (enoral pree&utloiis which should be observed in electrical 
measurements, and certain sources of error which should be avoided, are 
indioated in the following paragraphs. 

(a) The probable limit of accuracy of the standards, instruments 
and methods should be known. 

(b) As a general proposition, in other than rough determinations, one 
measurement should not be relied upon. Several readings should be 
taken, and the conditions should bo altered, wherever possible, in order to 
avoid accidental errors. 

(c) Indicating instruments should be of such a range that the quantity 
under measurement will produce a reasonably largo deflection on the scale. 
The percentage observational error decreases In direct proportion as the 
magnitude of the deflection increases. 

(d) The possible presence of externa] or stray magnetic fields, both 
direet and alternating, should always be borne in mind. Such fields may be 
produced by current in neighboring conductors, or by various classes of 
electrical machinery and apparatus, structural iron and steel in bmldinKa. etc. 
These fields introduce errors by combining with the fields of portable indi- 
cating instruments, galvanometers and other instruments utilising a maf^netic 
field, and, in the cose of alternating fields, by inducing small e.m.fs. in the 
loops formed in bridges, potentiometers, etc, 

(e) In measurements involving high resistances and galvanometers, 
such as bridges and potentiometers, possible "leakage" or ehunb circuits 
should be eliminated. This is done by providing a "ffuard" circuit the 
principle of which is to keep all points to which the current might flow 
improperly, at the same potential as the highest in the apparatus. See 
further discussion under potentiometers (Par. i9 to B2). 

(f) Temperature changes in various parts of bridge, potentiometer and 
similar circuits should be avoided because of thermo e.m.fs. produced at 
the junction of dia^milar metals. Such effects are often produced if the 
observer's hand comes in contact with the metal parts of the galvanometer 
key, switches, etc. 

(g) Instruments with covers made of glass and hard rubber should not be 
rubbed, especially with a dry dust cloth. The induced electrostatic charge 
on the moving element is often sufficient to change the deflection materially. 

(h) At potentials of 500 volts and above, the electrostatic attraction 
between moving and fixed parts may become serious. _ This is prevented by 
keeping the two parts at the same electrostatic potential. When grounding 
is pernusnblc, this can be done by connecting the circuit to earth at the point 
where the instrument is connected, care being taken that the moving-coil 
end of the instrument is on the ground side. In very high potential work 
this electrostatic attraction becomes very troublesome, so that the instru- 
ments must be connected in circuit at a grounded part of the line, or else 
be thoroughly insulated from ground and the moving element connected to 
the case or to an electrostatic shield around the instrument. 

OAITANOMETKSS 
S. QalTanometers are used extensively in all classes of electrical meas- 
urements. Strictly speaking, the term applies to many other instruments for 
measuring current, such as voltmeters and ammeters, but it is ordinarily 
understood to apply to those instruments which axe used to measure very 
small electrical quantities. 

114 n \ 

DglzedbyCjOOgle 



MSASURINO APPARATUS SeC. »-9 

•. Olanaa of fiwmaatUn. There sre two general elaasee: (1) 
moTliic maciMitie needle; (2) mtning coU. In the former clan, . .mall 
bikI {usually) permanent magnet is suspended at the centra of a coil of wire 
throuKh which flows the current to be measured, producing a deBection In 
moniLK coil galvanometers, a coil of relatively fine wire is suspended at the 
centre of a permanent or electromagnetic field; the current to be measured 
Bows through Uiis coil, producing a deflection. Moving-magnet instru- 
;?*"»?.»'*. ™"<'* prominently represented by the Ungent galvanometer and 
the Ivrlvin galvanometer: moving-coil instruments by D'Arsonval and 
etectro-iynamometer type galvanometers. 

». Direct-cmrent tyiwi of gaJTanometen are represented by the 
Vlrf"""*" t »"«*■", Ki'^^nometers, sine galvanometers, the Kelvin type 
I> Arsonval type, balli.itic type, differential Kalvanometers, electrodyna- 
Doroet«r» and electrometers. These are described briefly in the following 
paragraphs. ^ 

11. Tascent ralTanometen. In this instrument the magnetic needle 
IS suspended or pivoted above the centre of a circular scale, over which 
movr-» the pointer attached to the magnet. The coil carrving the current is 
"■ » plane perpendicular to that of the scale, so that the direction of the field 
which It produces is in the plane of the magnet, the earth's magnetic field 
being the direcuog force. The current is approximately 
. Srff tan a 
^^ ^ («n>p.) (1) 

when r — radius of coil in centimeters: H-horiionUl component of earth'* 
feldm gsuasea; n = number of turns in coil; and a - angle of deflection. 

!•- Tlie mine galTanometer is similar to the tangeni galvanometer, the 
eoetntisl diRerenec being that the coil is moved as the needle deflects so 
that they are finally in the same plane. In this instrument, the above 
formula becom^i: 

, SrIT sin o , , 

'- — — (wnp.) (2) 

U. XalTin ralTUiometer (asUUctTpe). In this instrument there are 
two macnetic need es or sets of needles, of slightly dilferent strengths, at 
o|>po«t« ends of a Ught quarts rod and oppositely directed. Each is at the 
centre of a pair of coils through which flows the current to be measured, these 
pairs being oppositely wound so that the moment eierted on the two needles 
IB in the same direction. Thus the moving system is almost, but not quite, 
astatic The controlling force is the earth's field modified as desired by means 
ej a movable permanent magnet. This galvanometer must be calibrated 
against a standard. It is one of the most sensitive types ol galvanometers 
known, instruments with a current sensibility of the order of 1X10"'« am- 
pere* having been built and used in research work. 

M. KovliiK coH or D'Araonval galvanometen consist of a coil of 
me wire suspended between the poica of a permanent horse-shoe magnet. 
The coil is usually suspended by a phosphor-bronio or steel wire, or flat 
strip, which not only conducts the current to the coil but provides the con- 
trolling force. Current is conducted from the coil by a helix of fine wire at 
the bottom. The strength of the field in the region occupied by the coil is 
iaereaaed by xnountin^ a soft iron core in the central space enclosed by the 
eaX, the pole pieces being shaped to give a uniform field throughout the apace 
in which the coil moves. While the D'Arsonval galvanometer cannot readily 
be used to make absolute measurements, but requires calibration, its many 
advant&xcff have made this the most generally used type of galvanometer 
in tlK? electrical laboratory. It is practically independent of the earth's 
6e!d or other external fields; its penod can be made short, which, with its 
dead-beat qualities, makes it a much faster instrument than other types; it 
is comparatively rugged, simple to use and one instrument can be employed 
for a wide range of work. 

U. Ballistic (ralvanometen are used .to measure quantity of electricity 
(coulombs) ; such, for example, as the discharge from a condenser or the in- 
duced charge in a secondary circuit. Ballistic galvanometers may be of the 
moring-magnet or the D'Arsonval type. In order that the instrument may 
be perfectlj balliatic the quantity to be meaaured muat be completely dis- 

Digilizedby^jUUyiC 



( 



Sec. S-16 UBAavRiNQ apparatus 

charged throush it before the suspended system has moved appreoiab^ 
The period, or time of Tibration, must tberdore be long compared with u 
time of discharge. This is accomplished by inenaaing the inertia of tt 
moving system. 

U. Defleotion of balllitlo BalTanometen. The magnitude of tb 
flrtt deflection is a measure of the quantity discharged into the inatrumen* 
In an instrument in which there is no damping (Far. t0) such as the movini 
magnet type, the quantity may be calculated directly from the constant 
of the instrument. Thus 

- 2Ht si n (i)a ,_ , . . ,, 

Q— ^'' (coulomb) (J 

or for small angles, 5 deg. or lesa, 

Q - — -;= — (coulomb) (4 

where Q — quantity of electricity in coulombs, ff — field strength in «ausaei 
G«> constant computed from the ooila, i^ period in seconds, a-* angle o 
deflection. 

IT. Balllstie galTUiomctar constant. In practice, ballistic galv«n 
ometers are usually standardised and the formula becomes very siinple 
Q — kd where d — deflection and Jfc — quantity per unit deflection or Ksiva 
nometer constant. The constant is determined ^ith a standard condense) 
or mutual inductance. The deflection obtained upon suddenly disohargini 
a charged condenser through the galranometer is d — Q — CE; and henoi 
k * CS/df where Q » quantity o f deetrioity in coulombs, S » potential to whid 
the condenser had been charged in volts, and C — capacity of condenser ii 
farada When a mutual inductance is used, the deflection is d-Q — AfZ/li 
and k — MI/dB, where Q • quantity of electncity in coulombs, U <= ooefficien I 
of mutual inductance in henrys, f — steady or Ohm's law value of current ii 
primary of mutual inductance in amperes, and JZ» resistance of seoondat] 
circuit (including the mutual inductance) in ohms. 

18. A differential nlTanometar is one provided with two independen 
coils or sets of coils by means of which two currents may be comparet 
simultaneously. This method provides a means of measuring a current with 
out making the circuit common with that of the comparison standard. Ii 
D'Arsonval instruments, the two coils are wound ride by side on the sanM 
frame and are connected in opposition, so that when the two currents beinj 
compared are adjusted for zero defleotion, their ratio is usually unity. Tbi 
actual ratio can be determined experimentally. 

1>. Ileetromctsn . In the electrometer, a piece of thin aluminium ii 
suspended by a metallic suspension over four quadrants of sheet metal whiol 
are insulated from each other and from the frame or support. Opposite 
<^uadrants are connected to each other and the two sets are connected respec- 
tively to the two sides of the circuit to be measured. If a charge from i 
condenser is placed on the moving vane, one end will be repelled and tlM 
opposite end attracted, producing a deflection which will be a measure ol 
the potential applied to the stationary quadrants. This instrument is ex- 
tremely sensitive, and while it is one of the earliest types of electrical measuT' 
ing instruments it is still used extensively in research work, especially whert 
the available energy is extremely smiji, as in measurements of radian< 
energy. 

M, OalTMtomctan m deteoton . The majority of galvanometers are 
used as detectors only, that is, in sero-defleotion methods where the kind of scale 
or proportionality of deflections doee not enter into the determination. In 
such eases a very short, straight scale is sufficient and space may be eoono- 
mised by placing the galvanometer on the wall above the table, with the 
scale directly underneath. The beam of light is properly directed by 
suitable prisms and mirrors. 

tl. Befleotlng f»lT»noinsten may b^read with a telescoim and seals, 
or with a lamp and scale. In the former, the scale is reflected from the 
plane mirror (attached to the moving system) to the telescope through which 
movements are observed. In the latter, an image of a narrow beam of light 
(issuing from a narrow slit in a vessel enclosiiig a lamp, or from a portion ol 
an isoandescent lamp filament) is thrown on to the scale by the mirror. In 

110 

DigilizedbyGoOgle 



"J ' 






USASUBINO APPARATUS SeC S-22 

orier to pt a aharp imase, either the mirror is raadfl oonoave (with a 1- 
m. focua if the Bcale is the lUiuil diatanoe of 1 m. away), or a leu is uaed. 
Fig. 1 ihowa the general azTangeuient. 

tl. OalTuioinstar tealtt. When readinge are to be taken, car* ibould 
he exerdaed that they are proportional to the angular defleotiona. On a 
•triitht scale the deflection in millimetan is 

d-Atan2a (5) 

vhere A —distance from mirror to scale in millimetres and a— angle through 
vhieh the moving ooil turns. If the angle is small, d is proportional to a. 
The error becomes about O.S per oent. at a — fi deg. Obviously a curved 
scale will elinunate this er- 
ror, and by properly adjust- ^ ^§ 
ing the curvature the read- 
ings may be made propor- 
tioiial to the angle or to any a ^ 
deared function of Uie angle. ^- 

n. The wnalMIlty ot a ' i 
^•Itaaoinatar ia expressed 
la oae of several ways, the 
Boiaerieal expreaaion of 
wUeh is called the (alva- Fia. 1. — Lamp and scale. Telescope and 
■ o m star eonatant. In in- scale, 

stmnents of the D'Arsonval 

type, the sensibility depends upon the moment of inertia of the moving 
•yitem, the torsional moment of the suspension, the field strength, and the 
■umber of turns and the area of the coil. 

St. DtBamtt forma of galTUiometer eonitenU. The various eon- 
itaats are uanatly defined as follows: 

(■) The ampar* eonstent is the current in microamperes (milUonths 
of sn ampere) which will produce 1 mm. deflection on a scale 1 m. 
distant. 

(b) Tbs msKohiu eonstMtt is the number of megohms in series with the 
tsiranometer through which one volt will produce 1 mm. deflection on a 
scale 1 m. distant. 

(c) Tlia Tolt eonatant is the potential in microvolts (millionths of a 
vcit), across the galvanometer terminals which will produce a deflection of 
1 mm. on a scale 1 m. distant. Or it may be expreeaed as the deflection in 
niHimetrra which will be produced by one microvolt. 

(d) Tha coulomb eonatant refera to balliatic galvanometera (Par. IT) 
■ad ia the quantity in microcoulomba (milliontha of a coulomb) which will 
fnxliuje 1 mm. deflection on a scale I m. distant. 

M. nch current lenslbiUty ia desirable for bigh-resiatanee measure 
sMits, such aa insulation reaiatance. High Toltags unilblUty is desir- 
able for measurements involving small potentials, such as low-resiatanca 
bridges, potentiometers, etc. Wffh eonlomb lanalbllity is desirable in 
magnetic tests. 

M. Damping. This term ia applied to thoee forces which collectively 
hriag the moving system to rest aiter it has been set in motion. In order 
to aborten the period and facilitate readinga, damping sometimes is intention- 
sOy produced mechanically with air vanes, or more generally by electrical 
■aeaaa. The latter meana include: (a) uae of a metal frame on which the 
■aoriag coil ia wound and in which eddy currents are produced; (b) uae of a 
doaed loop of copper wire attached to the coil and in which eddy currents 
are ivroduced; (c) use of the generator action of the swinging coil when its 
cimit ia closed. The latter ia the more convenient method for general pur- 
poses, beeaose the damping can be readily changed by means of resistances 
u aerias or ia parallel with the galvanometer. 

tT. Critieal damping is that condition of damping where the moving 
jyatem comes to sero position, or equilibrium, but does not pass through it, 
ia the shortest time alter deflection. A galvanometer is aperiodic when it 
■• critically damped. It ia dead beat when the coil deflects to its final 
Vcatioa or reading without oscillation. 

tt. Tbo period of a (alTanomatar is the time in seconds required for 
cat complete oscillation, or the time between two succea^ve passages through 
the sen or mid-poeition. 



117 Damped b, Google 




Sec. 3-29 MEASURING APPARATUS 

19. OalTuiotneter shunts aro combinations of resistances so arranged 
and BO connected to the galvanometer that the constant of the latter niay be 
quickly changed. Ordinary resistance boxes may be used as shunts for gai- 
vanometers when the resistance of the galvanometer circuit is not too small. 
In the latter case the box is connected as shown in Fig. 2, 
thus increasing the resistance Rg of the galvanometer cir- 
cuit. The readings of the galvanometer must be multi- 
plied by a factor 

wherein R^ is the reaiatanoo of the galvanometer circuit 
and Rt is that of the shunt. In special galvanometer 
Fio, 2.— Galva- shunts, ,, ^ ,> ^ 

nometer shunt. fi,-- ?> '^'y "' » -^ » etc m 

• 9 99 999 9999 "' ^*' 

then Jfc-10, 100. 1,000, 10,000 respectively. 

50. The Asrrton or universal shunt is so arranged that it can be used 

with any galvanometer. When, in Fig. 3, the movable contact x is at b, 
/'b — /rai/Crai+rg), where /'^ — current through galvanometer, /''current 
from battery, r«b» resistance between a and b, and r^ * resistance of galva- 
nometer. If the contact z is moved to c. 

It will be noted that r« is not in this equation; hence if the galvanometer 
constant is obtained with the shunt all in (x at b), the shunt ratio at any 
Other position of x is rae/rab and is independent 
of the galvanometer resistance. 

51. Alternating- current types of galvanom- 
•ters include the following: P^lectrodynamom- 
eters, or, as they are more commonly known, 
dynamometers; vibration galvanometers, ther- 
mogalvano meters, electrostatic galvanometers, al- 




ternating-current detectors, barretters and bolom- «|"*'W*AA^^AA/)j^^^AA^^ 
eters. 

$%, Dynamometer-type instruznents arc 
used extensively in measurements of alternating 
currents because they measure mean effective 

values and can be calibrated on direct current. *:..„ n r- • i ■ 

They can be used for a wide range of measure- '^°- 3— l^mversal gal- 
mento of current, e.m.f. and power, from ex- vanometer shunt, 

tremely small values to very large ones. 

9t, The operative principle of the dynamometer is the electrody- 
namic action between a movable coil (or coils) suapendcd between two or 
more fixed coils, all of which are energized. The Eowland electrodyna- 
mometer* is typical of this clo-is of instruments. It consists simply of two 
fixed coils mounted close together, between which is suspended a small 
coil of very fine wire. Each fixed coil consists of two separate windings of 
difterent current capacities brought out to separate terminals. For e.m.f. 
measurements the moving coil and the fine wire fixed coils are connected in 
series; for current measurements, the moving coil is connected across a non- 
inductive shunt in the current circuit; for power measurements, the moving 
coil is connected across the circuit to be measured while the proper fixed 
coil is connected in series with it. 

S4. Dynamometers are made astatic, or independent of external fields, 
b;^ having two sets of moving coils, oppositely wound, one above the other, 
with a common suspension. There may be one or more pairs of fixed coils. 
In henvy-currcnt in.struments, the fixed coils are wound with cable composed 
of many fine strands laid up in braitled form. This reduces the eddy currents 
which otherwise would bo set up and which would influence the moving coil. 

• Rowland. H. A. "Electrical Measurements by Alternating Currente; " 
Leeds and Nortbrup Catalogue No. 74, 1911; p. 294. 

118 ^ , 

DglzedbyCjOOgle 



MEASURING APPARATUS 



Sec. 8-35 



SS. Vibration c*lvuionieta»* can be used only with alternating our- 
rents. There are two types, the coil and the soft-iron maffnet. In the 
former, the moving clement is a single wire or narrow coil of very fine wire 
suspended between the poles of a permanent magnet. An exceedingly 
small mirror is attached at the centre of the wire or coil. When the naturu 
period of this moving system coincides with that of the current to be measured 
It will resonate and be sensitive to extremely small currents, the indication 
Keing the width of the spot of light on the screen or scale. The instrument 
is " tuned '* or adjusted to resonance by changing the effective length of the 
suspension or its tension. 

In the soft-iron magnet type, a very small piece of soft iron is suspended 
bj a silk fibre between the poles of a pernmnent horse-shoe magnet. Ad- 
iaeent is a coil carrjnng the alternating current to be measured, which pro- 
duces a field perpendicular to that of the permanent magnet. The tempo- 
rarily mAgnetiaed needle vibrates in synchronism with the period of the alter- 
aatiag current and with an amplitude proportional to the strength of the 
mrreot. The effective period of the movmg system is ad- 
justed to resonance, by shunting more or leas of the per- 
ntanent field by means of a movable keeper across the 
limbs of the magnet. Obviously these instruments can be 
■sed only for detector purposca, that is, in sero-method 
measuTpments. such as inductance and capacity measurements 
vithaWheatstone bridge.f They are extremely sensitive, be- 
ing capable of detecting currents of the order of 1X10~' amp. 
and are applicable to frequencies up to 1,000 cycles per sec. 

St. Tharzno-ffalTanometerfl utilise the beating effect of 
sn dectric current and are independent of frequency. They 
can be constructed with practically no inductance or elec- 
trostatic capacity, and are therefore used extensively in 
lugh-frrquency measurements. One of several forms is the 
Doddell type, Fig. 4, in which a moving coil, suspended be- 
tween Uie pole-8 of a permanent magnet as in D'Arsonval 
galvanometerB, includes a bismuth-antimony thermocouplo 
pUud imraodiatcly near an electric heater through which 

ries the current to be measured. The instrument can 
used for a wide range of measurements by changins the 
brater. It can be used on frequencies up to the order of 
100,000 cycles per sec. 

3T. Kl«ctrc»static galTanomatera utilise the force of re- 
polston between two bodies carrying electrostatic charges 
of the same polarity. One or more very thin metal vanes 
■re Buspendeo by a fine wire between two or more stationary 
VM3KS, so shaped (circular discs with opposite quadrants 
eut away) that when excited, the movable vanes swin^ outward from the 
fixed van^ between which they are interleaved. These mstruments require 
BO appreciable current and can be calibrated on direct current, thus pos- 
Kssing characteristics which make them valuable for measuring e.m.fs. 
^lere the current capacity is very small or nil. 

n. Altematlnff-cuiTcnt detectors. Other methods of determining the 
rendition of balance in sero-method alternating-current measurements are 
shown in Figs. 5 and 6. The former indicates the scheme of a synchronouB 
conanntator. t A commutator, C, and two slip-rings, r and r>, are mounted 
oo the sluft of a small synchronous motor. The bars in the commutator are 
RMTow, and equal in number to the poles of the motor and equally spaced. 
Two brushes, a, a<, connected to the galvanometer arc so spaced as to bridge 
two ban simultaneously. These brushes are mounted on a disc which can 
be rotated about the shaft. The bars are connected alternately to the two 




Pio. 4.— 
Dudell thei^ 
mo-galva- 
nometer. 



' Wenner, F. "Characteristics and Applications of Vibration Galvan- 
ometers;" Traju. A. I. £. E.. 1912, Vol. XXXI, p. 1343 

t Roea, E. B- and Grover. F. W. "Measurement of Inductance by Ander- 
■oa's Method Using Alternating Current and a Vibration Galvanometer;" 
Buresa of Standards Bulletin No. 3. 1905, p. 201. 

I See sIao Frederick Bedell, "Use of Synchronous Commutators in Alter- 
nating-current Measurements;" Jour. Franklin InttUtUe, Oct.. 1913, p. 386. 



119 



ibyv^iuuyie 



Sec. S-39 



MSASVniNO APPARATVa 



» 



rings which in turn are connected through the brushes, b, b\ to the al tempting 
current being measured. It is apparent that the connections to the eskl- 
vanometer are reversed every half cycle, so that the Indication is a steady ooe, 
the value of which may be made anything from sero to a maximum by shift- 
ing the angular position of the brushes. Thus the most sensitive i>oaition 
can be reauly found, irrespective of the phase relation between the current 
in the circuit being measured and the motor armature. The variation, in 
contact resistance at high speeds, and possible presence of thermo e.m.fa., 
may cause trouble where the resiatanoes or potentials are very low, «s in 
low-resistanoe bridge mMiorcmcnts.* 




Fia. 5. — Synchronous commutator. 



99. A ■ynchronous roTdrainc kty which overcomes the latter difficulty 
is indicated in Fig. 6. A cam, C, mounted on the shaft of a small synobrooous 
motor is so designed that it moves the lever, I, up and down in suob a maniur 
tii&t the pair of contacts, a and a*, at the end of the lever make alternate ooi>- 
taet with the pairs of stationary contacts, e and e^, once per evole. The num- 
ber of projections on the cam of course will correspond with the number o£ 
pairs of poles on the motor. The contacts are arranged as shown diagram- 
matically at the right of Fig. 6, from which it will be seen that the connectiona 
to the ^Ivanometer are reversed every half cycle, so that a steady deflection 
is obtained in the direct-current galvanometer. All the contacts are aup- 





'-0-' 



Fia. 6. — Synchronoua reveramg key. 



ported on a solid disc which can be rotated around the shaft, and hence re- 
versal can be made at any point on the wave as in the case of the synchronoua 
commutator. The contacts are all made of platinum, the cam is hardened 
steel and the lever I is kept in contact with the cam at all times by means of 
a spring. The roller r is necessary to insure contact at the low portion of 
the cam. 

* Sharp, C. H. and Crawford, W. W. "Some Recent Developments in 
Exact Alternating-current Measurements;" IVans. A. I. E. E., 1910, Vol. 



XXIX, p. 1618. 



120 



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MBASVSINa APPARATUS Sec. S-40 

M. A bsnatar * is a bridge arraogement (Par. 141) in whioh the change in 
leutanee with the passage of current of a high temperature coefiSdent wire 
ii utilised to measure currents of telephone magnitude and frequency. 

41. A bolometar is an instrument devised by Prof. 8. P. Langley with 
■Uefa extremely small temperature changes (order of OXWOl deg. fahr.) 
oiay be measured. A very thin strip of platinum or other metal is exposed 
to the radiation from the source being measured. This strip forms the 
snn of a balanced Wheatstone bridge and the change in resistance cone- 
ling to the change in temperature is indicated oy the galvanometer 



COKTIin;OirS-K.M.F. kxasttkbmehtb 

41. Stemdmrda of •.m.t. The legal unit of e.m.f. in the United States 
is the intarmtloiial volt sdopted by Act of Congress in 1894: in practice 
the prefix is generally omitted. This unit is the e.m.f. which, when applied 
to a oooductor having a resistance of one intenuitional ohm, will produce a 
current of one international ampere. The Act also states that the volt 
"is repreaented sufficiently well for practical use by 1000/1434ths of the 
c.m.f. Detween the poles or electrodes of the voltaic oell known as Clark's cell 
St a temperatoie o« IS deg. cent, and prepared in the manner described in 
the aceompanyinc specificaUott." The (^rk cell has since been superseded 
by the Wi»to& oell as the standard of e.m.f. The value of the latter as 
sdopted by the Bureau of Standards, Jan. 1, 1911 is 1.0183 at 20 deg. cent., 
which is now the standard of e.m.f. m this country. 

4t. TIta Clark eall was the. first form of voltaic cell to meet the require- 
aients of a reliable standard of e.m.f., namely, reproducibility and reasonable 
ixnnanenae. The elements are: positive electrode, metallio meroury; 
segstive electrode, amalgamated sine; electrolyte, saturated solution of sino 
•olphate and mercurous sulphate. Its e.m.f. in terms of fundamental or 
egjs. units was originally t^en as 1.434 international volts at 16 deg. oent., 
the value having been made legal in 1894 as stated above. Later and more 
careful detcnninations have shown, however, that 1.4328 is a more oorreot 
tgore. The e.in.f. of the Clark cell changes with temperature in accordance 
mh the formula: 

«-1.4328[l-0.00077«° C.-15)] (9) 

«h«e B~ international volts at any temperature, t deg. cent. 

44. Oblaetloiia to Clark cell. As the electrical art developed and mors 
VKose workine atandarda became necessary, the defects in the Clark cell 
«ere noted. The most conspicuous of these are large temperature ooefficient, 
luge temperature lag and difficulty in obtaining the temperature. This eell 
kss therefore been superseded by the Weston cells, which are practically free 
Inm these objections. 

41. Wsaton ealla.t There are two forms of Weston oells, the aaturatsd 
asO and the nsastarktsd call. The elements are: positive electrode, 
metallie mercu r y; negative electrode, amalgamated cadmium; electrolyte, 
•obitioa of eadminm sulphate and mercurous sulphate. 

44. Waston monnal call. In this eell the electrolyte is saturated. 
This form ia the official standard because it is more permanent and can be 
nnodneed srith greater accuracy than when the electrolyte is unsaturated, 
whea carefulty made according to the official specifications, cells will agree 
with each other within a few parts in 100.000. The e.m.f. changes slightly 
*ith temperature according to the following formula: 

jr-1.0183{l-0.000041«'C.-20)J (10) 

where X— international volts at any temperature, ( deg. cent. 

4T. Th* OBHitarated WMton eell, on the other hand, has practically 
no tenpeistnre coefficient (0.00001 per deg. cent.). Although it is not so 
nSaUe as a fundamental standard as the Weston normal cell, and each cell 
hss to be standardised, it is. nevertheless, more convenient for general use. 
This is the form furnished by the Weston Electrical Instrument Co. The 
I recommend that these oells be not subjected to temperatures below- 



*CV)hen and Shapard. "Telephone Transmission Measurements," Jaw. 
last B. E., 1907, Vrf. XXXIV, p. 603. 
t Bee (Snular No. 29, Bureau of Standards, 1910. 



121 Digilized by Google 



Sec. 3-48 MEASURING APPARATUS 

4 deg. cent, or above 40 dcg. cent., and that no current greater than 0.0001 
amp. be paued through them. 

48. ComparUonji of continuous electromotive forces with a stand- 
ard cell. Electromotive forces may be oomparrd with a standard cell by 
several methods. The more typical methods are baaed on the following 
principles. 

(a) In the subititution method, the current flowing through a high 
resistance (not less than 15,000 ohms) is measured with a hiah-senaibility 
galvanometer, first with the standard cell In the circuit and then with the 
unknown e.m.f. substituted for thp standard cell. The resistance being the 
same in the two oases, the deflec^ons are proportional to the e.m.fB. E -• od'/d, 
where £*"UDknown e.m.f., f = standard cell e.m.f.. d^dedecUoa with 
standard cell and d' = deflection with unknown e.m.f. 

(b) The equal deflection method is a modification of the above, in 
wmch the deflections are kept the same in the two cases by changing the 
renstance. Then E — tr* jr, where r ■* total resistance of the circuit, including 
the galvanometer, with the standard cell in the circuit and r' » total resitftanoe 
with the unknown e.m.f. Ttiis method is better than (a) because It ia a 
constant deflection method and the result depends on the known values of 
two resistances, rather than observed deflections. 

(c) In Wheatstone's modification of the equal deflection method, the 
galvanometer resistance does not have to be known. The deflection, rf, is 
noted when the unknown e.m.f., E, and a known high resistance are in circuit. 
Additional resistance, r', is added and the deflection, rf', again noted. Simi- 
larly with the standard cell of potential difference, p; the resistance ia 
adjusted until the same deflection, d, is obtained and then an amount of 
reustance, r. is added until the deflection d* is again obtained. The unknown 
e.m.f. is E^er*/r. 

(d) In the condenser discharge method a condenser is charged, first 
from the unknown e.m.f., then from the standard cell, and discharged in 
each instance through a ballistic gulvanomet^ir. The deflections will be 
proportional to the e.m.fn., hence E^etl'/d as in (a). Obviously, if the un- 
known e.m.f. is much smaller or much lart^r than the standard cell, tho 
deflection can be made about equal to that of the standard cell by using a 
larger or a smaller condenser. In that case the ratio of the caparjties should 
be known, and then E'^ed'C'/dC^ where C-^ capacity of condenser used with 
the unknown e.m.f. and C — capacity of condenser u»ed with the standard 
ceil. This method has the advantage that practically no current is re- 
quired, which is advantageous in making measurements of voltaic cells of 
very small capacity or rapid polarization. 

(e) The principle of the opposition or i>otentlometer method is that 
of opposing the e.m.f. of the standard cell against an equal difference of 
potential which bears a known proportion to the unknown e.m.f. This 
method ia the most accurate and by tar the most generally used, because it 
is both a sero-deflection and a sero-current method, the result depending 
only on the ratio of two resistances which can be very accurately determioad- 
Fotentiometere are instruments employing this principle (Par. M). 

49. Description of Leeds and Northrup potentiometer, low raalgt- 
ance type. Fig. 7 shows the arrangements of the circuits. The figures for 
the second decimal place and beyond are obtained from a slide wire at the end 
of the circuit, CB, along which a contact moves. A special dial is also pro- 
vided for the standard ocU (at the left) and separate contacts are provided 
for the standard-cell e.m.f. and the unknown e.m.f., so that do settings havo 
to be disturbed when checking the necondary current in the Dotentiometer 
circuit. The essential part of the instrument consists of 15 nve-ohm coUa» 
AC, connected in series with the extendfKl wire, CB, the resistance of which 
from to 1,100 scale divisions is 5.5 ohms. Thus when the current from 
the battery, B, Is adjusted by the rheostat, R, to 0.02 amp., the fall of poten- 
tial across each 5-ohm coil in ACIsO.l volt and across CB^ 0.11 volt. Sinoe 
the latter is divided into 1,100 parts, the e.m.f. may be measured to O.OOOl 
volt. At point 5 in ^C, a wire is permanently attached connecting to one 
point of the double switch, U. When this switch is thrown to tho left, the 
standard cell is connected through the galvanometer to point 5 and tho 
sliding contact T which moves oyer the dial at the left consisting of 10 resist- 
ance coils. Between a and A is a resistance which is adjusted to such a 
value that with 0.02 amp. flowing, the potential drop between 5 and a is 

122 Diglzedby^^iUUyiC 



MBASURINQ APPARATUS 



Sec. ^50 



1.0X75 with 0.0001 Toli additional drop acrosa each dial coil, giving a majd- 
mum of 1.0194. This range will include the uaual difTerencea between dif- 
ferent Weston standard celTa. To adjust the current to 0.02 amp., throw the 
svitch U to the position indicated by the dotted lines, set the contact T 
to correspond to the e.m.f. 
of the standard cell and regu- R 

late ^ until the galvanometer mwuv^wsvmV ^ 

*bon no deflection. The \ _^ ' 1|4- 

uokaown e.m.f. is then meas- 
arrd by throwing the switch 
[.' to the position indicated 
by the full lines and adjust- 
lag the contacts M and M' 
ociit no deflection is noted. 
After a balance has been ob- 
tained, the current may bo 
rhecked by simply ahifting 
I' to the first position and 
pressing the contact key. 

■0. Paul potantio meter, 
low reiittance type. Fig. 8 
is the coanection diagram. 
It is similar to the instru- 
ment described in Par. 49 in 
that the lower part of the 
reading is obtained from an 
extended alide-wire on one 
end. snd a standard-cell switch is provided at the other end. The rheostats for 
ftdjustiog the batt«ry current are within the instrument (A and r). The slide 
wire is laid straight, with divisions equal to about | in. (0.4 cm.), which 
correspond to 0.001 volt divided into 5 subdivisions. A special switch, 
>S, is so arranged that the various circuits 1, 2, 3, etc., may be quickly con- 
nected to the potentiometer circuit. The resistance of the standard type is 
10 ohnu per volt, with a range from 0.0002 volt to 1.8 volt. It is also made 
with raages as low as 0.000004 volt to 0.036 volt for thermoelectric work. 




M 



Fia. 7. — Leeda & Northrup potentiometer. 




X-\ X-2 X-8 X-4 




Fio. 8. — Paul potentiometer. 

II. WoU poUntlomater, hlch reiiatence type. Fig. 9 shows the 
diagrun of connections in the lutest model. The total resistance is 20,000 
ohms and there is no slide wire, all resistances being comprised in the form 
of 5 dials, having steps of 1,000, 100, 10, 1 and 0.1 ohm respectively. These 
tni 1, 0.01, 0.001, 0.0001 and 0.00001 volt respectively. Instead of ob- 
tajniDg a balance by moving along the main circuit the contacts connected 
to "X," as in the slide wire form, the &nal balance is obtained by adding or 
rabtnetinc leaiatance in the main circuit between these two contacts; the 



123 



y>-i 



joogle 



Sec. 8-52 



UEASVRINQ APPARATUS 



three low dials are so arranged that a correspondiDs change is automaUoaUy J 
made in the external part of the main circuit and the total resistance ia kepta 
constant. A separate dial is provided for the standard-cell adjuBtment^ 
together with a separate resistance which can be altered to aocoRimo<iat< 
different cells without affecting the measuring circuits. The total range \ 
the instrument is 1.0 volts. 




Fia. 9. — Wolff potentiometer. 



U. Care and \1M of potentiometers. The following notes apply to 
the use of potentiometers in ordinary work. 

(a) The accessories should be suitable for the particular type of in- 
strument, that is, high or low resistance, and for the class of measurement 
to be made. The galvanometer should be sufficiently sensitive to give a per- 
ceptible deflection when there ia an unbalance equal to the smallest ac&le 
division in the potentiometer curcuit. A low-resistance galvanometer, of 
the order of 100 ohms, should be used with a low-resistance potentiometer, 
and a high-resiBtance galvanometer of 500 to 1,000 or more ohms, witn & 
high-resistance potentiometer. Similarly, the resistance of the volt box 
(Par. SS) for low-resiatance potentiometers should be as low as the permijt- 
sible power loss in the resistance coils will permit. This is usually about 
5,000 ohms for 150 volts. For high-resistance instruments, the resistance ia 
1,000 ohms or more per volt. 

(b) The flnt trials for balance should always be made with a resiatance 
in series with the galvanometer. This is usually provided in the instrument, 
with facilities for readily cutting it out of circuit when an accurate balance ia 
being obtained. The resistance protects the galvanometer and alao the 
standard cell from the effects of excessive currents. 

(c) Trouble is sometimes experienced, especially in damp weather, due to 
current "laakdnc to ground'' from the potentiometer circuits in a manner 
which produces a false deflection. This can be obviated by providing & 
"ffuara circuit." In one scheme of this kind all of the apparatus is placed 
on small, hard-rubber pillars each of which in turn rests on a small metal 
plate. These are connected together and to the poaitive "x" binding-poat . 
By fine bare wire. Thus all points to which current might "leak** over the 
surface are kept at the highest external potential to whicn the potentiometer 
is connected. When the surfaces become noticeably moist, couditiona ccui 
be improved by carefully wiping with a cloth moistened with grain alcohol. 

(d) Calibration and checkdng. The essential requirement is that the 
ratio of the resistance of each step to that resistance between the standitrct 
cell terminals shall be the same as the ratio of the corresponding potentials. 
For example, if the standard cell e.m.f. is 1.0183 volts and the reatatance 
between its terminals is 101. S3 ohms, the resistance of the various stepa 
should be adjusted to 10 ohms per 0.1 volt. If the standard celt resiatance 
is 102.848 ohms the potentiometer is still accurate if the resistance throughout 
the circuit is adjusted to 10.1 ohms per 0.1 volt. 



124 



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itBASVRING APPARATUS 



Sec. 8-53 



. Talt boana. Wben the iwtentui to be meanired u creater than the 
_ t <d the potentiometer (uauiuly 1.6 Tolte) a volt box ia used. It oonaista 
of a namber of reetstance coils oonneeted in aeriea, with tape brought out to 
WwHng poata. F1^. 10 shorn the diaEnunmatie arran^ment, in two forma. 
la LI), the potentiometer is connected to the poets marked " + " and " l.fi." 
When the potential to be measured is between 1.6 and IS volts, it is oonneeted 
ts the " + " and " 16" poets, between which the resistance is just ten timei 
tliat between " + " and " 1.6." Hence only one-tenth of the unknown 
Botestial is anplied to the potetatiometer, the readinffs of which must therefora 
be Bultiphea oy 10. Similarly, when the potential is between 16 and 160 
nlia, it IB oonneeted to the " + " and " 150" posts, and the ratio becomes 
100. In (£}, Fig. 10, the potential to be measured is always connaotad to 
eae pair of poeta, dedciiated " + " and " — ," and the potentiometer eonneo- 
tiona am aniftea to obtain the desired ratio. Theoretically the former 
Bctfaod is the better because the resistance in parallel with the potentiometer 
is constant and the sensibility is tliersfore constant. In the latter ease, 
the amaifaility variea, bein« a minimum with the lowest ratio, or when the 
isaiimnm amonnt of reaistanee is in parallel with the potentiometer. On the 



To "x" e,m.L 



To"a)"ewn.t. 




Xo Potentiometer 



To rountlometet 



Fio. 10.— Volt boxes. 

atkcr band, the nnknown a.m.f . is always connected to a hich resistance, and 
htaoe there ia no danger of burning out the volt box; this occasionally happens 
«ith the first form, ' (.A), due to accidental connection with tne wrong 
tomiaala. 

64. Paflection petanttometan; Precision measurements obviously 
caa be made only with veiy steady soureee of e.m.f. If the e.m.f. is not 
•Uady, and a higher precision than OftA obtainable with secondary standard* 
(voilmetera) ia aesiied, a defleetion potentiometer may be employed. In 
this iaetnunent the greater pact of the e.m.f. ia measured by balancing 
•giiast the potentiometer current in the regular manner, and the remainder 
b sblaioed by meana of the average indication of the fluctuating galvanome- 
ter, which is preferably of the portable type. The Brooka dafleotion 
iMMttsntetar* ia of this type. 

H. Tdtmeten for continuotti e.in.ti. Indicating instrument* 
<aDed voltmeters are used in ordinary commercial measurements. They 
•n, essentially, low-*en«ibility galvanometers pro- 
vided with seaka over which moves a pointer attached 
to the moving system. The scale is calibrated in 
•olts by eompatison with an indicating inatnunent of 
Ugfaer (eaaibilitr, or by meana of a potentiometer. 
Piaetieally all mieet'-earrent voltmeters employ the 
praupie of D'Araonval cmtraaometan aa shown in 
nz. 11. They consist essentially of a light rectan- 
tular coil of fine copper wire wound upon an alu- 

■•Biam frame, pivoted in ieweled beatings and ea- . 

psbla ol rotating in the annular spsoo between the soft- meter. 
inn eoffe and the pole-pieces of the permanent mag- 

■st. The aluminium frame, being a doeed secondary circuit, acts as a 
B*>Ks or damper when the coil is deflected: the insteument is thus made 
"iMd beat.*' The pole-pieces are so shaped that the magnetic field 
mvngth is uniform throughout the space in which the eoU movee. The 
Md strength varies widely in different makes of instrument, ranging from 
M>to 3,000 lines per square centimeter in the air gap and 1,000 to 6,000 

* Bocaa of Standard* Bulletin; Vol. II, p. 226; Vol. IV, p. 276. 

laS DigilizedbyV^iUUgle 




Fio. 11. — Diagram, 
Weston d.c. volt- 



Sec. 3-56 



MBASURJNO APPARATUS 



lines por square oentimeter in the steel. A light tubular pointer attaohvd 
to the coil moves over a calibrated scale. The current is Introduoec 
into the coil by two spiral springs which also provide the controUini 
force. Since the field strength and the gradient of the controlling foTMl 
are uniform, the deflection is strictly proportional to the current paoHiii 
through the coil, and the scale divisions are uniform. A large amounia 
resistance is connected in series with the moving coil in order to make tbi 
current small. Thus the same instrument can be made suitable for a «>df 
range of voltages by changing the amount of series resistance. This n 
mstance is made of wire having a low temperature coefficient in order (t 
neutralise as much as possible the efTect of the large a>efficient of the cof^a 
in the ooil. 

•6. Voltmeter characteristics (continuous current). The usna 
resistance of portable voltmeters of this type varies from 50 to 150 ohmi 
per volt and the current sensibility from 7 to 20 milliamperes at fuU-scali 
deflection. The resistance of the moving coils is about 75 ohms. Tfai 
torque varies from 2 to 6 millimeter-grams at maximum current, with i 
ratio of torque to weight (in grams) of 1 to 5. The temjwratnn 
coefficient is usually negligible, being of the order of 0.01 to 0.02 per cent 
per deg. cent, at full scale. 

87. Laboratory standard voltmeters (continuous current). So 
called laboratory standard voltmeters are similar to portable instrument 
except that they are larger, have a longer pointer, a longer and more opei 
scale and are made with greater care. They are only semi-portable and an 
intended primarily for standardizing purposes. 

M. Switchboard voltmeters (continuous current) are usually of tb 
D'Arsonval type. The construction is the same as that of portable instni- 
inenta, except that they are more substantial and ruggea, especially ai 
regards the moving system, in order to withstand the harder conditions o 
continuous service and excessive fluctuations. They are mounted in iroi 
cases to protect them as much as possible from the normal stray fields dui 
to the bus bars. * 

H. Kffect of stray fields. The general effect of stray fields on the stand 
ard types of portable and switchboard instruments is shown in the table il 
Par. 60. These errors are usually only temporary and disappear with thi 
stray field. When the field is very strong, as under short-circuit condition! 
in a neighboring conductor, demagnetisation of the instrument magneti 
may result in a permanent error. Shields are likely to be of little value undo 
such conditions because the iron becomes saturated. 

60. Effect of Stray Magnetic Fields on Continuous-current Volt* 
meters and Millivolt meters 



stray field, 
lines per sq. cm.* 


Error at two-thirds full-scale deflection, per cent. 


Shielded 


Unahielded 


6 
10 
15 
20 

■' 


0.5 to 1.0 
0.75 to 1.75 
1.0 to 3.0 
1.25 to 3.25 


2 

S.Sto 5.5 
e.Oto 7.5 
7.5 to 10 



01. The measurement of very small continuous potentials may be 

effected by some of the methods outlined in Par. 48- 

A potentiometer is most convenient, high resistance for high resistance soured 
such as small galvanic cells and low resistance for low reaistanoe sources such ai 
thermocouples. 

6S. Oround detectors. Those of the direct-current type are usually 
special forms of voltmeters. In one form, there are two coils, differ en tlallv 
wound on the moving system. One end of each coil is connected to ground 
and the two free euos are connected respectively to the two aides of ths 

* The field produced at a distance of 30 cm. (12 in.) from a conductor caixy- 
ing 3,000 amp. is about 20 lines per square centimeter. 



126 



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MBASURISQ APPARATUS 



Sec. 8-63 



Qvtera. When there is no groand or fftult on the system, the pointer atanda 
M th« oentre of the scale, in normal equilibrium. When a ground or fault 
ocean, ciureDt flows through the coil connected to the ungrounded side, 
producinc a deflection. Id another form of detector a standard voltmeter, 
■itbout the series resistance, vb connected to the centre of a reajstanoe shunted 
unm the line, with the remaining terminal connected -to ground. 

ALTX&HATIHa-B.H.F. KSASinUEMIHTS 

U. MeuvrexaenU of ftlt«matlii|r e.m.f. In alternating e. m. fs. 
tikere am three values to be considered; the maximum, the average and the 
"root-meao-stiuare" or menn effective value (Sec. 2). The last value is 
the one uauiiily required, being the value of the equivalent continuous e.m.f. 
Knee the standard of e.m.f. is the standard cell, the measurement of altemat- 
ia« potentials involves, like continuous potentials, comparison with the stand* 
ud eeU. The comparison may be more or less a direct one, as in precision 
■asorementA. or it may be indirect by means of secondary standards 
wlueh in turn have been standardised by direct comparison. 

M. Prtdtlon iiMaaiar«m«ntt of ftltematiiw e.m.f. Obviously an 
tlteroating e.m.f. cannot be compu^ directJy with the standard cell, the 
(.aJ. of which is unidirectional and constant. The comparison is made 
therefore by a substitution or "transfer" method, A galvanometer of the 
ciKtrodynamometer type, or an electrostatic galvanometer, is connected to 
the alternating potential to be measured and the deflection noted. It is 
Acq coonecteu to an adjustable continuous potential which is manipulated 
BBtil exactly the same deflection is obtained. The continuous potential is 
^m compared with the standard cell by means of a potentiometer, in the 
mU manner. A double-throw double-pole switch is usually arranged so 
that the transfer from alternating current to continuous current can be 
QoicUy made, without allowing the deflection to change appreciably, the 
coBtiaaous potential having been previously adjusted to about the proper 
Tiiue. Two readings, direct and reversed, are taken on continuous current 
' ttUwaamc reading as the altcrnatinfC deflection; the average of these two is 
taken sa the true value, thus eliminating the effect of stray magnetic or 
''t^ctroFtatie fields. It is obvious that, on account of this indirect method, 
1 sltenuting-e.m.f. measurements cannot be made with the degree of 
' P«cifton obtainable in measurements of continuous e.m.fs. 

M. Bteondary ttandards. The dsmamometer type instruments which 
Bc wed as secondary standards of alternating current are adapted to 
t-KLf. measurements oy constructing the winmogs of a large number of 
tami of fine wires, instead of a few turns of heavy wires. See Par. M. 

W. CUiiiflcation of altamatlnff-ctirrent Toltznetan. The volt- 
"let^ni in jrfneral use may be divided into five types, as follows: dyna- 
BKKaeccr, soft-iron vane, induction, hot-wire and electrostatic. 

IT. I>7ii«iiiomet«r typo Toltmetan (alternating current) depend upon 
the reaction between % fixed and a moving coil connected in series. The 



\ F 

mm 

f ■ 

fto. 12— DiaKTam, Weston 
Qynamometer type a.c. volt- 

■■i^tmciil o( the movable coil u a measure of the current flowing through the 
°^ tul therefore proportional to the e.m.f. impressed at the terminals. In 
<" lora (Wnton model 18), a angle coil movea within two parallel fixed 




Diagram, Kelvin balance. 



/ 
\ 



127 



, Google 



Sec. 3-68 



UBA8VRINO APPARATUS 



coils u ahown in Fig. 12, where F-P" m the fixed edle and it ia the morinc 
soil, to whioh a pointer P ia attached. The deflection is approximately pro- 
portional to the square of the ounent. The scale is compressed at the umier 
end instead of extended because the coil movea beyond the uniform part of the 
field. The Thomson Inclined Coil TOltmeter ia similar, except that the 
plane of the fixed coib maliee an ande of about 45 dec. with the shaft of the 
movins coil for the purpose of making the scale more uniform. 

In the WestlncuouM type Q, the KelTln balanea principle ia used. 
This principle is shown in Fig. 13, where there are two coils, 3f Jtf', attached 
to onpoeite ends of a beam which is supported at the middle and free to move. 
Each coil mores between a pair of fixed coils, P P and P' P', and all of tho 
coils are connected in series in auch a maniker that the moments of all the 
forces on the movable system, taken about the beam axis, are cumulataTO, 
thus tending to produce rotation. In the Kelvin balance the eontroUins 
or opposing force ia a weight moved along a graduated scale attached to 
the beam supporting the movable coils; the moment of this weight about 
the beam axis, when the moving system is balanced, variee as the aquAi*o 
of the e.m.f. In the Westinghouse instrument the coils are arranged ver- 
tically and the controlling force is a spiral spring. The amount of oom- 
preesion of this spring necessary to balance the electromagnetic foroea, am 
indicated by a pointer moving over a scale, is a measure of the e.m.f. ffingle- 
ooU instruments are direct reading and hence fluctuating e.m.fs. can be mot* 
easily read on them than on the torsionhead instruments, but the latter aio 
astatie and therefore practically independent of stray fields. 

M. Sott-Iion-Tftne voltmetan (alternating current) utilise the t«. 
action between a temporarily magnetised piece of soft iron and the magnetis- 
ing field. In the Thomson inclined coil initrument of this type tho 




QP 



OooBMr Wh 

Fia. 14. — Diagram, Thomson inclined 
coil a.c. voltmeter. 




Fio. IS. — Diagram, Weston 
soft-iron type a.c. voltmeter. 



plane of the energising coil, C (flf. 14), makea an angle with the shaft, S, 
which carries a member, i, comprisiDg a rectangular piece of vety thin, soft 
iron. This piece of iron ia so attached to the shaft that rotation ia produoed 
by the tendency of the iron to become parallel with the field estabuahed bj 
the coil. In weiton inatrumanta of thia type (model 156), the resctiox 
wUoh produces the deflection takea place between two pieces of soft irox 
bent in the arc of a circle and placed oonoentrieilly, one of which, ^' (Fig. I S) 
is movable, and the other, F, is ststionaTy. When the surrounding coU. Jtf 
is energised, the pieces of iron become magnetised in like manner, so that th^ 
resulting force is one of repulsion. The stationary xrieoe P is made trianipilA; 
in shape, with the pointed end in the direction of rotation, for the purpooi 
of making the scale more uniform. Air damping ia obtained by means of i 
light aluminium vane, V, in an enclosing chamber, C. This type haa thi 
great advantages of low price, ruggedness, open scale and small weight. 

•9. Induction-type voltmetan (alternating current) utilise tha prin 
tiple of induction watt-hour meters (Par. lOt), or the rotative tendency of ( 
free cup of thin metal when placed within a so-called revolving magneti 
field. Actual rotation of the movable element is prevented by an oppooini 
spiral spring, so that the defleotiona become a measure of the current in tb 
energismg ooila. The WMtlacliOUM type P voltmeter ia an importaa 



138 



dbyv^iouyie 



MEASURING APPARATUS 



Sec. 8-70 



. ! of ttuB type, for which is claimed a very high ratio of torque to 
«a^t of moving element, nuued and rimple construction, extremely long 
■mle and compactneas.* The ar- 
nscement of the circuita u abown in 
TiK. 1 6. The primary winding, P, 
mhith a connected to the line circuit, 
iuluoea a current in the aecondary 
winding, 3, opposite in phase to the 
primary current. The secondary cur- 
nat paiea through two auxiliary 
nds, AA't wound in opposite direc- 
bms on the poles. The field pro- 
dsecd by tfacaa coils will be displ^^ed 
90 dcg. in time phase from the field 
podnced by the primary winding and 
approximately at right angles thereto 
inapaee, thus prodncing the necessary 
raCatins field to cause the cup. C, to 
tead to rotate. Incidentally, the in- 
kneat frequency error of induction 
tfjft ustruments ia largely neutralised 
hj this eomfatned transformer andin- 
daetioa motor action, the effect of fre- 
(pKoey changes being opposite in the 
two cases. 

n. Hot-wtr« ▼oltmetant (alter- 
kstiag-eurrent) utilise the expansion 
sad coDtraction of a wire carrying a 
carrcnt proportional to the e.m.f. to be 
Masnnd. Fig. 17 shows the princi- 
ps) features of the Hsftfnann &nd Braua Toltmoter. 




Fiq. 16. — Diagram, Westingbouse 
induction -type s.o. voltmeter. 



_____ __ The current 

iovs through the platinum-silver alloy wire, AB, which expands under the 

beat produced. This ex- 
pansion reduces the tension 
on the fine phosphor- 
bronse wire, CF, wnich in 
turn allows the silk fibre, 
HE, attached to the spring, 
5, to be pulled to the left. 
This fibre passes around a 
small pulley on the shaft of 
the moving system and 
thus produces a deflection 
of the pointer. Damping 
is effected by the alu- 
minium disc, D, moving be- 
tween the poles of the per- 
manent magnetj M. The 
hot wire, AB, is in series 
with a large non-inductive 
resistance, H, so that the 
current is proportional to 
the e.m.f. 

71. KlectroBtatlc volt- 
meters (altcrnftting-cur- 
rent) are similar to eler- 
trostatic galvanometers 
(Par. 17) or electrometers, 
except that thejr are de- 
signed for measuring larger 
potentials and are provided 




f>c. 17. — Diagram. Hartmann & Braun hot* 
wire type a.c. voltmeter. 



* MscGahan. P. "Induction Type Indicating Instruments;" Trans, 
A 1 E. E.. 1912. Vol. XXXI. p. 1565. 

t PSeree, A. W. and Tressler, M. E. "Hot-wire Instruments;'* Trans. 
*- L E. E., 1912; Vol. XXXI, p. 1691. 



129 



i,y^^^OOgle 



Sec. S-72 



MBASURIIfa APPARATUS 



with scales whieh make them diraet rekdins. TheyanmadeinatiaatTariety 
of forms, for both portable and switchboard use, but an used commsnaalb 
much more in Europe than in this country. Theprincipleof tbeiroperatioan 
shown in Fi^ 18, in whichmm' is a thin aluminium vane suspended or pivotad 
between two pairs of fixed vanes, //'. The deflection througn moderate xancM 
is proportional to the square of the jpotentislandis controlled either by a qjizai 
■prtng or by gravity. Damping is produced magnetically, by air Tanea, or 
by immersing the elements in oil, For ordinary oommercial voltaces a nuin- 
ber of sets ox vanes are arranged one above the other in a vertical poaitioii* 
and oonnected in paralld, thus multiplying the effect (Fig. 19}. For hicfaer 
Tf^taffSS, one set ox vanes is sufficient and they are usually placed in a vertical 
plane wltii the moving element mounted on a horisontal shaft. In tba 
wastlnrbouse alectroitatle Toltmatar, the moving system is not oon- 
neoted to the circuit; Fig. 20 shows the arrangement of the parts. Whan 
potential is uipUed to ^and A', the hollow cylinders C and C Moome oppo- 
sitely charged by induction. The resultant attraction produces a deflection 
because of the shape of the fixed plates, P and i". The condenseia K and 
K' are each formea by two flat plates and are connected in series with A 
and A' to increase the range. For lower ranges these ooodenseis ars short- 
eireuited, so that ranges of 30,000, 60,000 and 100,000 volts ars available in 
the same instrument and on oqe scale. The elements are entirely inuneiaed 




Fio. 18. — Dia- Tia. 19. — Dia- Fia. 20. — Diagram, Westins- 
gram> electrostatic- gram, electrostatic- house high-tension volt- 
type a.c. voltmeter. type a.c. voltmeter. meter. 



in oil which permits a relative!]^ eompaet construction, increases the toraus 
because of the greater specific inductive capacity of the oil and provioas 
damping. 

Tl. Altemating-eurrent switohboard voltmstan are xnade in all of 
the types described above (Par. 6( to TO), although in this country the 
dynamometerj soft-iron vane and induction types are in most general uas. 
lliey are similar in general to the portable instruments, due regard beuog 
given to the more severe requirements of switchboard service. 

n. Oalibration of altamatlng-eurrent Toltmatan. The djn*- 
momatar type of voltmeter gives the same indication on continuous current 
as on alternating current and may therefore be calibrated with continuous 
currents, direct and reversed readings being taken. The inductanoe ia 
i QStruments of commercial ranges is so small that the readings are independent 
of standard frequencies. 

The soft-iron-vane type of voltmeter should theoretically be used only 
on alternating current because hysteresis occurs to some degree in the vane. 
Practically, however, the hysteresis is so small that there is very little differ- 
ence between the respective indications with increasing and decreasing 
potential. Provided with a steady source of e.m.f., under suitable control, 
these instruments may be calibrated with continuous current by taking the 
average of the "up" and "down" potential readings corresponding to the 
various points. Care xhould be taken that the potential is increased or 
decreased only to the desired value and not beyond it. Theoretically, in- 
struments of the soft-iron type are not independent of frequency or wave- 
form; practically, however, the variation is not measurable throushout 
ooromeroial ranges. 



190 



y Google 



MEASURING APPARATUS SeC S-74 

ToltmeWn ar« theoreticaUv and practically independent of 

_ I in frequency and wave form, and can therefore be calibrated with 
ec^^inuoua current. They are eapeeially suitable for high-frequency 
m eaau rcioenta- 

Indaetlozi-tjM Toltmeten are affected by changes of frequency. 
They most ther«ore be calibrated on altematinff current of the frequency 
lor whicfa they have been adjuated, in comparison with some secondary stand- 
aid which c&Q in turn be calibrated with continuous current as described 
sader precision measurements. Errors which result from ordinary varia- 
tJona in commercial wave forms are negligible. 

SI*ctro«tatic TOltinetorB are indeoendent of changes both in frequency 
sod in wave form, and ma^ therefore be calibrated with continuous current 
where the ranse wiU penmt. 

T4. Tb* all«ei of stnj fields on altamating-currezit Toltmeten is 
very marked in some types of instruments. The error will vary with the 
deflection And with the direction of the suiwrposed field. In the case of 
oB^ucldcd, siniJe-coU dynamometer instruments, the error caused by a 
nagDctic stray fi^d of five lines per square centimeter may vary from 25 
per cent, at quarter scale to 5 per cent, or 10 per cent, at three-quarters 
scale; with a field of 10 lines per square centimeter these figiues may oecome 
73 per cent, and 25 per cent., respectively. Soft-iron-vane instruments are 
much leas affected, a stray field of 10 lines per square centimeter causing 
about 10 per cent, error. Hot-wire and electrostatic instruments are not 
sSerted. Shielded dynamometer instruments are available in which the error 
with stray fields of 20 lines per square centimeter is only 1 or 2 per cent. 

Tt. Moararement of small alternating e.m.fs. The single-coil 
^mamometer type voltmeter is practically the omy one available for potentials 
01 leas than 25 vdta. Since the deflections in tnis type of instrument are 
p roport i onal to the square of the potential, the lowMt value that can be 
meamrwd with a 7.5-volt instrument is about 2.5 to 3 volts. By separately 
exeiriDS the fixed coils the sensibility will be greatly increased, because 
the denBctiona will then be directly proportional to the potential impressed 
on the moving coil. The "unlplyot dynamometer ^pe instrument 
CPaol) with separate binding posts for fixed and moving eoiiR is intended to 
be Dsra in this manner, full scale deflection being obtained with 1 volt. 

For the accurate measurement of potentials of the order of 0.26 volt 
and less, dvnamometer instruments must be of the suspension, reflecting type. 
Care sbould be taken that the excitation is in phase with the potential bemg 
M ea s ui ed and that the current through the instrume nt remains proportional 
to the potentiaL This current is J — BJ's/B? -^lAtt^ wherein J? •-impressed 
voltage being measured, A •> resistance of instrument, L •■ inductance and 
»»2rX frequency. When R is targe the inductance is negligible, but when 
it ****>'*^*** small as in very low reading instruments, it may have to be 
coeMdeted in the measurement. In that case, the instrument can be cali- 
brated as an ammeter on continuous current and the alternating e.m.f. 
rocapoted with the above formula. For similar reasons, the temperature 
eoeficient may beoome significant. 

t«. Measurament of large altematlnff e.m.fs. Theoretically, any 
fJTfmatiffg potential can be measured with any of the voltmeters described, 
if soficaeat eeriea resistance is used. In a pr&ctical sense, the large energy 
roBsamption and the insulation difficulties nmit their use to measurements 
of a few thousand volts, and then only for testing purposes. In connection 
■Hh eoamiercial generation and transmiarion, potentials up to about 33,000 
Tclts are almost universally measured in this country by means of step-down 
tfistntment transformers (shunt type) connected to ordinary voltmeters. 

TlMmeasuremeDtofpotentialshigher than 33,000 volts is usually required 
oahr in connecrtion with high-voltage tests. The various methods of making 
Rich measurements are as follows: 

(a) Balio of the step-up power transformer, in connection with an 
ordiflary voltmeter on the low tension side. This method requires an accu- 
rste knowledge of the transformer ratio under various conditions of load and 
potential* information which is often dilBcult to obtain. 

(b) ttepHSown Instnunent transformers (shunt type) with an 
orfiaary Toltmeter. This method requires an accurate knowledge of the 
tnasfonaer ratio at various potentials, with the voltmeter as the secondary 



131 



DigilizedbyV^iUUyie 



SecS-77 



MBASURINO APPARATUS 



load. The method is simple, convenient and accurate, but the power con- 
sumption and the cost of the transformer become prohibitive at hisli 
potentials. 

(c) Sl»etrottatlc TOltmeter. Commercial instruments are available 
' up to about 200,000 volts. They require no appreciable power and are quite 

satisfactory. The principal objections are the high cost of large sises and the 
lack of dead-beat qualities. 

(d) Test coil. Where the source of the high potential to be measured 
is a testing transformer, an ordinary low-reading voltmeter can be connected 
to a few turns of the high tension uinding brought out to separate terminals. 
These turns should be at the grounded end of the winoing. The ratio, 
under aM conditions, will be that of these turns to the total turns in the hiah- 
tension winding, if the transformer has been well designed. This methoois 
generally sufficiently accurate and is verv convenient. 

(e) Spark (ftps. The sparking distance between two terminala in 
atmospheric air is a standard method of measuring high potentials. The 
maximum length of gap which a given potential will break down depends, 
in this case, on the maximum value and not upon the virtual or effective 
value which is the value obtained in the other methods. The manmum 
value, however, is the important one in tests of insulators and insulating 
materials. When the wave 

form is not a sine curve the ^ 

maximum value may deviate _ (3 

materially from the theoretical 
value, which is the virtual 
(voltmeter reading) value mul- 
tiplied by V^ 
77. N»«dl6-point and 

*^* ^f'^ 'f^'i, '^^^'O.as^ 
needle-point spark has for ^ 

many vears been the standard 
metnoa of measuring high 
voltages, but it ia unsatisfac- 
tory for very high potentials 
because of variations due to 
atmospherifi pressure, humid- 
ity, proximity of surrounding 
objects and sharpness of the 
needle-points. It has been 
proposed* to use spheres in- 
stead of needle-points and the 
1014 A. I. K. E. Standardisa- 
tion Rules recommend the use 



M^ 




i4-—i,tSA—*i 



umA- 



of the needle gap for voltages 
from 10 kv. to 50 kv. sod the 



Note: 
A Variation of I Cm. in Thickness and 
Width of Wood Parts is Permiaaible 
Fio. 21. — Sphere sparlu gaps. 



rohere sap for voltages above 
oO kv. A gap mth carefully 
machined and polished spheres gives very reliable and eonsistent results due, 
probaUy, to the fact that the gap breaks down before corona forms and per- 
haps also to the lesser dielectric spark log.f 

78. A. I. K. K. itandard iparUnr diitencei In air, with needle- 
point and tphere caps are given in Sec. 24. 

79. Satio of Ihunt-tjrpe instrument trangformer. When a very 
accurate measurement (within 2 per cent.) of a high potential is to be 
made with an instrument transformer of the shunt type, the nominal ratio 
cannot be relied upon as being sufficiently correct and the true ratio should 
be determined by a direct measurement. In the accurate measurement of 
power and energy the phase angle should also be known (Par. 179). For 
the accurate determination of the ratio of instrument transformers of the 
shunt type, the following methods are typical. 

(a) Dlreot meaiurement of the primary and the secondary voltage, 

'Farasworth, S. W. and Fortescue, C. L. "The Sphere Spark Gan." 
Proe. A. I. E. E., 1913, Vol XXXIl, No. 2. p. 301. See Fig. 21. 

t Minton, J. P. " Effect of Dielectric Spark Lag on Spark Gap*," Oeneral 
*Iec<rfc Bevitv (1913), Vol. XVI, p. 514. 



132 



dbyv^iuuyie 



MBASVRINO APPARATUS 



Sec. 8-79 



pn^enUy with two siiiiilftr voltmetera. Fig. 22 shows diagrammstirally 
tte conihBctions for this method. The voltmeters V'l and Vi are eimilar, and 
the reaistanoe R ia adjusted until the two deflections are about alike. The two 
Toltiiietera are then connected in parallel on the secondary of the transformer 
sad the indication of Vx, corresponding to the previous indication of Vu 
is noted. The ratio is given by ; 

/K+r.\Xi 

Vr. /it 

wherein X — resistance in series with Vt: r. i* resistance of voltmeter Vt; 
Ji» first reading of Vt; Xs — second reading of Vt. 



(11) 




Flo. 23. — Connections — ratio of 
shunt type transformers. 



Flo. 22. — CSonmectiona — ratio of 
ahont type transformers. 

(b) Oppodtian method. The secondary voltage is reversed and con- 
nected in cmpoattion to a part of the primary voltage, the ratio being measured 
is terms of two resistances. Fig.^ 23 shows the scheme. The resistance r 
ii varied until the detector. 3*. indicates xero or a minimum deflection. The 
imiei ratio is evidently expressed by {fi+r)/r. 

The detector may be either a telephone receiver, a dynamometer instru- 
nmit, or a synchronous reversing key with direct-current galvanometers 
(Far. (t). The telephone receiver is not sensitive at commercial frequencies. 



:^=b! 



V^'r 




r->!) 



OiODnd 




~?~Gcoaad 



Ma^ Phase Detector Xhtee Phase Detector 

Flo. 24. — Diagram, Westinghouse a.e. grotmd detector. 

ttd if bannonics are present the precise balance point for the ftmdamental 
ueqiKney is difficult to locate. When using a dynamometer, the fixed coils 
sn eonneeted in series with A (not r) and the moving coil in place of T. 
'heo a rectifier is used, it is connected directly in place of T. 
(c) ComiMxlaon with standard transformer. F. B. Brooks* proposes 

' Bnxrio, F. B. Scientific paper No. 217, Bureau of Standards, Feb. 7. 



133 



yGoOgk 



Sec, 8-80 MEASURING APPARATUS 

n simple and convonient method of comparing two transfonnen by : 
of a wattmeter. 

80. Alternatinff-currant ground detecton are usuallv electro- 
■tfttlo inatrumentfl. Fis- 24 ahows diagrammatlcally the principle of West- 
tnfhouM detecton. The stationary vanes are connected tnroush con- 
densers to the main lines, and the movable vane is connected to srouiul. 
In the single-phase detector, a charge will be induced on each end of the mov- 
able vane, opposite in sign to that on the corresponding stationary vane, 
setting up forces of attraction. When the system is free from grounda, 
these attractive forces are equal and opposed to each other; hence the mov- 
ing system stands at lero. A ground on either phase wire produces an ud- 
buanced condition and a deflection away from the grounded conductor. In 
the three-phase detector, the vanes are sectors of spheres, the movable vane 
being mounted on a universal bearing. 

81. General Klectiio vround detaoton operate on a principle similar 
to that last described. Four quadrants, or fixed, flat vanes are croaa-^on- 
nected and mounted between them is a moving vane connected to sround. 
Opposite sets of fixed vanes are connected to the two sides of the Itoe circuit 
ana the action is the same as described in Par. 80. The three-pbase 
detector is similar, consisting of three pairs of fixed quadrants mounted 
120 deg. apart on a common base plate, and a flat moving vane witli three 
corresponding sectors. 

GONTIMTrOUS-CnKKKNT MKASXTBSMXKTS 

88. Absolute meaaurementi of current. The fundamental unit d 
current, as derived from the centimeter, gram and second, is defined in 
terms of the dimensions of the conductor and the strength of the magnetie 
field produced by the current. Absolute measurements of current are thei«- 
fore made with instruments so carefully constructed that the current can 
be calculated from their dimensions. 

88. Inatrumonta for abiolute meaauremant of current. Abeolute 
determinations have usually been made with two classes of Instrumente. In 
the first, the deflection of a magnetic needle at the centre of a coil is measured, 
and the current ia calculated from the fiimensions of the coU, the strength of 
the earth's field and the torsion of the suspension. The best known example 
of this class is the tangent galvanometer (Par. 11). This method involves, 
of course, any error in the determination of the earth's field. In the other 
class of instruments, the needle is replaced with a suspended ocnl. When the 
length and the radius of both movable and fixed coils are in the ratio of 
v3 : 1, when the centres coincide and when the dimensions of the fixed cml 
are large compared with those of the movable coil, it has been shown by 
Gray that the torque exerted by the moving system is expressed by 

r- - ,- i^^ (dyne-cm.) (12) 

where AT « number of turns in fixed coil, n •- number of turns in movable ocnl, 
D «" diameter of fixed coil in centimeters, L = length of fixed coll in centimeters, 
r^radius of movable coil in centimeters, and / — current (coils in series). 
Hence by measuring the torque (weighing it), the current can be determined 
directly in C.G.S. units. 

84. Practical unit and itandard of current. It would be quiu 
impracticable to make ordinary measurements in terms of the fundamental 
unit, by the methods indicated above (Par. 88 and 88). The Act of Con ai w 
of 1894 which legalised certain practical units of electrical measure defined 
the practical unit of current, or the International ampere, as one-tenth 
of the fundamental C.G.S. unit. This Act also defined the standard unit 
of current as the rate of deposition of silver at the cathode of a silver vol(> 
ameter (Par. 86) constructed and operated under certain prescribed coiuU- 
tions, the ampere being the current which will deposit 0.001118 k- of 
silver per sec. in a standard voltameter. 

88. Methods of meaanrinff conttnuoui currents. The eeTeral 
methods of measuring continuous currents may be classified as followflt 
voltameter; potentiometer; and ammeters. 

88. Voltameter method of current measurement. When a . coi^ 
tlnuoiu current is passed through an electrolyte, the latter la decompoeed at' 



184 



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MBASURINO APPARATUS 



Sec- a-87 



% rate which is proportional to the oiurent strength, and an apparatus for 
Burarinc curreDt by auch meana is called a voltameter. In the lUver 
" ' r, the cathode or negative electrode is always platinum, the anode 
or positive electrode is pure sifvor, and the elec- 
trolyte is silver nitrate. Fig. 25 shows the general 
form. The anode is usually a silver rod projecting 
into a i^atinum bowl, which rests in turn on a cop- 
per plate. In cheaper forms, plates of silver and 
platinum are supported in a glass jar. The solution 
18 usually about 15 per cent, (by weight) silver ni- 
trate, and the effective area of the anode is about 
50 sq. cm. per ampere. In order to prevent disin- 
tegrated silver on the anode from dropping on the 
cathode, the anode is aurrounded with pure filter 
paper or a porous cup made of unglased porcelain: 
m other cases, merely a shallow glass dish is placed 
beneath the anode. Recent investigations at the 
Bureau of Standards* have shown, however, that 
the chemical activity of filter paper results in ao 
excessive deposit of silver and that the porous cup 
is much more suitable. The average current in 
amperes is computed from the formula 




Flo. 25. — Silver 
voltameter. 



(amp.) 



(13) 



O.OOlllW 

vlMre Jf« weight of silver deposited in grams, <■• total time in seconds 
sod O.XX>n 18 — electrochemical equivalent of silver (Sec. 10). 

tr. The coppar Toltazneter is used to measure very large currents. 
The anode is efectrolytically pure copper, the cathode is either copper or 
^atiaam, and the electrolyte is a solution of pure copper sulphate in the 
proportion of 10 g. of crystals to 40 cu. cm. distilled water. Two anodes may 
be nsed in order to utilise both sides of the cathode (Fig. 26) and the current 
capacity may be further increased by connecting additional 
I^atcs in parallel. The current density should not exceed 1 amp. ^ 

per square centimeter of cathode area. 

n. In the cai or water Toltameter the electrodes are Nf^Sf^ 
two plates made of platinum, and the electrolyte is a 10 per 
eest. solution of sulphuric acid. In the electrolysis of this solu- 
tkn, hydrogen s»" i^ formed at the cathode and oxygen gas 
at the anode. The total gas formed collects above the liqmd, 
sad is measured voluroetrically in a closed graduated tube form- 
iog the upper part of the containing vesseL 

W. Potentiometer method of measuring continuoui 
Wfouts* Although the silver voltameter is the legal standard 
for Ute meaaurement of current, its use is practically limited to 
reference measurements or primary standardisation. It is 
addom used in conxmerdal measurements because it is much 
nwre convenient to measure current in terms of the volt and the 
ptun. Even in measurements of the highest precision, current 
■ detcnnined from the fall of potential across a standard resist- 
SDce (Par. IIS), the potential being measured with a potentiometer (Par. 48 
(c),49, M, 81). The potentiometer method is not only more convenient 
thaa the Toltameter method, but it is much more rapid and at least equal 
la aceoracy, because it depends only on the measurements of a difference of 
potential and a resistance, both of which can be determined with a very high 
aegree of precision. 

M. Indicating contfnuona-ctirrent instrument! which indicate 
cvirent directlv by the deflection of a pointer over a marked scale are called 
anuneten. Modern continuous-current ammeters are almost universally 
ample millivolt meters of the D'Arsonval type connected to the terminals of 
^^c^staoce (shunt) which in turn is connected in series with the main circuit 
^y°s e current is to be measured. The deflections of the instrument -viiW be 
P't'portional to the f^ of potential across tbe shunt, and therefore to the cur- 
rent flowiiig through it. A millivoltmeter may be made an ammeter of any 
yrity by simply changing the resistance of the sh unt. 

*Bveaa of Standards BoUetin. Vol. IX (1912). No. 2. 



Fio. 26.— 
Copper 

voltameter. 



135 



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Sec. 8-91 



MSASURTNO APPARATUS 



•1. D'ArtonYal type of eontinuoixs-eiifT«nt unmatar. The prin- 
ciple of these inBtniments has been doAcribed under "e.m.f. measurements" 
(Par. 66). They are usually desiRned to have a full scale deflection with 60 
to 200 miUivoJts (thouaandtns of a volt) at the terminals. The reidatauce of 
the moving ooil is much lower (0.5 to 5.0 ohms) than that of Toltmetcre, In 
order to make the millivolt constant high. 

92. Continuous- current ammeters of the switchboard tjpe are 
intended for continuous operation and the shunt loss should therefore do low. 
They are designed for 50 to 75 millivolts at full scale deflection. HiKh-grade 
portable ammeters are designed for 100 to 200 millivolts at full scale deflec- 
tion, in order to permit the use of resistance in series with the movinx coil, 
thus reducing the temperature error, which is more important than the larger 
shunt loss. 

98. Shunts for eontinuous-eiifTant anunetort. In switchboard 
ammeters and the lower grade portable ammeters of 26-amp. ratings and 
less, the shunt is within tne instrument case. Above 2&-amp. ratings, the 
shunt is usually separate from the instrument and means of connection aro 
provided by special flexible leads, which are included in circuit when ihB 
instrument is calibrated, since they form a part of the resistance of the entire 
instrument circuit. Obviously, these leads should , never be altered 
without recalibrating the instrument. In high-grade ammeters the shunts 
are separate for all capacities. 

94. Construction of ammeter shunts. Ammeter shunts are so 
eonstnicted as to have a resistance which will be constant, as nearly as 
possible, under all conditions. The resLstance metal has a low temperature 
coefficient, and the temperature Is kept low cither by connecting several 
strips in parallel and making the current density low, or by making the cur- 
rent density high and using short lengths of the resistance metal with heavy 
copper terminals desip^ed to dissipate the heat by conduction and radiation. 
The former method is most generally used, the strips being silver-eoldered 
into relatively heavy copper or brass terminals which are connected into the 
circuit to be measured. The resistance metal should also have a low thenno 
e.m.f. (Sec. 2) in junctions with copper. 

96. Seduction of temperature errors In continuoas-cuiTont 
ammeters. Because of the large temperature coefficient of copper, it is 
very undesirable to oon- 

C B, 
p f'OOir^ V WAWW^WWWW^ O 

Fta. 27. — Temperature compensation in 



miui vol tmeters. 



Re 



I— "VVW\AAA\WWV- 
I C R 

o— i-^W?p ^AM 



AAAWV- 



Rm 

-JVWNAr— O 



nect the moving coil of the 
instrument directly to the 
shunt. Temperature er- 
rors are reduced to a negli- 
gible value by connecting 
sufficient resistance having 
a low temperature coeffi- 
cient (manganin or similar 
metal) directly?' in series 
with the moving coil as 
shown ^ in Fig. 27, or by 
arranging a compensating 
circuit as shown in Fig. 28, 
where C = moving coil, Rm 
* low-coefficient resistance 
wire, and ^ ^e " copper re- 
sistance wire. 

96. The calibration of D'Arsonval type ammeters is effected by 
adjustment of the resistance of the shunt, the reeistance of the millivolt 
meter circuit, or both. Formerly each instrument and shunt wore adjusted 
together, but it is becoming customary to adjust all of the instruments of 
a given type to deflect full scale with tne same potential in millivolts at the 
terminals. The shunts for these instruments are all similariy adjusted to 
give the same potential drop, thus making all shunts and instrumenta of a 
given tj^pe interchangeable. The shunts should be acUusted by varying 
the mom-line resistance between the potential taps and not by adjusting 
resistance wire connected in series with the instrument leads. In calibrating 
switchboard instruments and the lower ^rade portable instruments, the 
potential tenninab are attached to the main current terminals and adjust- 



Fza. 28. — ^Temperature compensation in 
raiflivoltmeters. 



186 



dbyv^iuuyie 



MBASURXNO APPARATUS Sec, 8-97 

ment it effected by reducing the croas-eection of tho resistance atrips which 
hm been purposely left too large. Id imtruments of higher grade, the poten- 
tial termiiulB are connected to the reaistance strips inside the main terminals: 
k|q>roximate adjustment is obt&ined by trial, and after soldering the tap wire 
to the resistance atrip, final odjustnieut is obtained by var>'iug the cross- 
■ction, or by cutting back a tongue-shaped piece of the atrip whose end 
k Mldered to the tap wire. 

ALTXXKATXXO-CVBBXNT MXASUKEMXHTS 

tr. M«aAar«menta of altamatinff currents. There are, in the case 
€l •hemating currents, three values to consider, the maidmum, the average 
sad the mean effective or root-mean-equare; the last is the value usually 
dearcd. Altematizkg currents, like alternating e.m.fa., can only be compared 
with the standard by means of a " transfer" instrument, that is, one in which 
the cfleet produeed bsr a current is the same whether the current is continuous 
fir aherarang. Havins determined the indication produced by the alter- 
MtiBg cumni to he measured, the value of a continuous current which will 
praihiee the same deflection is obtained in terms of the standard. 

N. FreefsicMt iBMasiirements of alternating current are made with 
"trsnrfer" instramenta (Par. M) which are usually of the refleeting. suspen- 
lioa, dectrodynamometer class. The principle of these instruments is 
deeoAied in Par. M to S4. P. G. Agnew has developed a tubular water- 
cooled dectrodynamometer having a capacity of &,000 amperes and an accur- 
sey of Ol06 per eent.* 

M. ItroBdMy standards for sltemating-oiirrent maaiuremanta, 
idspted for direct observation, mxist obviously be capable of calibration 
SB omtinuoos current. There are several instruments which fulfil this 
Rmdrement. 

TW ***"^M«T elAetrodyn*mometer consists of two stationary coils 
connected in seriee. with a moving coU suspended between them by a silk 
fifan. The deflecting force or moment is opposed by a spiral spring, which 
i> twisted by hand (in the so-called UVftion head) until the moving coil is 
farovKht back to the aero position. The amount of this twist, as indicated on 
a Kale over which moves a pointer attached to the torsion head, is a measuro 
o( the current. The final relation of the fixed and moving coils is therefore 
alwsyi the same. The current in amperes is I — k'^L, where !, = twist of 
toraon bead in degrees and Jb»a constant determined by calibration on con- 
tnuoQs current. The instrument is sensitive to stray fields, from both 
diRet and alternating current. The presence of such fields can be detected 
by^esiing cnrrent through the moving «>U only; a deflection under such con- 
dnwes indicates a stray field. Its effect majr be reduced to a negligible 
qaiBtity by turning the whole instrument until no deflection is noted. 

lit. The XeWin balance (Par. 67) is an dectrodynamometer type 
of iflstnunent which is astatic and in which the forces of attraction and 
Rpnbion are actually weighed as in an ordinary balance. Kelvin current 
buaaees are troublesome to use unless the current is extremely steady, a 
eoBifitioo which rarely exists with alternating currents; they have therefore 
heen practically superseded, in this country at least, by other and more 
■duble, convenient instruments of the dynamometer type, of which the 
Vcrtiaghouse "preciaon" ammeter is an example. 

The WeatlnglLonia "precision" anuneter is practically a Kelvin 
ha k n ee, of relatively small dimensions, in a vertical instead of a horixontal 
piu*. The eteetromagnetic forces are opposed by a helical spring which 
■ twislcd by means of a torsion head as In the Siemens dynamometer. The 
Mffhr owvement oi the torsion head necessary to keep the moving system 
» the sero position is a measure of the current. The actual value of the 
cwsat is equal to tho square root of the deflection, multiplied by a constant. 
ItL Types of altamating-ctzrrent ammeters. The four principal 
tnea of commercial ammeters are as follows: dynamometer, soft-iron vane, 
^vacfion, and hot wire. They are similar to the voltmeters of the same types 
Crir. C7 to 70), except that the windings consist of relatively few turns of 

^ " AfBcw, P. O. "A Tubular Eleotrodynamometcr for Heavy Currents." 
«vriBi No. IM, Bureau of Standards, June 17, 1912. 

137 Diglzed by Google 



Sec. 3-102 



MEASURTtfO APPARATUS 



i 



coarse wire instead of a large number of turns of fittft wire, the ftmp^re-iiimfl 
being about the same in both cases. Hot-wtre ammeters with ratines of 
more than 1 or 2 amp. are usually small current instruments connected to 
non-inductive shunts, as already described in principle (Par. fO). 

iOt. Mvftauremants of large alternating otirrents. The only type 
of ammeter which is generally used in the direct measurement of large 
alternating currents is the hot-wire ammeter, because it can be used with 
shunts, while shunt? are made for capacities of 1,000 amp. and over, the 
accuracy with shunts of very large capacity dei>ends upon the care jtaken 
in the design to eliminate the eddy-ourrent and BKin<«ffect errors. The moat 
common method is to use current transformers of the series type, to etep 
down the current to a small value, usually 5 amp., which is convenient to 
measure with standard instruments. 

103. Seriei-type Initrument trantformen (also known as current 
transformers) serve two purposes; the convenient measurement of large cur- 
rents, and the insulation of instruments and apparatus from high-voltace 
oirouits. They are similar to so-called power transformers, except that t£e 
latter are connected in shunt across the line and the secondary potential 
remains substantially constant irrespective of the connected lovd. Series 
transformers are connected in series with the primary line, and the secondary 
current remains substantially constant for a wide range of loads. The load 
consists of instruments or other devices which are connected directly in series 
with the secondary winding. 

104. Heaiurement of ratio of seriea traniformen. The ratio 
of series-type instrument trannformers may be determined b^ measuiins the 
primarv and secondary currents directly with current-measuring instruraenta, 
but obviously such 

Trana Hi D* 



l^ 



^>^3|^s 



— <Tjinr> — 



29. — Connections for measuring ratio of 
series type transformers. 



Trana B^ 

tmo — rvww 



method is much less ac- 
curate than null or "aero'* ^ ^nnnr v .aa aa* 

methods. The principle MK>00^ tVVW^ 

of the latter is the same f' CTg ffgr 

as that of the potenti- 
ometer, A non-inductive 
resistance in the second- 
ary circuit is adjusted 
until the potential drop 
across it is eaual to that Fio. 
in a non-inauctive re- 
sistance in the primary 
circuit. The ratio of the two resistances 
is equal to the ratio of transformation. 
The differences among the various null 
methods are largely in the manner of de- 
termining the balance and in measuring 
the phase angle. Fig. 20 shows the scheme 
of a method used at the Bureau of Stand- 
ards, * where a reflecting dynamometer is 
used as the detecting instrument. R^ and 
/2' are the resistances in the primary and 
secondary circuits, rospectivelpr. The fixed 
coil of a dynamometer, Di, is connected 
in series with the primary; then, with the 

switch S thrown to the right, Rt is adjusted until sero deflection is obtained. 
The component of the potential drop in Rt, which is in phase with that in 
Ri, is thus equal in magnitude to the drop in R'. Since the phase angle is 
always very small, the ratio of Ai toJ^i may be taken as the transformer 
ratio. The phase angle is then determined by measuring the component of 
the Rt drop which is 90 deg. from the Ri drop, by means of another dyna^ 
mometer, Di, the fixed coils of which are excited by a current displaced 90 
dog. in phase from the primary current. 

Fig. 30 sbowstho scheme of a method used at the Electrical Testing 

and secondary rerastances. 




Fig. 30. — Connections for 
measuring ratio of series type 
transformers. 



Laboratorics.f Ri and Rt are the primary 



* Bureau of Standards Bulletin, Vol. VII, 1013* No. 3. p. 423. 
t Sharp, C. H. and Crawford, W. W., rrans, A. I. E. E., 1910, Vol. XXIX. 
p. 1617. 



188 



dbyv^iuuyie 



MSASURTNG APPARATUS SeC. $-105 

zespeetiY^y, and C i> the detector which in this case is a aynchronoiuly driven 
rrrcfsing key (Par. M) connected to a Paul "unipivot" galvanometer. The 
Koondary of a mutual inductance, M^ is in the detector circuit and "the pri- 
nary ol the inductance is in series with the secondary circuit of the tran»- 
lorzaer. After the value of Rt has been found which will make the "in- 
phaee" potential firope balance each other, the quadrature ~drop in Rt is 
balanced by the o.m.i. in the secondary of the variable mutual inductance. 
Knowing the value of this inductance, the value of the phase angle may be 
ealcidated. 

IM. Batlo of Mri«t-t7pe instmmant trftnsformert. Theoretically, 
the ratio of transformation should be the same as the ratio of the secondary 
tarns to the ^rimajy turns, and the secondary current should be in exact 
phase oppoeition to the primary current. Actually neither of these condi- 
tiotts exists because of the current required to excite the core and supply the 

In many eommercial measurements these errors can be neglected, but 
in accurate measurements of current, power and energy, the true ratio 
Aonid be known. In power and energy measurements, the phase angle 
(an^ between the actual vector position of the secondary current and the 
themetioid position which is 180 aeg. from the primary current) should also 
be known. See Far. 179. 

lot. BfeMmramonts of small alternating current!. The methods 
desnibed for measuring small alternating e.m.fs. (Par. Ti) may be used 
for rimilar meaaurements of current. Portable ammeters of the soft-iron- 
raae type are made with ratings as low as 50 or 75 ndlUamperes at full scale; 
the impedance of such instruments is much higher than that of dynamometer 
instnunentB. The dynamometer tjrpe, when separately excited, can be used 
to measure currents as low as 10 milUamperes, with fair accuracy; one form 
made by Paul has a maximum range of 20 milliamperes. For very small 
eun«nta« reflecting dynamometers are the most suitaole. 

liT. Maasnramenti of high-frequency altematizig currents. 
ffi^Hfrequency currents are best measured by methods involving the beating 
effect of the current. In the Fleming thermoelectric ammeter for relatively 
large cuxrentt the high-frequency current 
flows through a number of very fine copper wires 
stretched between the two terminals. These 
wires are separated in space and each carries 
about 2.5 amp., additional wires being added up 





Fia. 31. — Diagram. Paul high- Fio. 32. — Diagram, high-frequency 
frequency galvanometer. ammeter. 

to 30 amp. of total capacity. At the middle of the centre wire is placed a 
tbermoianetion connected to a sensitive galvanometer, whose indications 
•m pnportiMial to the mean effective value of the high-frequency current. 
Tor tfistruments need in Radiotelegraphy see Bee. 21. 

Imatt hSgh-firaqaanoy ourrantt are sometimes measured with the ther- 
iBogslvaaoineter described in Par. M. In a high-frequency galvanometer 
■Mde Iqr Paul, Hg. 31, a ther mo junction may be formed with an iron wire, 
s. and a eur^a wire, b, looped together in such a way that the high-frequency 
mreot traverses the junction from one side while a sensitive galvanometer is 
waittud to the other. Similar instruments in which the measured current 
COM not flow through the joint are stated to be superior because of the absence 
«f the Peltier effect* (Sec. 2). 

* Douse, C. M. TJU ^(aefrteian. London; Aug. 10, 1910; p. 765. 

**^ DiglzedbyCoOgle 




Sec. 8-108 MBASURTNG APPARATUS 

Another practical method ofmeuuriog Bixudl hij|h-freque&oy eurr«nte i« 
indicated in Fig. 32, where a and a' are two fine wires of diCferent material* 
stretched between two terminals. The wires leading to the galvanometer 
are of the same materiaU, but so connected that a' and bare alike, and a and 
6' are alike. Thus there are two themu^ 
couples in series. Obviously the connections 
should be at the same potential, and thia is 
adjuflted on continuous current with <lxreot 
and reversed readings. In a bridge method, 
the current is measured by the change in re- 
BLBtance. of a carbon lamp (with a very small 
filament) in one arm of a bridge. Fig. 33 : in- 
ductance ooiU, a and a' prevent the liisb- 
freauency current from flowing through the 
bridge. 
108. M«Miirement of raetUler ourrentg. 
T^ »» M- I. # Either of two valuoa of the current from a 

Fig. 33.— High frequency rectifier may be required, the average Talue, 
current measurements — qj. ^^e root-mean-square value. In eonneo- 
bridge method. tjon with storage-battery charging, the average 

value corresponds to the equivalent c.o. value 
and a permanont-magnct typo of measuring instrument should be used. 
On the other hand, the power taken by inoandesoent lamps varies aa the 
square of the current, and the equivalent e.c. current should be measured 
with instruments which indicate tho mean effective value such as hot-wire or 
dynamometer ammeters. 

109. Measure menti of telephone curronti. Telephone currents may 
be measured with a form of potentiometer* or with a barretter (Par. 40) but 
since telephone currents arc of constantly varying amplitude and frequency* 
measurements made by this and the above methods are usually of little 'value. 
Telephonic intensities are usually compared by ear with a telephone, usins 
artificial standardised cables. Where quantitative measurements are r^ 
quired, a high-sensibility oscillograph can be used.t 

BS8I8TANCE MBASITBUCEHTS 

110. Besfst&nce stsndards In general. The practical unit of resist- 
ance, the ohm,' 18 represented by a column of mercury having certain dimen- 
sion<4 (Sec. 1). This standard is obviously difficult to construct, maintain 
and use; and, in general, will be found only in the laboratories of the 
national custodians of the fundamental electrical standards. 

Secondary standards are therefore employed in actual measurements. 
These arc made with metal of high specific resistance, in the form of wire or 
ribbon. Manganin (a copper-nickel-manganese alloy) is most used, 
because, when properly treated and aged, it meets the necessary requiremente. 
These requirements are: permanent electrical and physical cfaaractenstiea; 
low thermo e.m.f. in junctions with copper; small temperature coefficient of 
resistance; and relatively high specific resistance. The completed standard 
must, in addition, be unanected by immersion in oil, or by changes in 
atmospheric conditions. 

111. Classes of reslstsncd standards.* In general, resistance standards 
may be divided into two classes-, standards of resistance, or those used 
primarily for the measurement of resistance; and current standards, or 
those intended primarily for the measurement Of current. 

lis. Oeneral construction of standards of reilitanee. Standards 
of resistance have very small current capacity. They are made in two forms, 
the Reichsanstalt and the N.B.S. (National Bureau of Standards). t The 
former is shown, partially in section, in Fig. 34. The N.B.S. form is shown in 
Fig. 35. The distinctive features of the latter form are that itfs immersed 
in oil and hermrtically sealed. This prevents the abdorptidn of moiature by 

* Drysdale. C. V. "Alternating-current Potentiometer for Measuring 
Telephone Currents/* London Blertrician, Aug. 1, 19t3. 

t CJnti, B. Keport of Second International Conference, European Tele> 
phone and TelpRraph Administrationa; 1910. 

% Bureau of iStandards Bulletin, Vol. V, 1908, p. 413. 

140 — I 

L),g,l,.edby*^OOgle 



MEASURINO APPARATUS 



Sec.S-ll3 



the riwUftc and the eonaequent expannon of the fine wire used in the larier 
mintanrm * Both forma are intended to be hung from mercury cups by 
KKans of lucB, and Buepended in an oil bath in order to measure the tempera- 
tare more accurately. The N.B.S. form ia made only in sises larger than 
I ohu. 





Fig. 34. — ^Standard resistance — 
Reichsanstalt form. 



Fio. 33. — Standard reeiutance — 
N.B.8. form. 



US. Current standards ar« mad* In two forms, the Keiohsanstalt and 

•fa'-eoolad- The Reichsanatalt standards are made in two types, the small 

Kttern for moderate currents, and the large pattern (in low resistancen) 
' Large currents. The Bmall-pattem form is similar in appearance to Fig. 
34 except that for 1 ohm and less, separate potential taps are pruvided. 
They are suspended from mercury cups in an oil bath for cooling purpoHCs. 

Tbe current ratings assigned by Otto Wolff and the Leeds and Northnip 
Company to small-pattern, Ileichsanstalt form of standards are as follows: 
When used for resistance measurements 0.3 and 1.0 watt, for still-air-cooling 
sad oil-crx>Iin^ reroectivcly. When used for current measurements with a 
temperature nac* of^lO deg. cent.. 2.5 and 10 watts for still -air-cooling and oil- 
coohns respectively. Large-pattern low-resistance current standards have 
capacities from 100 watts to 2,500 watts and over. 

114. Air-cooled current standards employ sufficient material to permit 
of UM in air without exceiwive temperature rise. While they are not as 
ftccurate or as reliable as 
the Reichsanntalt form, 
they are amply satisfactory 
for much commercial work, 
espeeially where oil baths 
woold be inconvenient. 
Fig. 36 afaowa a Leeds and 
Northnip Co. resistance, of 
0.00002 ohm, and 2.000 
amp. capacity, for which 
an accuracy of 0.04 per 
cent, is claimed. 

lif. Iteasiirements of 
conductor resistance. 
There is no sharp disiino- 
tion between materials 
commonly called eonduct- 
oct and thoee called in- 
sulators. Reaistances of 
the former class may, however, be relatively high or relatively low, and 
eertaia methods of measurement are especially applicable to each class. 

11%. The faU-oC-potentlsl method consists simply in noting the voltage 
drop with a known current flowing through the renistance, and cntnilnting 
th* resistance from <W»m*« law, R — E//. This methrnl in not wuitiible for 




Fia. 36. — Leeds ft Northrup air-cooled standard 
resistance. 



*BaKau of Standards Bulletin. Vol. IV, 1907, p. 121. 
141 



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Sec 5-117 



UBASURINO APPARATUS 



> 



very high or very low resistances and the accuracy depend* upon the i 
meat of two unknown quantities with indicating; instruments. Furthermora 
the current required to give a readable drop may cause overheating. The 
method should therefore be used with caution and only where acciu-ctcy M 
subordinate to simplicity and convenience. The potential should be 
measured, when possible, between points well within the current connec- 
tions, especially when the rt^sistance is low and the current is high. Greater 
accuracy can be obtained by substituting a standard resistance in place of 
the ammeter, and noting the drop across it, and across the unknown reaist- 
anee, in succession. The latter is then equal to the ratio of the two reaclinss 
multiplied by the standard resistance. The accuracy will be greatest^ vrhen 
the two reaistanoea are nearly equal. 

117. Bridge xnethods are the most accurate for resistance measurementa 
because: (a) they are lero methods; (b) comparison is made directly with 
standardised resistances, the accuracy of which can be made very high. The 
principal types of bridges are known as Wfaeatstone, slide-wire, Ct^rey- 
Foeter and Kelvin. 

118. Wheatitone brldffe. The Wheatetone bridge is most i^norally 
used for the measurement of all but the highest and the lowest reeutazioes. 
fig. 37 shows the theoretical arrangement of a Wheatstone bridge ^rhere 
r, n, and n are accurately known resist- 
ances and r« ia the resistance to be meas- r-^i 
ured. When usin^ the bridge, the variousj i^ ' 
resistances are adjusted until the galva- 
nometer, G, shows no current flowing; 




1000 leo w . M 100 uno 

3p- "^^ 



100 100 '{40 30 «0 I ■ 

SI I ' 

I 400 loou yio 1000 w oo 



M 



Kt^J\^Ki 



B 



fW\- 




Fia. 37. 



-Diagram of Wheatstone 

bridge. 



Fia. 38. — Wheatstone bridge — 
Postoffice form. 



then, r>— (n/n)r. The battery switch, iSi, should always be closed before 
the galvanometer switch. Si, in order to protect the galvanometer from the 
momentary rush of current. The galvanometer and the battery may be 
interchanged without affecting the result (Sec. 2, Par. SO). 

119. Fonni of Wheatitons bridffsi. These bridges are made in a 
variety of forms. In most forms the resistances, r, n and rs, consist of a 
number of resistance coils or units carefully adjusted to various multiples 
of 10 and so arranged that they can be conveniently connected in and out of 
the circuit by means of plugs or switches. The resistancea, n and n (Fig. 37) 
are commonly called the ratio arms and r the rheostat arm. A very early 
form, which is still in use in small portable sets, is the Foitoffloe pattern, 
shown diagrammatically in Fig. 38. Coils are cut out by short-circuiting 
them with plugs, so that there may be several plug-contact resistances of an 
unknown and variable amount in a given arm. In the Anthony form^ anown 
diagrammatically in Fig. 39, this objection is overcome by arranging the 
coils of the rheostat arm on the "decade" plan in which there are nine l-ohm 
coils in the "units" division, nine 10-ohm coils in the "tens" division, etc. 
Any number of coils in a given division can be connected in circuit by 
changing only one plus. In many later types, the ratio-arm coils are alao 
connected on the decade plan, which in addition to eliminating plug-contact 
resistance errors, permits interchecking the coils. Furthermore, the decade 
arrangement permits the use of slidiQg-brush or dial construction instead 
of plugs. 



142 



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UEASVRTUO APPARATUS 



Sec.S-117 



Q~5^-6 C h 




IM. Vm tt Whaatatoiu BrldfM. Such bridcea are best miit«d for 
J raistanoea of the order of about 1 ohm to 100,000 ohms. Accor- 
I of the order of O.OS per eent. are obtainable with a Srat-claas bridge 
if the nnknown remstanee is intermediate in value between the limits last 
named. The maiitniim precision is obtained when the four arms are 
•qssl; hence this condition should 
always be approached as nearly as pos- 
■hie by keepinc n/n amall, and n and 
n ss nearly equal to r as convenient. 
A catvanometer with lOO ohms to 600 
ohms resistance will be satisfactory for 
seaily all rlnswn of work. The resist- 
SBCe coils will diaaipste about 1 watt 
vithont OTcrhemtiiis, but care should be 
tskstt that the emrant does not become 
««saiT« when the ratio becomes larce. 

in. TIw ■Ud*-'Wlre bride* is one 
of the cariiest forma of the Wheatstone 
llridce. It is convenient and rapid 
where many similar measurements are 
to be made. It di£fera from the stand- 
ard Wheatstone bridge in the respect 
tlaat balance is obtained by varying the 
ntio Tt/n, instead of the resistance r 
(Hi. 37). Thia is accomplished by 
neriac the contact. 6, Fig. 40, alone s 
«ire, a<^wfaich forma the resbtance n 
+rx. This wire should be uniform in 
o n ss s rrti on and homogeneous, so that 
the resistance per unit length will be 
coHtsnt. At exact balance, the ratio 
<< the Irngtba bc/ah — n/n; and r.- 
trt/n)r, as oefore. The precision is a 
siaiinnim when the sliding contact is 
at the centre. When the slide wire is 
ifacrt, the precision decreases rapidly 
with settiB^ toward either end. The 
itsfth may be increased, in effect, by 
UMtrtiag equal resistances at n, n , 
vUdi iaereaaea the sensibility, but also 
decreases the permissible difference bo. 
twten r and t,. 



(kX30000CH 
©OCSDOOOO 

©ooooooo 

SSDOOOOOO 
©OOOCSDOO 

©ooooooo 

©OOOOOOSD 

©ooooooo 

©OOOOOOO 

©pqpopop 



Flo. 39. — ^Wheatstone bridge — 
Anthony "decade" form. 



US. Tha Oaraj-Tostar bridga is particularly adapted to the compari- 
OB of low leaistaneea. The distinctive feature is the elimination of the 
eoataet Teaistanoe and other unknown resistancee, in the arrangement shown 
in Fig. 40, by taking two readings. The bridge is first balanced with the 
eoatact at x. The resistances r and fx are next interchanged and a balance 
sbuined at zi. If the resistance of the slide wire per unit length is p, then 

rs— r— p(2i — z). This method 
is especially aidtable for com- 
parison of standard resistances 
with each other and for tempera- 
ture coefficient determinations. 

111. Tha XslTin doubla- 
bridfa is espedally suitable for 
measurementa of low resistances. 
It ia the most generally used 
form, even in the most precise 
work, because of its accuracy 
and convenience. The principle 
is shown in Fig. 41. The resist- 




Fio. 40. — Carey-Fcater bridge. 



■ass of the connection between r and ra is made nejdigibly small and the 
Hidgs sssames the form of the Wheatstone bridge (Fig. 37) with the addi- 
lioa ai aa extra pair of ratio arms, a and fi. When a balance b obtained: 



i^.'i^i /_l_\ /:?_i\ 



(W) 



143 



yGoogle 



SecS-iaO 



USASVRtNO APPARATUS 



In practice, n/rt is kept equal to a/p and the resistance d Is made nexlisibly 
small. Then Tm^fv/r\, as in the Wheatstone bridge. 

In the Wolff bridge, Fig. 42, the ratios n/n and a/0 are aatomaticslly 
adjusted rimultaneouBly, by sliding contacts on the four dials. In the i^toc^km 
and Northrop bridge, Fi«. 43, both r and the ratio n/n an adjusted. 



■o- 



l" 



Fig. 41. — Diagram of Kelvin double bridge. 



Specimen 




Fia. 42. — Kelvin double bridge — Wolff form. 

IM. Oonduetivity maaiuramanta. The specific conductance or 
conductivity of a material is the reciprocal of the specific reaistanoe or 
resistivity. The relative conductivity is the ratio, expressed in per cent^ of 
the specific conductance of the sample to that of a standard material. The 
relative conductivity may be based on equal masses or equal volumes. The 
former is in most common use because conductor metals are usually sold on 
a weight baais (see See. 4). 



144 



yGoogle 



USASUBIt/a APPARATUS 



Sec. S-124 



IH. ConduetiTlty stendarda. The present official standftrd of the 
A. I. E. £. ia the Intanukttonal Annaalsd Coppar Btendard,* defined u 
(oUovb; 

Maaa-rMistlTitr at 20 deg. cent. : 

0.1532^ ohm (meter, gram) 
875 . 20 ohma (mile, pound) 
Volnzn»-TasUtlTlty at 20 deg. cent, and 8.89 decidty: 
1.7241 microbma (cm.*) 
0.67879 microhma fin.n 
10.371 ohma (mil, (oot) 
For ea rl i er standards of copper rcaistiTity, see Sec. 4. 



K5 
Ba. 




> > > < t 



u^ 



T-Y 



«B 



1 



L ^-Q 

Qa. 



Pi<i. 4-3. — Kelvin double bridge — Leeds & Northrup form. 

US. Method* of maaaurinc eonduotlTitr. Conductivity may be 
determined by calculation from the measured rcBistance or Dy dveet 
eompariM^a with standards of conductivity. When the conductivity is 
to be calculated from the resistance, the spaoimen must have a uniform 
eroai-eeciion. The resistance of a definite length is carefully determined, 
tbe temperature being noted. Then the resistance of a piece of copper having 
100 per sent, conductivity and the same weight and length as the specimen 
(or, for volame basis, the same cross section and length) is calculated from 
the stated definition of the standards. The ratio of uiese two resistances is 
the conductivity of the spedmen. The direct comrarison methods employ 
conductivity bridges which are adaptations of the Kelvin bridge. They are 
intended for eommerdal work, where speed combined with moderate accuracy 
ifl important. 

Scale H 




rig. 43a.- 



Scale/ 
-Diagram, £oope's conductivity bridge. 



in. In the Boopa'i oondaetivltgr brldM,t the conductivity of a speci- 
men of wire is read oirectly from a graduated scale. The principle is shown 
ia F%. 43a where r, is the specimen to be measured, r a standardised wire and 

ri Tta,0, are the double ratio coil. All four of the latter are made equal, 
* Standardiaation Rules, A. I. K. E., Dec. 1914 and Bureau of standards 

CSrealar No. 31. CopP« Vr\ie Tables; 2d edition, 1913. 

tHoopea, Wm. '"A New Apparatus for Making Direct Measurements 

of Elee^l Conductivity," BUetrieal World and gnginttr, Nov. 14, 1903. 



10 



145 



yGoOgk 



Sec.S-128 



MEASURING APPARATUS 



^ 



about 300 ohms each, in order to eliminate the effect of contact 
at a 6, c and d. When the bridge ia balanced, the nnutanee between c 
and d on r, ia equal to that between a and b on r. The ui^own specimen 
r. is cut to a certain definite length and carefully weighed. The contact, 
b on the standard is then set at the point indicated on the carefully crsdiuted 
scale H, which corresponds to this weight. Then the resistance, oi, la equal 
to that of a piece of wire having 100 per cent, conductivity, a length equal to 
100 parts in the scale I and the same weight per unit length as r,. Contact 
d is shifted until a balance is obtained and the conductivity is read direetljr 
from scale I, 100 scale divisions corresponding to 100 per cent. eonduoUvity. 
One standard is provided for every three aires of wire in the Amenoan 
(B. * S.) gage. The standards are usually of the same material as that beinc 
tested, so that the temperature does not have to be observed. 

US. BeiUtance ol r»U Jolnta. The testing of rail bonds oonaiata 
in determining, either, (a) the ratio of the resistance of a given lepg:th of rail, 
including a bonded joint, to that of the same length of continuous rail; 
or (b) the length of solid rail which has the same reaisUnce as the joint. 
The resistance of rail bonds is usually expressed in the Istter manner, whether 
measured in that way or by the former method. Three methods are em- 
ployed: millivoltmcter, bridge, and opposition. 

1S9. MilliToltmatsr method of maaiurlnc rail bond*. In the milU- 
voltmeter method, simultaneous readings are taken with 2 millivoltmeters. 
one connected across the bond and the other across a defimte length of rail. 
If the current fluctuations are not too rapid, only one instrument is noees- 
sary, provided there is a suitable arrangement of keys to change the con- 
nections in quick auoceeaion. 

130 In th« BoUsr bond testar the principle of the slide iriro form at 
Whoktlton* bridge is employed (Kg. *4). Balance is obtained by movinc 

the contact B back and forth _ 
At balance, ab/be— (ri + m'i/ 
(ri+n); where at •• resistance 
of bond and be — resi8tan«)e of 
the standard length of rail. 
The resistances n and n Have 
the effect of extending the slide 
wire and pravi<ting greater 
accuracy (see Par. ISl). In 
the actual instrument, the alide 
wire takes the form of ■ <arcle 
and the scale is grsduat^d to 
give the resistance directly in 
terms of the number of feet of 
the solid rail being tested. 

ISl. The Conant bond 
tester is an example of the 
class in which the drop across the joint is opposed to that aerosa a length of 
solid rail the outer contact on the latter (c. Fig. 44) being moved alons until 
the two potentials are just equal and opposite. The detector is a telephone 
receiver in series with a make and break device operated by a clock. 

ISt. Iniulatlon resistance. The resistance of insulating materials 
is usually measured by deflection methods. In the ease of resistances 
of the order of 1 megohm and less, a Wheatstone bndp may be used, bat 
the accuracy will be low becauso of the extreme ratio required (Par. lai) 

and the low insulation resistance of the bridge. j o ^. 

Two leneral classes of deflection methods are used: (1) direct deBection 
and (21 leakage The direct-deflection methods involve a simple application 
of Ohm's law" the current bring measured with a voltmeter used as an am- 
meter or with a galvanometer. 

MS Dir«ct-deaection method (Insulation reilatanoe). When 
the resistance is of the order of 1 megohm an ordinary voltmeter 
irill ^o results which are sufficiently accurate for most Purposes Two 
readings ore taken, one with the voltmeter directly across the battery or 
geMrator. and the other with the resistance to be measured connected in 
wries with the voltmeter. The rewstanoe is R-r. (d-dO/di; whera r.» 

146 




Fio 



Diagram, Roller bond tester. 



MSASURINO APPARATUS See. 3-134 



of voltnwtor ({ha creater the naiatance per toH, the bighor tb« 
preoaon^, ^w deflection of roltmeter in first reading, di > deflection in gec- 
ond readme. Obvioualy a portable galvanometer with series resistance may 
be oasd as a voltmeter. 

Wlian tha rMUtene* U modar^taly Uch, a higb-resistance reflecting 
IVAnonTal nlvanometer is employed. Fig. 46 sbows tbe diagrammatic 
•irangement lor measuring tbe inaiuation of a cable. The measurement 
is made as follows: after the galvanometer shunt, i, is set at the highest 
nlue (Par. 19 and BO) and r, is short-circuited, the main circuit is closed. 
The shunt is then decreased until tbe largest readable deflection is obtained. 
A reading is taken after 1 min. This procedure is then repeated with tbe 
standard resistance r, (usually 0.1 or 1 megohm) in circuit and the specimen 
skort-drenited. The resistance of tbe specimen in megohms is: R^G/di»; 
wheie di— first reading, s— multiplier corresponding to the shunt setting 



i' 



Fio. M. — Diagram, insulation resistance of cable. 

(that is, 1, 10, 100, 1,000 or 10,000) and(7> galvanometer megohm-constant 
'Par. M) as obtained from the second measurement. Tbe constant is 
^r«^,; where d' deflection, s* shunt multiplier, r«M standard resistance 
IB megohms. 

U*. TiMlraf mathod of inaainrinx InsuUtion rasistenea. Very 
Ugh reaistancea snch ss the resistance of porcelain and glass, and surface 
leakage reeistanea of Una inaulators, are best measured by the method 
a< leakage, also known as the losa-of-cbargs method. This method is based 
oa the theory that if the insulation resistance of a condenser is infinite, it 
•31 retain a charge indeSnitaly; whereas if the resistance between tbe con- 
denser terminala (either the uitemal resistance or a resistance connected 
eXcmaily) ia finite, the rata of loas of the charge (or leakage) will be a meas- 
■te of that reaiatanoe. The principle of this method ia shown in Fig. 46 
where the reaiatanoe to be measurea, r, ia connected in parallel with a con- 
denser C. Kejr a is dosed and immedutely opened, thus charging tbe con- 
4eaaer. Key h ia olossd immediately after a is opened and the deflection, 
A, of tbe ballistie ^Uvanometar noted. The process is repeated, a being 
left open a definite tune, t seconds, before b is closed and a second deflection 
A obaemd. The waistance in megohms is then: 

r — ' j^ (megohms) (13) 

2.303CL 



nog..(D 



"here C is tbe capacity of the condenapr in micro-farads. 

The insnlation reawtanee of the condenser is usually not infinite. 
Conection should be made by measuring the resistance of tne condenser in 
aamilar aminer, r being disconnected. If n is the resistance of the condenser 
aad n the resistance obtained above in Eq, 15, the corrected value is 

r'- — — — (megohms) (16) 

Uf. ItMMiraBMnt of spaeiflo reci<tuie« (roalatlTity) of loUd 
niiilatliiy mstoriate. This is obtained by calculation from the resist- 
•aee be t wee n two similar metallic electrodes of known area in intimate con- 
tjwt with tbe opposite and parallel faces of a specimen of the material. 
n»-f«0 maka* convenient and satiafaetory electrodes if backed with 
testliag paper aad sufficient weight to insure good contact. 

Ut. Tha gpMlfle raalstene* of liqnid Inaulatinf matarlala may be 
■Pfnusiantely determined by pouring a specimen into a round glass cylinder 

U7 

DigiiizMbjV^iUUyHJ 



SecS-137 



UBASURING APPARATUS 



» 




Fia. 46.— Leakage 
method of meaauring 
insulation resietance. 



or graduate in which two circular, cloeety 6tting diec electrodes are supported. 
One of the eleetrodes should be movable so that the resistance of columns 
of several different lengths can be measured. The first measutement should 
be takpQ as the zero or base reading and the results checked by cjilculation 
of the increase in resistance and the corresponding increase in the spacing 
of the electrodes at different settings. 

187. Precautioni lif meaatuinff Inaulation rsaUtanca. In the meaa- 
uremcnt of the insulation resistance of apocimens having electrostatic capac- 
ity, sufficient time should be allowed for the specimen to become charged, 
that ia, until the deflection becomes constant, at a 
minimum value. This usually takes place vitnln 1 
min., except in long lengths of cable. In order to 
eliminftte uncertainties in this oonnection, it is 
customary to specify 1-minute "electrification."' 

As the apparent insulation resistance varies with 
the testing potential, one hundred volts is usually 
prescribed as the mixiimum pressure that should be 
used. 

Leakage over the surface of wire or other speci- 
mens may be a source of much trouble in damp 
weather. In wires and cables, the lead or braid 
should be removed for 2 or 3 in. from the ends and 
the exposed insulation coated^ with hot, clean 
paraffine; or, just before measuring, these prepared 
ends may be carcfullv dried with an alcohol, Bunsen 
or other flame free from carbon. As a further pre- 
caution, a "guard** circuit may be arranged as shown by the dotted lines in 
Fig. 45. This consists of a few turns of fine copper -wire twisted around 
the insulation close to the copper conductor and conncct>ed to the battery 
side of the galvanometor. In the case of solid specimens, the twisted wire 
is replaced with a ring of tin-foit as shown in Fig. 07. 

BpsetniMia haTlnc •lootrostatie emprndty should be put in a neutral 
oondition by rapidly reversing the current a number of times, beginning at 
a low rate of reversals and gradually increasing. Where the capacity is 
high it may be advisable groidually to decrease the applied voltage at the 
same time. 

The side of the circuit which contains the galvanometer should be well 
insulated throughout. The battery also should bo insulated as thor- 
oughly as piMwibTe: this is a relatively easy matter when dry cells am used. 
The important point is to insure that all current passing through the speci- 
men, and only that current, passes also through the galvanometer. 

The galvanometer should, preferably, have a high resistance (order 
of 1,000 ohms) and a megohm sensibility (Par. IS and S4) of several hundred 
megohms. The temperature 
should always be noted, be- 
cause of the large coefficient 
which most insulating mate* 
rials have. 

1S8. Msaturinc the insu- 
lation retistanee of circuits. 
The insulation resistance of a 
"dead" circuit is conveniently 
made by the voltmeter method. 
When there is no source of 
e.m.f, available, various port- 
able instruments described be- 
low are especially applicable and convenient. (Also see Sec. 21.) 

When the circuit is "alive" the following method may be used.* Fig. 
47 represents diagram maticaliy a system with lamps and motors connected. 
The resistances .Vi and Xt represent the insnlation resistance from the posi- 
tive and negative sides respectively to ground. 

Xi» — .— — t andAt« ; (ohm»> (17) 

at at 



Bi 






fx, 



Fio. 47- 



-Iniiulation resistance of ' 
circuits. 



live" 



* Northrup, K. F. "Methods 
McGraw-Hill Book Co. Ino. p. 910. 



of Measuring Electrical Ke:<i8tanre;' 



148 



, Google 



MBASVRIXG APPARATUS 



Sec.»-139 




Fia. 48. — Evenbed Megger. 



when S^raaistanod of Tcdtmeter; i>* deflection (scale diviaioiifl) corre- 
Rxmdisg to circuit voltage* R'» <Ji ^ deflection corresponding to Vi: di^d^ 
Hctua eorTesponding to Vt. 

Should the aystem be continuous current, a D'Arsonval-type volt- 
iwter IB preferable; if it' be alternating current, an electrodynamcmeter- 
t]rpe instmrnent ahould be used. This method in general will measure 1 
la^Dhm with lufficient acciiracy to check specificationa. If the resiatmnee 
n onr 1 megohm a galvanometer method is more accurate. 

119. Foitable iikstrumenti for the direct maaniremant of Intnla- 
ti«i rMlatanc* are elaaeed either as testing sets or ohmmetera. Tasting 
Mti range from a simple Wheatatone 
badge with aelf-eontained galvanometer 
sad battery, to elaborate cable-testing seta 
which include a small Wheatatone brid^, 
tikaadard 0.1 megohm reaivtance for lo- 
nlation testa by the aeriea galvanometer 
aetfaod, and a standard condenser for 
ofiacity measarementa. 

OhmmatavB indicate the re^iatanee 
diieetly. In inatrumenta of the Saga 
tfV^, the prineii^e of the alide-wire bridge 
ia cnployed. A ecale beneath the rilde 
ebe ia calibrated directly in ohma, ao that 
afcn bahuee ia obtainted, the resiatanoe 
i> read off directly. The range can be extended bv means of a number of 
Cerent ratio arma, a aeparate scale bein^ provided for each. Where alter- 
nating current ia neceaaary, aa in meaaunng electrolytes, an induction roil 
ii introduced in the battery circuit and a telephone replaces the usual galva- 
Mmeter. This type ia not auitable for measuring high resistances. 

Tht Kvarshad "Maggar" ia an obznmeter wbirh indiratea the 
migtanoe by the movement of a pointer over a calibrated scale. * The 
principle employed ia indicated in Fig. 48, where ii ia a coil in aeries with the 
Kaitance to be meaaurcd and B, Bt are coils, which, with the resistance R, 
are connected to a hand-driven generator D. All three coils are rigidly 
coupled together and are connected to the circuit b^ fine copper stripe 
vbicb exert no controlling force. When the generator la actuated a current 
3o«t tbrou|rh coils B, Bi proportional to the e.m.f. generated. If the ex- 
ternal circuit ia open, B and Bi arc deflected to the position where the Icaat 
flux from the permanent magneta M Mi will inter- 
sect them, that is, opposite the gap in the C-ahaped 
iron piece about winch the coils A and Bi move. 
The pointer then stands at "infinity" on the scale. 
If now a finite resistance ia connected across the 
terminals, the current flowing in A ^ill produce a 
deflecting torque toward the position shown in the 
figure, and, as the system moves, the coils B and Bi 
exert an opposing torque of constantly increasing 
magnitude. Hence the system cornea to rest at a 
point where the two forces are balanced, the position 
depending upon the amount of the external resist- 
ance. 

140. Kaaiurament of tb« rtaUtanea of elae- 
trolTtas. Electrolyte reuatancea are more difficult 
to measure than metallic resistances because of the 
counter e.m.f, of polarization. The several nii»thoda 
in use are baaed on the method first proposed by 
Kohlrausch, that ia, a simple bridge arrangement in 
which alternating current ia employed instead of 
direct current. 
A atandard Wheats! one bridge may be used, jjut 
&iUda-vln ^pe is found more convenient, especially if the slide wire Is a 
^(a>f one wound apiraUy on a marble cylinder. When such slide-wire resist- 
*A« ia a aeparate pieoo of apparatus, a bridge may be eiurily made up and 
wed as mdicated in Fig. 49 where B is a non-inductive resist ince box and r, 

'Biddle J. G. Circular No. 740; Philadelphia, Pa.. 1910. 




Fig, 49.— Resistance 
, of electrolytee — Bridge 
method. 



149 



),g,l,.edbyC00gle 



Sec. 8-141 



USASUniNO APPARATUS 



the eleciroly t«. If the sUde-wira scale is divided into 1 ,000 parte, the ] 
aaoe of the electrolyte ia, at balance. 

If the flouroe ie alternatinK-ourrent power of oommeroial frequencies 

an alternating -current galvanometer (reflecting electrodynamometer) may 
be used, the fixed coils being connected in aeriee between the source. S. mjui 
the bridge and the moving coil in place of D (Fig. 49). A Vrsel&iul mcUIa- 
tor (Par. SM) is very satisfactory as a source of energy becauee the w»y« 
form ia a pure sine curve and the frequency ia 
sufficiently nigh to make the telephone sensitive. 
141. Bpeolflc retUt&nce of electrolyses. 
Where the apeoific resistance or renstivity is re- 
quired, a column of the liquid of known dinsen- 
Bions must be isolated. Fig. 50 shows a sstisfao- 
tory method.* The glaaa tube ia about 20 cm. 
long. 1 cm. internal diameter and open at both 
encu. The electrodes are of gold or platinum., the 
lower one being fixed in position and performted* 
while the upper one ia adjustable. The average 
cros»-section must be carefully determined, prefer- 
ably by volumetric meaaurement with mercury. 
The temperature ia readily kept constant by 
stirring the liquid in the containing vessel. 

141. internal reaUtance of batteries. This 
measurement involves difBcultiea because of polar- 
isation. One simple direct-current method is 
Fio. 50. — Specific resist- aa follows. The e.m.f. of the cell or battery is 
ance of electrolytes. first measured on open circuit. The circuit is 
then closed through a known resistance and the 
e.m.f. measured again quickly before polariiation begina. The roslstance is 




B, 



■voltage before and after cloaiiic 



where R. known reaiatance, E and Bi' 
oircuit, reapectively. 

This method assumea that the internal reaiatance will remain oooatant 
under all oonditione, which la not alwaya the oaae, eapeoially in dry oella. 
In a modification of this method, both readinaa are taken with the circuit 
cloaed, but with two slightly different values of R. Then 

(Ei-Ej)RiRi , , , 

'-EJii-BJi,- <'"™'> t20) 

where Ri and Ei are the first reaiatance and e.m.f., respectively, aad Jts 
and Et are the corresponding values with the second resistance. 

In general, euch direct-current methods should be used only with primary 
batteries of very low resistance and with secondary or storage batteries. 
Alternating-current methoda are more reliable. 

148. Alternatlnff-ciirrent method of maaiurinff internal resiat&no* 
of batteriaa. The Kohlraunch bridge shown in Fig. 49 can be uaed in this 
method, by inserting the cell or battery in place of the electrolyte cell. 
Without resistance R' connected, the resistance of the cell will be 

If the resistance R* ia oonnectod, the resiatance of the cell with a current 

corresponding to R' flowing, will be 

IM. BffeetiT* reaiatance of altemating-ourrentoiroutti. Thepaasace 
of alternating current through a circuit is opposed by the ohmic resiatance, 

* Northrup, E. F. "Methoda of Measuring Eleetrical Reaiatanoe," 
McGraw-Hill Book Co. Inc., p. 241. 



160 



V Google 



MEASVRINQ APPARATUS SeC. 8-145 

kbo by Uir rMiBtance-equivalaat of all the enaroy loaaea exeapt the Ion 
due to ohmio reaiatanee, and by the reaetanoe. The *'ohmio reaulanee" 
ii the resistanoe to the paeaage of continuoua current and is therefore 
xaeaauied with continuous current by the methods previously described. 

IW. Tha efleetlTe or altcnuttlnc-euzrant rstUtanoa is that value ' 
of resiatance which repraaonts the total energy Loaa. It includes in addition 
to the ohmic resistance^ the effect of any other source of loet energy, such as 
iroD loaaea in a zna^etio circuit, dielectric losses, and induced currents in 
a Detghboring circuit. This effective resistance produces a potential drop 
which is in phase with the current. The simplest method of determining 
it ia from the relation : W -> VR, where W — watts measured with a wattmeter, 
/^earrent (amperes) and i2 -> alternating-current resistance (ohms). 

14>. Kaasurement of iflactlTa rsalatanes. When the power is small 
and the power-factor is low, two-circuit electrodynamometora (Par. M) 
■ay be used. The exciting current must be in phase with the current 
tknogh the reaistanca to be measured, in order to insure that the reading 
obtained when the moving coil is connected across the resistance ia the oom- 
pceent in phase with the current, that is, the alternating-current resiatanoe. 
This condition can be eatablished in several ways: (a) By connecting the 
fixtd e^la aeroes a non-inductive resistance which is in series with the reaiat- 
tnee to be measured; (b) by connecting the fixed coils to a phase shifter 
jPar. nS) which is first aidjuated^ the moving coil being connected to a non- 
ladnetive reeiatance in aenea with the resistance to be measured, until a 
naximum deflection is obtained. A more sensitive method is to connect a 
coadenaer in eerie* with the fixed coils and adjust the phase ahifter tor sero 
dtSeetioo. The dynamometer can be calibrated on a non-inductive reoist- 
aaea or on eontinuous current. 

MT. mMAtatone-brtdn methoda of maMurinc aSestlTa rail»t»naa 
Bay also be uaed by providing facilitisa for obtaining a balance for both re- 
■mnce and inductance. The two "ratio" arms should be non-inductive, 
sad the "rheostat" arm should contain both a variable resistanoe and a 
Tiiiable inductance, so that complete balance may be obtained. The 
detector must indicate both atatea of balance and should be a two-circuit 
ckctrodynaznometer or a synchronously driven reversing key fPar. t9). 
When using the former instrument, a resistance balance is obtained with the 
Exed coils excited from the same circuit, that is, in series with the bridge 
or aeroaa a ahunt. Inductance balance ia obtained with the fixed coua 
tscited from a areuit 90 deg. from the first, the moving ooUa being connected 
•cross the bridge in the usual manner. 

1«. Tha measurement of reaetwioe and Impedance of an alter- 
Bating-enrrent circuit may be effected very simply with an ammeter, a volt- 
■eter and a wattmeter, as indicated by the following relations, where Z — 
ifflpedanee in ohms, X — reactance in ohms, R — alternating-current resist- 
aoee in ohms, IF ••power in watta, J — current in amperes, £ — total potan- 
ul-drop in volts, cos f — power-factor— W/Bl. 

(a) Z-j, (6) Z—^J~^^, (c) X-j^ tan». (d) X-Z sin » (23) 

POWXS MXABTrSnmfTB 

M>. Oenaral eonridarationa. When a quantity of electricity, g, is 
piMpri throiigh a circuit against a difference of potential, e, the work oone, 
thst is, the amount of energy expended, is qe. Power is the rate of expend- 
iag ener^ and at any instant is tBq/dt — ie, because dq/dl — i, where i and 
• aie the instantaneous values of current and potential, respectively. Power 
iimsiij in watts is the energy expended per second, or, W — QB/t, where 
(^—qaaatity in coulombs, £— potential in volts and t — time in seconds. 

1(0. CoBtinaotu-eiirTant iiowar. In a circuit supplied by a battery 
or a eoBtinnoas-current generator, energy is expended at a uniform rate; 
•eaee. tin/at^QB/t-IB, where Q-quantity in coulombs, E-eA.t in 
wfcs. t»t»nie in seconds and J — current in amperes. The power in such 
oxeoita is usually determined by measurins the current and the potential, 
^roaltanfoasly. Wattmeters may be used, but they are leas sccurate^than 
permaaeat-masnet instruments, principally because of the non-uniform 
fale. giasler temperature etrora and greater aensitiveneas to stray magnetic 
Mda 

IJl DigilizedbyV^iUUyiC 



{ 



► 



Sec. a-151 MBASURIHQ APPARATUS 

151. Pulflftting pow«r. Where there are instantaneous ▼arwtiocu 
in the current and the potential, the power varies from instant to inatanl. 
The averase power will be the average of the products of correapondia£ instan- 
taneoua vahiea of current and potential and it can be measurea with Mriet ae- 
. curacy only with watt-meters of the dynamometer type. In rectifier circuits, 
the power consumption of a storage battery or a motor can be appro xiiiuitelsr 
measured with a voltmeter and an ammeter of the permanent magnet type. 
Such instruments would give a more nearly correct result than dynamoizketer 
instruments. On the other hand, the reverse will be the case with a load of in- 
candescent lamps or heating devices. The error will de|>eDd upon the "wmve 
shape and the character of the load. The safe method is to use a dyna- 
mometer-type wattmeter. 

IM. Altematinf-current power. The power in an altematins-oui^ 
rent clrowt, at any instant, is the product of the current and potential at 
that instant. When the load consists only of 
resistance, the ourrent wave, /, and thepotei^ 
iiaX wave, E, are in phase as shown in fls- 51, 
and the power-factor is 100 per cent, or unity. 
If the products of the instantaneous vaJnee <rf 
current and potential are plotted, the curv« J* 
is obtained. The average value of this curve 
is the power equivalent of a continuous cur- 
FiG. 61. — Relation of cur- rent producing the same effect. Also, W^ 
rent, e.m^.f. and power in EI, where IF — average watts, J?>-mean 
a.c. circuit. effective volts and / * mean effective aiup>cre«. 

These values of potential and current are in- 
dicated by instruments in which the deflections arc proportional to the 
square of the current. 

168. When the power-factor it less than unity, due to the fact t4iat 
the circuit contains inductance or capacity (or tho equivalent), the current 
and the potential will not be in phase. In the case of an inductive load., t^he 
current will lag behind the potential, as shown in Fig. 52. The powrer 
curve then will not be all on one side of the axis, but a part will be negative. 
If the current lags sufficiently, Fig. 53, the power curve will be positive balf 
of the time and negative the other half; the average power will then be aero 
(or lero power-factor). This difference in phase, or time relation between 
the current and the potential, iS called the phase angle and is usually ex* 
pressed in degrees, an entire cycle being 300 deg. If the current and the 




A A" A 




Fio. 52. FiQ. 53. 

Figs. 52 and 53. — Relation of current, e.m.f. and power in a.c. circuit. 

voltage are sinusoidal, the average value of the power is W^BI oos 0, 
where ^ is the phase angle. Therefore if the current and the potential are 
not in phase, it is necessary to know the value of the phase angle if the poorer 
is to be determined from the current and the potential. Fortunately, 
instruments called wattmeters are available, which not only automatioalTy 
integrate the power curve, but take into account the factor, cos 9. 

164. Precision measurements of power must be made with an instru- 
ment which is equally accurate on continuous and alternating currenta, in 
order that it may be calibrated on continuous current. Such meaaurementa 
are most accurately made with reflecting eleotrodynamometers ix^ 
which deflections are measured by means of a mirror, with a lamp and scale 
(See Par. 8S, 64 and 97.) The nied coils are often divided into several sec* 
tions, which may be connected in various series and parallel combinatioiiA 
to give large deflections over a wide range of power intensities. Instrumentci 
of this typo made by the General Electric Company have current capa.c-> 
ities from 5 amp. to 125 amp. and above, with corresponding sensibiUtioa 

. 152 Diglizc lhy»^TUUyiC 



MBASVRINQ APPARATUS 



Sec. S-156 



of 10 and 200 watta respectively at full scale deSection, icith a SO-cm. 
(U.7 in.) geale at 100 cm. (39.4 in.) distance. 

IH. Tha Weatlnclioiiw '"precision" wattmeter ia similar to the cor- 
mponding ammeter (Par. 99). except that the moving coils are wound 
«ith fine wire and are coonected across the lino instead of in series with the 
fixed coil. There are usually two or three current ranges, and the series 
lOBitanco for the moving coil is mounted in a separate box. It therefore 
can be used with a wide range of voltages, from 10 volts up. Although con- 
aderaUe metal is used in the construrtion of this instrument, it is so arranged 
that the eddy-current error ia not appreciable at commercial frequencies. 

IM. The Duddall-Mathar type of wattmeter as made by Paul ia a 
earefully constructed, aemi-portable, secondar^r standard in which the current 
dement eomprises four fixed coils connected in scriee, and the potential or 
voving element consists of four coils connected in series, all astatically 
tizaiiced. The moving element is suspended by a ailk fibre and a spiral 
•priag fomiahea the controlling force. It is a torrion-head instrument like 
the WsMinshoiue wattmeter. 

UT. ComiiMrelal indloaUnc wattmctan are made in two general 
fflrms, the eieeirodynamometer type and the induction type. 

UB. The Warton inodel-16 and the Qencral Blectric type Pi Initru- 
menti are well-known examples of the electrodynamometer clau. Fig. 
M sbowv the general arrangement. The current or series element con- 
■bts of two fixed coila wound with heavy wire or strip, which are connected 
ia aeries with each other and with the main circuit. The potential or 
ihant element ia a moving coil mounted on a shaft supported between 
Mvel bearings and placed between the two fixed coils. This coil consists of a 
luve number of turns of fine wire, as in voltmetera; it is connected in series 

with a relatively large amount of 
non-inductive resistance, across the 
main circuit. The oontroUing fore* 
eompriaes one or more spiral spring 




^Flzed Oolle 
_ . (carrent) 
McnlBsCoU ^ 

(potential) 

Fie. 54. — Diagram, eleotrodsrnamom- 
eter type wattmeter. 




Fio. 55. — Diagram, Westinghouse 
induction type wattmeter. 



m. The inclined-coil type of wattmeter (General Eleotrio Company) 
■aaailar io principle (Par. IH), but the ceatie lines of the fixed coiu and 
the moving coil make an angle of about 45 deg. with each other, instead 
<f 90 deg.. the object being to make the scale more open, or more 
■aifonnly graduated. 

Ut. The WeetinKhoase portable wattmeter is the most important 
cxsmple of induction-type wattmeters. The principle is exactly the same 
>s thn of the induction watthour meter (Par. SOI) : but instead of allowing 
the moving element to rotate, the torque is opposed by a spiral spring ana 
heaee tlie deflection is proi>ortional to the power. Fig, 55 shows the sche- 
■*•>< arrangement, where AA' are the current or scries coils, PP' the po- 
"•••"l or ahaot crals and SS' the compen,<!ation coila by moans of which, 
■•ither with the adjustable resistance, R, the exact quadrature relation is 
*<«i«*d lain watt-hour meters. This type is also made in polyphase form 
Vhavint two leta of current and potential elements actinc on a oommoD 



153 



edbyV^iUUyiL' 



Sec. 8-161 MEASURING APPARATUS 

moving diac, or drum, aa in the polyphase watt-hour meter. It is obvioua 
that instruments of this type are Umited to the frequency for which they are 
designed. 

161. The WhiUiey wattmeter operates on the dynamometer principle 
(Par. lUj except that it la a torsion-head instrument, the moving clement 
being kept in a fixed position by twisting the torsion head to which the 
control spring is attached. The pointer attached to this head moves over 
the scale. This method permits using a very long scale, extending around a 
full circle. 

16S. W&ttmetera for switchboard use employ both the electrodvnamio 
and the induction principles. Weston instruments are simitar to the por- 
table electrodynamometer instrument (Par. 158). The General Electric 
edgewise type "H" instruments are dynamometer types while type I 
is of the induction type. Westinghouse switchboard instrumenta are 
also induction type. 

163. The oftlibration of wattmeters of ^he dynamometer type 
should be done with continuous current. It is customary to make such tests 
at a fixed potential, usually 100 or 200 volts and to vary the current to give 
iho required watts. The potential is held constant at the desired value by 
means of one standard (standard voltmeter or potentiometer) and the 
current is read on another standard (standard ammeter, or potentiometer 
with standard realBtance). It is more convenient to obtain the potential 
and the current from separate souroea, because the process of adjustment of 
one circuit will not affect the other. In the case of instrumente- of laive 
capacity this method economises energy, because only three or four volte 
are necessary for the current circuit. 

164. Calibration of Induotion-tsrpe wattmeters. These instruments 
must be checked on alternating current of the frequency for which they are 
designed. This check is made by comparison with a secondary standard, 
which in turn ia checked on continuous current. Polyphase instru- 
ments may ^ be checked as single-phase instruments by connecting the 
current circuits in series and the potential circuits in parallel. In the case 
of induction- type instruments stray magnetic flux from one element may 
affect the other, in which case the calibration should be made on a polyphase 
circuit 

165. The induetance error in wattmeters may, under certain condi- 
tions, become very important. While the theory of the electrodynaznometer 
type of wattmeter assumes that the potential circuit is non-inductive, this 
is not strictly true in the actual instrument because of the inherent Induct- 
ance of the moving coil. Ordinarily, however, the non-inductive series re- 
sistance is sufficiently large to make the effect of this inductance neKligible 
At ordinary frequencies and power-factors. But with low power-factora, 
the lag angle in the potential circuit may have to be considerea. The power 
in an aJtemating-current circuit is W^EI cos 9, where W — power, / — current, 
K — e.m.f. and cos tf = power-factor of circuit. When the power-factor ia 
unity, I and E are in phase, but the potential-circuit current lags slifcfatly 
behind E, thus producing the effect of a small power-factor. If. for example, 
the lag-angle, 0, is 2 dcg., cos tfn 0.9994 and the error is ordinarily negli- 
gible. If the power-factor is 50 per cent., the lag angle in the wattmeter 
is (00-2) - 58 deg. The cosine of 00 deg. is 0.50 while the cosine of 58 deg. 
is 0.53, thus introducing an error of 6 per cent. 

166. The stray-field error in unshielded, non-astatio, eleotrody^ia. 
mometor wattmeters may be anything from sero to 25 per cent, tvith 
an alternating magnetic field of 5 lines per square oeatimeter, and from soro to 
75 per cent, at 10 lines, depending upon the direction of the field and 
the coil deflection. A shield, properly made and placed, is extreziMily 
efficient, reducing the effect of a field of 20 lines per Hquare centimeter to 
practically Bcro, without introducing eddy current or other errors. 

Wattmeters of the Kelvin balance tjp^, in which the coils are a^ta- 
tically arranged, are practically immune from these troubles except Ixk aa 
intense field which is not uniform throughout the space occupied by the 
moving system; such a condition may arieie, for example, when the watt- 
meter is clcMBe to a conductor carrying a very large current. Induction- 
typo instruments employ much stronger field strengths and are not appreci- 
ably affected e^oept oy very strong fields 

Digitized by VjOOQIC 



MBASVRINO APPARATUS 



Sec. »-167 



Vtt. Wattnuter oonnaetioiu to line. Care shoold be taken m to 
cooaect a wattmeter into the main cireuit that the moving-coil end of the 
potential drruit and the current coil are on the same lide of the circuit 
Miiix measured. Otherwiae there may be sufficient electroatatic attraction 
between the two windinicB to produce an error; or, if the potential is sufficiently 
Ucb, the ineulation between the windings ma^ be broken down. The 
Utter may be guarded against by connecting the bincUng post at the moving- 
eoil end of the potential circuit to the proper current post with fine fuse wire. 

in. Ourre etl on for wattmeter Iomoi or ancrc7 eoniiunptloii. 
Vfacxe small quantities of power are being measured, the losses in tne cir- 
niu of the instrument itself should be taken into account. It will be noted 
is Fie- 56 that the instrument is measuring ite own current circuit loss, or 
Mries I'B lo«L If the instrument loss cannot be neglected, it is better to 





, Fto. M. — Power measurenaenta Fia. 57. — Electrodynamometer arrange- 
ii ihigie phase circuits with watt- ment for measuring small amounts of 
Bcter. power. 

eonnect the potential drenit to the load side (6 instead of a) and include the 
potential dreuit loss in the measurement instead of the current drcuit loss, 
DKsose the former not only remains constant but is more easily calculated. 
Wattmeters are often arranged to correct or compensate automatically for 
tUiliias by means of a few turns on the fixed coil, connected in series with the 
potential circuit and in opposition to the fixed coil. This arrangement can- 
aoi he used with shunt-type instrument transformers nor when checking the 
nitmeter with separate sources of e.m.f. and current. A separate connee- 
tioa ii usually provided, however, for this purpose. In general it is safer 
livays to use this "independent" eonnection, m^lring allowance for the 
potential loss, when necessary, by calculation. 

M. lleaatirenuiit of vary unall amounta of power. Where the 
Pover is extremely small, only a few watts, reflecting electrodynamometers 
us nest accurate. This is espedally true when the power-factor is low, the 




no. S8. — Power in single-phase 
ORint, three-voltmeter method. 



Fio. 69.— Power in single-phase 
drcuit, three-ammeter method. 



pstastial high and the current low, or mc« verm, as for example the losses 
**^ttniating-cnrrent conductors, in dielectrics, instrument drcuits and mag- 
yjs circssts. The fixed coils may be connected directly in series with the 
■n dremt or to a non-indvctive shunt in the drcuit. At low potentials, 
I* series resistance in the moving-coil circuit may not be suffident to elimi- 
■■ti the efleet of inductance but this can be aocompUshed by shunting the 
"■tsaee witli a o<»denaar as shown in Fig. 57. when the potential dr- 
?*issbart-dnniitcd at a, 6, the capadty C orreaisUnce Rtis adjusted until 
ItiK ii so deflection with fall currant in the fixed coll. CaUbration is of 
*•>■ made with eontiitaoiia cmtent. 



ISi 



Digilizod by V^i 



uugle 



4 



Sec 8-170 



MEASURING APPARATUS 



170. Keaiurvmant of power In & lingle-phaie eSrcuit. One watt- 
meter oonncoted as shown in Fig. 56 vfiM read true watts. The power may 
also be measured without the use of a wattmeter, by three voltmetarB or 
three ammeters. 

In the "three-TOltm«ter" method, a known non-inductive rewstmnce, 
R, is connected in series with the load as shown in Fig. 58, where £. Sg and 
Et are points where voltmeter readings are to be taken. The power in 
watts 10 

Similarly, in the "thrM-ammatar" method. Fig. 59, the power in waits is 

circuit. Two wattmeters, connected i 
these conditions being equivalent to tm 
flinsle-phase circuits. The total power 

:_ -vS 1.. *i._ -_:«i. ■- . - .. 



(watts) 



<25) 



171. Two-phaae. four-wire 

shown in Fig. 60, are sufficient, 




is obviously the arithmetical sum <^ the 
readings of the two instrumento. 

17S. Two-phase, three-wire ctreuit. 
— Two wattmeters should be connected 
as shown in Fig. 61, the total power bcinc 
the algebraic sum of the two readinn. 
This connection is correct for all condi- 
tions of load, balance and power-factor. 
One wattmeter may be used as in Tig. 62, 
provided there is no load across the outer conductors and the phaaes are 
ixUaneed as to load and power-factor, 

178. Two-phaae, four-wire, interconnected circuit. Three watt- 
meters can be used, connected as in fig. 63, the total power being the al^f^^ 



FiQ. 60. — Power in two-phase, 
four-wire circuit. 





Fig. 61. — Power in two-phase, 
three-wire circuit. 



F I Q . 6 2. — Power in two- 
phase, three-wire circuit. 



hraic sum of the three readings. This connection is correct under all con- 
ditions of load, balance and power-factor. Two wattmeters, one in each 
phase, will give the true power only when the load is balanced. 

174. Three-phase, tlvee-wire circuits. Two wattmeters may be used, 
connected as in Fig. 64, the total power being the algfbraic sum of the two 





F I o . 6 3 - —Power in two-phase, 
four-wire interconnected circuit. 



F I a . 6 4 . — Power in three-phase,, 
three-wire circuit, two wattmeters. 



readings. At unity power-factor, each instrument will indicate half the total 
power and at 50 per cent, pownr-factor one instrument will indicate the total 
power, the other inntrument reading aero. At less than 50 per cent, powers 
factor, one instrument will read negative. (See Par. S09 for mewod <d 
verifying power-factor.) 



1,66 



yGooglc 



MEASURING APPARATUS 



Sec. 8-175 



ITi. Three-pb&se, thre«-wlra circuits, bftlaneed load. When th« 
load u baiatuxd the power may be measured with one wmttmeter by the follow- 
ing methods. 




(ft) With "itar" box or arti- 
fidal neutral as shown in Fig. 65. 
The total power is three times 
the reading of the wattmeter. 
The nsist&nce in each leg of the 
»tar box should be non-inductive 
sad small compared with that 
of the potential circuit of the 
vsttmeter, so that the cur- 
rent taken by the latter will not 
disturb the potential at the neu- 
tisl point. 

(D) With *'T" box as shown 
Ib Fig. 66. The total power is three times the wattmeter reading. 



^I 



Fig. 65. — Power in three-phase, three- 
wire circuit, one-wattmeter, with 
"star" box. 




p^r 



The 
arrangement is mmilar 
to (a), one leg of the 
star box being replaced 
with the potential cir- 
ouit of the wattmeter 
itself. The other two 
legs have the same im- 
pedance as the poten- 
-» tial drcuit of the watt- 



Fw. 66. — Power in three-phase, three-wire oircuit, ""f^f'u-.. ,,— „ 

ace wattmeter, with "Y" box. W With a "T" re- 

actance cou as shown 
in Fig. 67. The total power is twice the wattmeter reading. The im- 
ot ih» reactance 




ad anct bo small com- 
pared witli that of the p<^ 
tcatial circuit of the watt- 
Brter, so that the current 
iskea by the potential eir- 
nit will Bot disturb the 
potential at 0. 

in. Threc-phaie, 
ikar-wlracireiiita. Three 
wittmeters are used as 

ta2j^--, u*;*.- ^rfJw^ P'O- 67.— Power in three-phase, three-wire 
iSf rtto £.S^SdtSSf "««'•• one^ttmeter, ,-ilh •4" reactance coil. 
TUi method is correct 

an conditions of load, balanee, and power^factor. A three-phase, 

"star" system with a grounded 
neutral is virtually a four- wire sys- 
tem and the power should be meet- 
urod with three wattmeters. Ob- 
viously, if the load is balanced. 
one wattmeter can be used, the 
total power being the Indication of 
the wattmeter multiplied by three. 
The current coil should be con- 
nected in series with one conductor 
or phase wire and the potentitd 
coil between that conductor and 
the neutral. 

177. «N" -phase drcttit. In 
any system whatsoever, of **n** 
phases, the true power may be 
measured by connecting a watt- 
meter in eaeh phase, the current 
eoU being in seriee with the line 
•Bd the potential coil connected between that line and any common 




Fio.eS. — Power in three-phase, 
four-wire circuit. 



167 



ibyv^iuuyie 



Sec.S-178 MBASURIKG APPARATUS 

pcHnt P of the system, which may or may not be the neutral. The total 
power is the algebraio sum of the readings of all of the wattmeters so 
connected. * 

ITS. Power maaiurenieziU o& high-Toitftga cireulti should preferably 
be made with aeriea-type and ahunt-ty^pe instrument transformers. If thm 
instrument wattmeter is connected directly to the circuit with series re- 
sistance in the potential circuit, the circuit should be pounded at the 
instrument in order to avoid errors of electrostatic attraction, and also poa- 
Bible injury to the instrument or the observer. The current-capaaty limit 
of commercial wattmeters is about 200 amp. beyond which series trana- 
formera with 5-amp. instruments are used, irrespective of potentiml. 

179. Gorreettona where inatnimant traiiaforman arauMd in aoeu- 
rate powar meASUrementi. In every case the true ratio and phaie aji^o 

should be known (Par. TV and Par. 10^ lOS). The general effect of the phaae 
changes in the instrument transformers is to make the angle between the 
current and the potential in the wattmeter larger or smaller than that be- 
tiffeen the current and the e.m.f. of the circuit being measured. 

If cos $ 'true power-factor and cos 0iv apparent power-factor (i.e., powrer- 
factor in the wattmeter obtained from the ratio of the watts and volt-aznperea 
in the wattmeter), true watts » (cos 0/cos fc)X wattmeter reading. The 
apparent power-factor, cos 0i — cos {6±a±0±y)j where 
9 "■phase angle in main circuit, 
a ■« equivalent phase angle in wattmeter, 
— equivalent phase angle in current transformers, 
y ^equivalent phase angle in voltage transformers. 
I'he angles a, fi and y are given positive ( + ) signs when they tend to de- 
crease and negative ( — ) signs when they tend to increase the phaae angle 
between the current and voltage in the instrument-t 

180. Power-f aetor. The power-factor of a circuit is the ratio of the t^e 
power in watts, as measured with a wattmeter, to the apparent power ob- 
tained, from the product of the current and the potential, in amperes and 
volts respectively. In the ordinary continuous-current circuits, the power- 
factor is obviously unit^ but in rectifier circuits, for example, it may be 
slightly less than unity. In alternating-currrnt circuits, the power- 
factor ia usually less than unity because the current and t^ potential are 
not in phase. When the wave form is sinus<Hdal, the power-factor ia eQual 
to the cosine of the angle of lag. 

ISi. The power-factor of tinffle-phase drouita is obtained from 
wattmeter, voltmeter and ammeter readings, by the relation W/BI^^eam 
$ where W — watts, £* volts and / — amperes. 

181. The power-factor of polyphase circuits which are balaneed ia 
the same as that of the individual phases. When the phases are not 
balanced, the true power-factor is indeterminate. For all practical 
purposes, however, it is sufficiently correct to assume the power-factor to be 
that obtained by methods which give the average of the power-factors of the 
separate phases. In the wattmeter-TOltmstsr-ainineter method, the 
power-factor is, for a two-phase, three-wire circuit W/'v2 (.BT), (J In 
middle wire, B between outer wires) and for a three-phase, three-wire circuit 
the power-factor is W/Vs iSI), wherein ^ — watts, £ — volts and /■■ 
amperes. In the two-wattmstsr method, the poweMactor of a two-phase, 
three-wire circuit is obtained from the relation Wi/FTi— tan 0, where Wi is 
the reading of a wattmeter connected in one phase in the same mannrr as a 
single-phase circuit, and Wt is the reading of a wattmeter connected with its 
current coil in the first phase, in series with the first wattmeter, and the 
potential coil across the sooond phase. Obviously, if the load is steady, one 
wattmeter is sufficient. If the phases are not balanced, the readings should 
be repeated with the instruments in the second phase, the true power-factor 
being taken as the average of the two results. In a thrss-phase, three- 
wire circuit, the power-factor can be calculated from the readings of two' 

* Bedell, F. "Direct and Alternating-current Testing." D. Van Nostraad 
Company (1912), p. 228. 

t Robinson, h. T. "Electrical Measurements in Circuits Requiring Current 
and Potential Transformers." Tran^. A. I. E. £., 1909, Vot XXVtll. p. lOOi. 

ifiS Digized by v^iuuy le 



MSASURISa APPARATUS 



Sec. ^183 




Fig. 69. — Dugram, Weston singla-pbase 
powar-factor meter. 



■mttmeteiB eonneoted in the standard method for measuring powor, as follows: 
\{Wi-Wt)/(Wi + Wtyiy/3-tiMS,vrbeif> Wi u the'larger reading, which is 
atwKfn {KMBtive, and Wt a the smaller reading which may be either positive 
orBagative. 

in. Powar-faetor maton are instrument* which indicate directly the 
powcMaetoi of the circuit. Commercially there are two general classes, those 
lanlTia^ the principle of electrodynamometer wattmeters and those based 
on the pnneiple of induction wattmeters. The essential features of a Weston 
■ngle-phaae pow«r-f actor meter of the first class are shown in Fig. 69. 
It will be noted that the ar-. 

nnaement is similar to that in jfi^ h 

wattmeters, except that there /^.v^ 

■R two eoila. M. Jf>, in the 
■orinf system instead of one. 
One e<al. V. is connected across 
the line and in aeries with a re- 
•Manre Jt, while the other coil, 
Jfij is connected in series with 
•a indoctanee L. The current 
ia the coil, lf>, will therefore 
be sboat 90 deg- out of phase 
with that in e<^ M. When the 
Vawrr^betor is uni^, the re- 
action between the fixed coils, 
^, V^t and the moving coil M 
wlU be a maximum while that between TF^ and M^ will be a minimum. The 
Win^ exerted on M will cause the moving system to take the position of 
■imimim torque, that is, where the plane of Af will be parallel to that of FFi; 
the eorrespondins mark on the scale will therefore be 100. Similarly, at 
■era power-factor, coil if will exert all of the torque and cause the moving 
•fMem to take a position where the plane of if' will be parallel to that 
M Wf' the corresponding indication is therefore lero. Theoretically, the 
■Mfieations will be aSaetMl b7 Um frsquenoy^ because the current in h 
depcnia upon the frequency, but by proper design of the reactor, Z>, the 
•fleet of moderate vaiiatioos in frequenoy can be eliminated. 
Ia the pelTphaaa metar. Fig. 70, the inductance h is not required and 

the instrument is therefore entirely 
independent of the frequency. 
There are three coils in the moving 
system, one connected across each 
phase. The principle of operation is 
exactly the same as in the nngle- 
phase instrument, the moving sys- 
tem taking up a position where the 
resultant of the three torques will be 
a minimum, which position will vary 
with the average power-factor of the 
circuit. 

IM. In WaitinchouM iiower- 
factor msten, the dynamometer 
prindpla deseribed in Par. IBS is 

Fio. 70.— EHagram, Weston polyphase ."TT*!? "*"S *'^- • '" o'!'*"' th" 
Donr«r-faLctar metS- induction principle is employed in 

power-factor meter. ^^ ^^^ manner that is applied in 

•raehraseopea (Par. IM-Ml). 

Ui. Oaaaral Hactrle ppwar-fkotor matan employ the electrodyna- 
wcoeter principle (Par. lit) in polyphase instruments. No single-phase 
iMtrameals are made by this company. 

WKtajXT MKASITSnmiTB 

Ut. Tha praetleal unit of alaetrioal anargr is the watt-hour, which 
■ the energy expended in 1 hr. when the power or rate of exiienditure 
Hi vau 

UT. bargy ia nsaalljr maaiurad in watt-houri, with wktt-hour 
■Man (often incorrectly called integrating or recording meters). All 
■Mt'kou matan an, ia reality, small motors in which the speed is proper- 




159 



JbyV^iUUyiL' 



Sec. »-188 



UBASURIJfO APPARATUS 



> 




Fia. 71. — Diagram, commutator- 
type watt-hour meter. 



tional to the power and the revolving element operates a reentering meehi 
anism on which the energy consumption is recorded. Meters for ooB' 
tinuoufl current are uaualTy of the type which utilise the electrodynsmii 
principle of direct-current motors, while those for alternating curren' 
utilise the principle of induction motors. 

188. ConttnuouB-curr«nt watt-hour metan. Continuous-ourrenl 
meters may be divided into two classes, the eommatator typ* and tin 
mercury motor tjpe. 

189. Commutator-tjpe metan are similar in principle to shunt moton 
The essential features are shown in Fig. 71. The moving element constat 

of an armature, a, a commutator, e, am 
a light metal disc, d, all mounted on ] 
steel shaft which rotates in a jewe 
bearing. The armature is connectec 
to the external circuit by means of ver^ 
light silver-tipped brushes. Ini acria 
with the armature is a light-load com 
pensation ooU, «, and a resistance, r 
The field coils are indicated at/, /. 

190. Ch»r&ctoristlci of commii- 
tator-type maters. The eaaentia 
differences between this type of '«r»tt 
hour meter and a two-pole shunt moto 
are as follows: (a) entire absence o 
iron in the magnetic circuits; (b) tb 
armsture element is connected mcrtm 
the circuit and carries a very sma] 
current, while the field element is ii 
series with the circuit and carries th* 
main current; (c) the speed increasie 
as the field strength increases which i 
opposite to the effect in a shunt motof 
191. Tha principle of oparatlon «t oonunutator-typa metars i 
as follows. The torque is proportional to the current in the armature coil 
and to the field strength. Since there is no iron in the magnetic rirouit. th< 
latter is always proportional to the field current, hence the torque ia pro 
portional to the two currents (as in a dynamometer wattmeter). The cur 
rent in the armature being proportional to the line potenti^, and the fieli 
current equal or proportionsi to the line current, the torque is proportions 
to the power. In order to make the speed proi>ortlonal to the poirer, i 
mechanical load must bo provided, in which the counter-torque wiu be pro 
portional to the speed. This load usually takes the form of a circular disc 
d (Fig. 71) of thin copper or aluminum which revolves between the pole 
of one or more permanent horseshoe magnets, with poles very close togethei 
The eddy currents induced in the disc react with the pcrmanent-xnagne 
field, producing a counter-torque which will always be proportional to th 
speed. As the load current increases, the torque of the motor element in 
creases and the speed increases, becmuae there is practically no countc 
e.m.f. in the armature, t. But as the speed increases, thd counter-torqn 
of the disc or generator element also increases and a speed is finally resLchei 
where the two torques balance each other and the speed remains constanl 
Thus, theoretically, the speed will always be proportional to the power in th 
rircuit. Kacb revolution represents a dffinite amount of energy, and b; 
connecting the shaft to a suitable recording mechanism similar to that oi 
gas and water meters, the total energy consumed is automaticatl; 
registered. 

19S. XfTacts of friction Mid tamparatura in commutator- ftypi 

maters. In practice, certain conditions prevent the speed from beini 
always proportional to the load, the principal factors Imng frictioD am 
temperature. Bearing friction is reduced to a minimum by using polishes 
sapphire or diamond jewels, with either a polished cone-shape snaft-^iu 
or a 8tcel ball. Thus the contact surface is reduced practically to a poini 
The weight is reduced by using hollow shafts and very light alumlnunn o 
non-metallic frames for the armature windings. Commutator fHc^oi 
is reduced to a minimum by making tha commutator diameter small, am 



160 



dbyv^iuuyie 



MEA8VRIN0 APPARATUS 



Sec. 3-193 



nine nnmd bnishea so that eontact is mode practically at a point. The 
lean in the resisteiing mechanism are made as light as poeaible. The effect 
of friction is sznaUer an the torque is increased; hence the ratio of torque to 
v«lf ht is made as large as possible by making the armature spherical, which 
gives the maiimum torque for the minimum amount of wire (weight). 

IM. Compensfttion for friction in conunutator-tTpo maton. 
Friction cannot be entirely eliminated and its effect is marked at light load, 
Deceasitating the use of a compenaatlnff darlco. This usuallv consists 
of a few tunu of fine wire on the field coil, which are connected in series 
with the poteatial circuit. These turns are wound in a separate coil and the 
amount of compensation can be adjusted for each meter individually cither 
by kltering the position of the coil with respect to the field coils, as in General 
Electric and Westinghousc meters, or by changing the number of turns as 
ia Columbia and Duncan meters. 

IM. Compensation for tamparatura In eonunutator-tTpa matari. 
Temperature affects the performance of meters by: (a) changing the resist- 
SBce of potential cirruit; (b) changing the resistance of the drag disc; and 
it) changing the strength of the permanent magnets. These changes pro- 
ouM a rombioed or resultant effect, which ia compensated for by using for 
the series resistance in the potential circuit, one or more materials so com- 
bined that the final temperature coefficient of resistance counteracts the other 
effects when the air temperature changes. 

IM. Th« mercury-motor-type meter is most prominently represented 
by the direct-current meter made by the Sangamo Electric and Manu- 
(aetoring Co. Fig. 72 shows diagrammatically the oircuita and scheme ol 
operation. /> is a solid copper disc floating 
ia mercury, F a float which supports the 
ihait and eliminates a jewel bearing: ff is a 
laminated iron core and C is a chamber 
Wed with mercury. The flux produced in 
the core, H, by the shunt coil, traverses 
the disc at ttro points which are diametri- 
eally opposite. The line current passes 
fram L to L\ through the mercury and dia- 
netrirally through the disc. This disc 
being cut by flux, a torque is produced 
vhicn 19 proportional to the current and 
the em J. 

IM. Compansation for friction in 
— I ui J -motor-type meter. The fric- 
tion doe to the disc rotating in the mercury 
» eompraaatad in two wa^. One 
■wthod IS shown in Fig. 72. A high resist- 
saee. r, is connected in shunt with the 
•nnatore, D, and the e.ro.f. circuit is com- 
pfeted by the sliding eontact, P. When 
the did^ is at b, practically all of the shunt ouirent will pass through D 
beeanae of the resistance, r, thus adding to the torque. When the slider 
ii st a, practically none of the e.m.f.-coil current will traverse the arma- 
tare. tn the second method, a circuit cbnsisting of two wires of dis- 
■milsr metals, which form a thermocouple, is connected in parallel with 
tb* mercury chamber terminals, L, L\. This couple is surrounded with a 
b*aiing roil connected in series with ^h.e potential circuit. The e.m.f. 
prodund by the couple causes current to flow through the disc thus producing 
the neccflsary torque to overcome the effect of friction at light load. The 
tMreaaed mercury friction at high ipeed is compensated by a series 
t«ra (or half a turn), /, on the core H. The drag or counter- torque is 
obUiEtfd with a separate disc and permanent magnets (not shown) in the 
asQftl manner. 

Uf. Ipeed adjustmente. The speed at all loads is equally affected 

fay shiftiay the drag magnets diametrically with respect to the meter shaft. 

vas altcnng the retarding torque. This torque is a minimum with the mag- 

I *Bts dos e to the shaft and a maximum with magnets near the edjte of the 

> «e- The speed at light load is adjusted independently as indicated in 

! J^lM. 





ll H 




l-'^m^j 


k 




/.■''--"• ■-J"-"" ■■" 


.1 








" IM"" 


u- 


a 


^A^/Wv^ 


^1 

6 




Lin 


e 


Loud 



Fio. 72. — Diagram, Sangamo 
mercury-motor-type watt-hour 
meter. 



( 



u 



161 



V Google 



Sec. 3-198 



MEASURING APPARATUS 



IM. Typical Data Applytnc to Modem 110-Tolt, <-unp. 
amp., Dirtet-eurrant Watthour lletan * 



10- 



to a. 

H6i 



•|!a 






a a 

« 






Speed, full load, r.p.m 

Torque, full load, rom.-grin 

Weight, moving element, grm 

Ratio, torque to weight 

Drop, current circuit, volts at rated 

current. 
Loss, current circuit, watta at rated 

current. 
Loss, potential circuit, watts at 110 

volts. 

Resistance, armature, ohms 

Resistance, compensating coil, ohma. . . 

Resistance, series resistance, ohms 

Resistance, potential circuit, total ohms 

Ampere-turns, field j 

Ampere-turns, armature : . ,. 



46 
170 

97 
1.75 
1.15 

5.75 

5.1 

825 

66 

1,640 

2,430 

300 

800 



41.7 
140 
80 

1.75 
1.0 

5.0 

4.5 

1,185 
315 
800 

2,300 
600 

1,500 



25 
55 

n 

18 
0.03 

0.3 

5.0 

1,8501 



36.7 
180 
130 

1.39 



5.0 



450 
2,300 



910 



30 

go 

90 

1.0 

0.54 

. 5.6 

2.0 

2,600 

4fi0 

3.000 

6.1 10| 

700 
2.100 



IM. Thraa-wlr* eireuitf are metered with two, two- wire meters ol 
the kind described (Par. ISS to Par. 198), or a three-wire meter. The 
latter which is usually made in the commutator type, is the same as the 
two-wire meter except that the two field coils (which should be alike) %re 
separated electrically, and one is connected in each outer wire in such a manner 
that their fields are cumulative as before. When the load is exactly balancsed, 
the conditions are obviously the same as in a two-wire meter, and irhen 
unbalanced the two field strengths add together so that the speed is pro- 
portional to the total current.! 

100. The metering of heary-current drenite by means of standard 
meters becomes troublesome because of the large conductors required in the 
fields. While such meters have been made in capacities upto 20,000 amp., 
they are very costly and not satisfactory at light loads. Watthour meters 
have been developed by some manufacturers, along standard lines, for opei^ 
ation with shunts. In order to develop sufficient torque without an ezcee- 
aive shunt loss, it is neeessary to employ shunts having smalt drop, large field 
coils on the meters and relatively large leads from meter to shunt, ^^here 
the meter has to be some distance from the shunt^ the leads may have to be 
nearly as large as the wires in the main circuit, in order to keep down the 
resistance. 

.\nother way _ to avoid the use of large meters is to connect "so veral 
smaller meters in parallel. Care should be taken to make the resistance 
of the several branches equal, if the meters are of the same capacity; or, if 
the meters are of different capacities, inversely proportional to the capaci- 
ties of the meters. This will insure that none of the meters are overloaded. 

SOI. Altematliiff-cuirent watt-honr meten. Altemating-ourrent 
energy is almost always measured with induction typo meters. Com- 
mutator meters are seldom used on alternating-current circuits for the very 
practical reason that induction meters are not only more accurate, but 
much leu expensive in first cost and in maintenance. 

* From Electrical Meterman's Handbook, N. E. L. A., 1912, to vrhich 
readers are referred for further data. See also Fitch, T. T. and Huber, C. J. 
*'A Comparative Study of American Direct-current Watthour Meters," 
Bureau of Standards Bulletin, 191S, Vol. X, p. 161. (Reprint No. 207.) 

t The Sangamo Co. has recently developed a three-wire mercury meter (see 
Par. 199). 



102 



y Google 



UBASVBINO APPARATUS 



Sec. S-202 




^.^ 



Fio. 73. — Diagram, induction-type watt-hour 
meter. 



Mi. Indnctton-^M wstt-honr maters operate on the principle of the 
rotaUng magnetic field of the induction motor. The essential features of 
the t^incipal makes of watt-hour meters are shown in the diagrammatio 
ifcetcfa. Fig. 73. P iM the potential coil; S the series coil, and C a compenaat- 
ihk rail. A metallic disc is free to revolve between the poles. The alter- 
uting magnetic fluxes from these poles will establish currents in the diao 
about as indicated by the arrows in the sketch at the right, which shows 
■ portion of the disc and the poles. The potential wincUn^. Pt has many 
turns and is therefore highly inductive, while the scries wintling, S, is piai^ 
tically non-inductive ; 
thus the fluxes produced 
by these two cireuits are 
praetieaUy 90 time-de- 
prees apart. Each flux 
is io phase with the cur- 
rent which produces it: 
and the e.m.f. ^Derated 
in the disc, which is cut 
by the flux, is in time 
quadrature with the gen- 
ciBting flux. Therefore, 
if it is assumed that the 
flans duo to P and 5, 
RSpectively, are in quad- 
rstore, the eddy currents 
produced by P will be a 
BMtimnm at the same instant that the flux from 5 is a maximum, and vice 
•tr«a. Thtts a torque will be produced which is proportional to the instan- 
taoeous product of the eddy currents in the disc and the flux from the pole 
sader wmeh the current is flowing. This toroue is nroportional to the power 
wed in the load circuit providing the time-phase difference of the currents 
in eolls P and S is exactly 00 deg. at unity power-factor. The necessary 
ntardtng aetion or oounter>torque is obtained with i>ermanent magnets on 
this same disc as described under direct-current meters (Par. 191). 

W. Coinp«xisatia|^ coil on induction-type meters. If the phase 
qoadratore is not exact ^Par. SOS), the meter will obviously not register 
correctiy under any condition. In consequence of the ohmic resistance of 
Ue potential circuit, the current is never exactly 00 dog. behind the impressed 
f-m-f. At any instant, the flux Ef (Fig. 74) from the potential pole, 
iMtnd of bans in phase with the eddy currents, /«, due to the line current, 
b di^tly behind, as indicated. The torque is therefore proportional to 
tbe imduct /• and oo, instead of J* and E//, The meter will therefore run 
dew, but as a practical matter the error is so small that at unity power' 
beter it is insignificant. The error rapidly becomes large, however, as the 
power-factor decreases. As practically all alter- 
. E 7 nsting-current circuits have a power-factor less 

- ' than unity, a oompensfttinc coll is used to elimi- 
nate the error. This coil is a short-circuited coil 
. placed on the potential pole (see Fig. 73) and in 
1 which a current is induced 90 deg. behind the 
' generating (potential) flux. Its flux, Sr, will be in 

Bhase wiu that (induced) current and therefore 
[) deg. from Bt* with which it will combine. By 
adjusting the vsJue of the resistance (lag adjust- 
ment) r (.Fig. 73) the resultant flux can be brought 
into exact phase with /« and the meter will then 

piQ 7* Theorv of '*8i«ter correctly on all power-fnctora. It is evi- 

1m sdjus^ment. mduo- dent that «ith lagging ^wer-factor in the circuit, 
tiui n«(-k«.<- r^*4.M> * meter will be slow ii under-lagged and fast if 

Mwwaiwiour mexer. -ovei-lagged." The oppomte results wiU occur 

with a leading power-factor. 
M. Friction compensation. The friction in an induction-type meter 
M much leas than in a commutator-type meter because of the absence of a 
CMsmotaior and an armature. On the other hand, the torque is less (com- 
FKt tables of characteristic data. Par. IM and Par. S06) and the effect of 
"ie^ at light load has to be compensated. The principle employed in 




i 



108 



i.jv^iuuyic 



See. 3-205 



MBASVRINO AFPARATVS 



) 



practically all meters is that in which a flux is produced at the potential 

Kle face, sUcjhtly out of phase with the main flux. Thus eddy currents wiS 
produced in the disc which will be in phase with a small com|>onent of the 
main flux« giving rise to a slight torque which can be made sufficient to over- 
come the friction torque. This " out-of-phase " flux is produced in varioui 
ways in different meters. A common method is to place a short-circuited 
copper circuit or thin copper punching ("shading strip") in the potential- 
pole air-gap, in an unsymraetrical position, so that the aeaire<l unbalanced 
flux will be obtained. In the Columbia meter, the effect is accompli^ed 
by unbalancing the flux of the two potential poles by means of macnetic 
shunts. 

MS. Adlnitmcnta of induetlon-^p« meton. Facilitie* are usualb 
provided for conveniently adjusting the meter accuracy at light and full load. 
The position of the light-load compensation coil can be changed witli 
conveniently located screws, and the light-load speed thus altered. Speed 
adjustment at all loads ia obtained by shifting the drag magnets witji 
respect to the axis, as in direct-current meters, or by shunting the flui 
by means of a movable soft-iron keeper bridging the air gap. Th< 
power-factor or lag adjustment is made at the factory and if properly doM 
should never require readjustment. 

106. Typical Data Applying to Modem 110-TOlt Slnfla-pluwo M- 
eyela, 5-ainp. induction-type Watt-hour Meton* 



load, 
load, 



Speed, full 
r. p. m 

Torque, full 
mm. -grams 

Weight, moving eel- 
ment, grams 

Ratio torque to 
weight 

Drop, current circidt 
volts at 5 amp. . . . 

Loss, current circuit 
watts at 6 amp. . . 

Loss, potential cir- 
cuit, watts at 110 
volts 

Power-factor, poten- 
tial circuit, per 

■ cent 



G.E. 
Co. 
I-IO 



36 
46.6 
26.3 
1.77 



0.98 



2.5 



Westing- 
house 
0-A 



26 

36 

15 

2.32 
0.3 
0.75 

1.6 

18 



Fort 

Wayne 

K-4 



36.7 

45 

21 
2.14 
0.12 
0.59 

1.75 

17 



San- 

gamo 

H 



40 

40 

15.6 
2.5 
0.1 
0.5 

1.85 

35 



Duncan 
M 



Colum- 
bia C 



36.7 
115 
46 
2.5 



1.25 



lOT. Measurement of energy In alternating-currant drooita 
The energy consumption in alternating-current circuits is measured wiU 
watt-hour meters connected in exactly the same manner as are wattmeten 
for the measurement of power. (See Figs. 00 to 68.) In three-wiro, two- 
phase or three-phaie syatenu, polyphase meten may be used. SucI 
meters comprise merely two single-phase meters in one case, with a commoi 
shaft, and connected to the mam circuit in the same manner as two mngle 
phase meters. 

Vour-wire aystema, unless balanced, require three linclo-plimai 
meters. A three-phas* lyitem with a grounded neutral should b 
considered a four-wire system requiring three meters, unless it is completely 
balanced. 

tOS. Tho total anorgy in a three-phasa oirouit is the algebraic sun 
of the indications of two single-phase meters, just as the total power i 
the algebraic sum of the readings of two wattmeters (Par. 174). If i 
polyphase meter is used, the summation is automatically performed, an< 

* From "Electrical Meterman's Handbook," N. E. L. A., 1912, to whioh th< 
reader is referred for further data. 



164 



y Google 



MEASVniNO APPARATUS 



Sec. 3-209 



vbnt oDe alement tends to run baokward (power-factor loss than 50 per 
CBBt.), it simpiy reduces the torque of the other one, so that the actual speed 
» still proportional to the net power in the circuit. 

m. Polyphmse znet«r oonnsctlozu. Obviously it is extremely impor- 
ttBt that the various circuits of a iwlyphase meter are properly connected. 
lU for example, the current-coil connectioDs are interchanged and the 
foe power^aetor is 50 per cent., the meter will run at the normal 100 per cent. 
pover-faetor speed, thus givins an error of 100 per cent. 

A tmX for corr«ct ooniMcaoiw is as follows: If the line power-factor is 
vver 50 |>er cent., rotation will alwaj^ be forward when the potential or the 
evrent circuit of either element is disconnected, but in one case the speed 
■i& be leas than In the other. If the power-factor is less than 50 per cent. 
the rotation in one case will be backward. 

When it is not known whether the poweMactor is less or greater than 50 
per cent., this may be determined by disconnecting one element and noting 
Uw speed. Then change the potential connection from the middle wire to 
the other outade wire and again note the speed. If the power^factor is 
over 50 per cent., the speed will be different in the two eases, out in the same 
Erection. If the power-factor is less than 50 per cent., the rotation will be 
is opposite directions in the two cases. 

lit. Vam of Inatrumsnt traxufoniMn with watt-hour materi. 
When the capacity of the circuit is over 200 amp. series-type instrument 
trsDsformers are generally used to step-down the current to 5 amp. If the 
potential is over 440 volts, series transformers are almost invariably used, 
RRSpecttve of the nuignitude of current, in order to insulate the meter from 
the Une; in such cases, shunt-type transformers are also used to reduce the 
railage to 110 volts. The ratio and phaso-aogle errors of these trans- 
focvers (Par. 79 and Par. 104) should be taken into account where high accur- 
sey is important, as in the case of a large installation. These errors can be 
Isi^y compensated for by adjusting the meter speed. The per cent, error 
cttrssponding to various phase angles is given in Par. 179. 

til. The acourAcy of a watt-honr meter is the percentage of the total 
csergy passed throau a meter which is registered by the dials. The watt- 
boors indicated by the meter In a given time are noted, while the actual 
■^ts are simultaneously measured with standard instruments. On ao- 
WSBtof the time reqmred to get an accurate reading from the register, 
it is cvstomary to count revolutions of the rotating element instead of the 
Kfister. The accuracy of the gear ratio between tne rotating element and 
the fint dial ot the register can be determined by count. Since the energy 
Rpmented Inr one revolution, or the watt-hour COUtUltt has been assigned 
by the manufacturer and marked 



the meter, the indicated 
vstt-hours will be KkXR, where 
Kk » vati-hour constant and R * 
the nnmber of revolutions. (See 
Terting Formulse, Par. StS.) 
, <19. Laboratory tests. Ob- 
vioasly the source of energy for 
iseter testing should be as steady 
as possible. Storage batteries 
ate Urgiriy used for direct-current 
Bcters; and special alternators, 
*hose speed can be controlled, 
are ssea for alternating-current 
BctCTs. Tbe testing load may 
be banks of lamps, to which the 



Watt- 

hour 
meter 



Amperes^ 

.Uzi. 



Tolta 



Sa/ww — I 



Fia. 7fi.— Connections for testini( watt- 
hour raetexv — Bej>arate circuits. 



Bcter sod standard instruments are connected. 

A bettw mattaod is to asparate the current and the potential circuits 
sad onnncrt them to in^pendent sources, the former being a relatively 
Isme i uisu t. low-TOltace source and the latter a hi^b-voltage, low-current 
•sane. Conditions are more easily adjusted by this method and in large 
asters a sarinf of energy is effected. 

^^here separate sources are used for the current and the potential coils, 
<srt>oa rbeoststs are convenient for adjuatiiig the current, and high-resistance 
fkanuts connected "potentiometer style are convenient for controlling 



165 



zedbyV^iOUyie 



Sec. 3-213 



MSAaVniNO APPARATUS 



► 




Fio. 70. — Power-f ac- 
tor variation — tran»- 
former method. 



Fia. 77. — Power-^c- 

tor variation— ' 

former method. 



the voltage, as indicated in Fig. 76. Resistance in the potential osrcuit of 
alternating-current meters will alter the quadrature phase relation, and there- 
fore voltaKc regulation should be obtaiaed with a variable ratio mut<^tcmii»* 
former, an induction regulator or by field control. 

SIS. Power->fftctor Taiiation, in znetor t«itlnff, can be obtained by 
several methuds. In the two-alternator methodf, two generators ar« 
mounted on a common banc, with a common nhaft. The stationary meznl>ers 
(armature or field) are made movable about the shaft with respect to the baiae 
and to each other. Thus with the potential coil of the meter connc^cted to 
one machine, and the current coil to the other, any phase relation can be 
obtained by ndjusting one movable member with respect to the other. 

In the transformer method, a transformer with a large number of atepe, 
or a variable-ratio auto-transformer, is connected acron one phase ofa 
polyphase circuit and the potential coil of the meter is connected in auch a 
maniwr that any phase relation can be obtained. Thus, referring to Fic- 76* 

the current coil. of the meter 

is connected in series with 

conductor a of a three- 
phase circuit, and the po- 
tential coil is connected to 

o and to c, the latter being 

a tap on a transformer con* 

nected across phase be. It 

is apparent that any phase 

angle between the current 

and the potential can be 

obtaiaed in a range from 

deg. to 60 deg. by moving 

the connection point c 

alon^ the transformer 

windmg. Angles from 60 
deg. to 00 deg.. lead or lag, can be obtained by changing the transformer to 
either of the other two phases and the meter connection from o to x or y. 
These changes can be instantly made with suitable switching arrangexnenta 
A similar arrangement can be made for a two-phase circuit. Fig. 77. It 
is also convenient to introduce such a transformer between the taps o, c and 
the meter, for the purpose of compensating for the variations in the voltage 
between o and r, and keeping the voltage constant at the meter. Two 
variable-ratio auto-transformers arranged in this manner make a convenient 
phMO ihlfter. 

In the raactanoe-ooll method, a reactance coil is introduced in the 
current circuit, the reactance being varied by moWng an iron core in and 
out of the coil. It is difficult to obtain low power-factors with thia method 
unless a separate low-potential current circuit is used, and then there ia 
danger of waTe-form distortion. 

tl4. MeMuremant of metar torque. The torque is measured under 
normal conditions at full load by measuring the force in grams exerted at tbe 
edge of the disc, or ut the end of an arm attached to the shaft. This force 
may be measured by means of weights, a calibrated watch spring, or by 
utilising the principle of the pendulum.* By measuring the radius of the 
disc or the arm in millimeters, the torque is obtained in miUimetcr-grama, 
the usual unit. 

515. UeMurement of watt-hour meter losses. The losses in the wind- 
ings of c.c. meters are calculated from the resistances, as determined with con- 
tinuous current by standard methods. The losses in alternating-current 
meters arc measured directly with wattmeters, but great care is required 
because of the very small amount of power and the small power-factor. 

516. The standards for direct-current meter tests may be ammetera 
and voltmeters, in portable or special laboratory types, or ^otentiomotora; 
in alternating-current meter testa, use is made of indicating wattmetora! 
The time in measuring the meter speed is usually determined with atop-^ 
watches, reading to tenths of seconds. Where a large number of tnetera 



*Agnew, P. G. Buroau of SUndards Bulletin, 1911, Vol. VII, No. i 
(Reprint No. 145.) 



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MEASURING APPABATUS 



Sec. 8-217 



ftn banc xljufited, it ia customAry to use Btandardiied ot master watt- 
bour meters and tbua eliminate the meMurement of time and watte. 

tlT. Serrico tests of watt-hour meten. There are two general methoda 
of making teats on meters where they are Inatalled; (a) with indicating 
iMtrumenta and a atop-wateh and (b) with atandard watt-hour meters 
(Par. 118}. 

Id the indirmttng-lnatrument methCMl, the time of a given number of 
rerolutiona at a known load ia dul}' noted. The load on direot-current 
metera is measured with an ammeter and a voltmeter. In a modified 
form of this method, the load 'm an accurately standardised resistance and 
oaUy a voltmeter ia required, the watts being W=^B*/R, where TT^^watts, 
K^voH and R » ohms resistance of load. In the case of altornating- 
ewrent metera, the load is preferably measured with a wattmeter. 

SIS. Th« rotfttlnc-itftiidard method of w»tt-hour meter teitlnff 

ia the most used, because only one observer ia required and it ia more accurate 
with flactuatins loads. Kotatinff itajidarda are watt-hour metera similar 
to ftandard house-type service metera, except that they are made with extra 
care, are usually provided with more than one current and one potential 
range, and are more portable. A pointer, attached directly to the shaft* 
mores over a dial divided into 100 parts, so that fractions of a revolution are 
eaaily read. This atandard meter la used by connecting it in series with the 
meter to be tested; the accuracy of the latter is determined by the "switch** 
method or the "eye-and-ear" method. 

In the "switcn" method the regiater only (in direct-current atandarda). 
or the entire moving element (in alternating-current atandarda), is atarted 
at the beginning of a revolution of the meter under test, by means of a 
saitabte switch, smd stopped at the end of a ^ven number of revolutions. 
The accuracy ia determined by direct comparison of the number of whole 
revolutions of the meter un- 
der test with the whole revo- ' ^ ' f " - ' ' > 

Intwna, and a fraction* of the 
atandard. 

In the "eye and ear" 
method, the number of 
whole revolutions of ^ the 
standard is compared with a 
whole number of revolutions, 
asd a fraction, of the meter 
sader test. The revolutions 
of the standard are counted 
hf ear by means of a tele- 
pbooe recerver and an elec- 
trical contact on the shaft, 
efaile UuMe of the test meter 
«« obserred by eye. 

tl». ▲ Whoatttone- 
Mdffe metbod for testing 
bipe watt^lioor metera 

vfa^ cannot be conven- 
iently cut out of service, and 
are on a load which fluctuate a 
exeeasively. such as a railway 
kiad, hae been developed by 
Mcaars. Incalla and Cowlea * 
The coanectione are shown 
ia Fig. 78, where o and 6 are two fixed standard real stancea or shunts, f orminff 
two anas of the bridge. The third arm is ahown at c. A rotating standard 
*>th aa adjoetable fixed resistance d and a carbon rheoetat e constitute the 
leerth arm. When « is adjusted until the portable galvanometer shows aero 
the ratio of watts passing through the two meters ia a/ia + b). 




Fig. 78. — Connections for testing large watt- 
hour meters — Wheatstone bridge method. 



* logalla, C. H. and Cowlea. J 
Method of Teeting Large-capaci^ 
Ita VoL XXXI. p. 1061. 



W. "Wheatstone-bridge Rotating- atandard 
ity Watthour Meters" Trons. A. I. K. K.. 



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Sec. 8-220 



MEASURING APPARATUS 



tlO. Oenoral prtcauUona to be obaerred in testing watt-hour m#t«n 

are as follows: (a) The t«8t period should always be suffioienily Ions aiuj 
a sufficiently large number of iade^ndent readings should be taken tt 
insure the desired accuracy. In service teats, the period preferably shoulc 
be not less than 30 sec. and the number of readings not less than three. Xx 
laboratory teats, 100-sec. periods and five readings are preferable. (b] 
Capacity of the standards should bo bo chosen that readings will be taken ml 
reasonably high percentages of their capacity, in order toinake observationm 
or scale errors as small as possible, (c) Where indicating instruments an 
used on a fluctuating load, their average doflectionj should be estimated ii 
such a manner as to include the time of duration of each deflection, as well ai 
the magnitude, (d) In-itruments should be so connected that neither tht 
standards nor the meter being tested are measuring the potential-circuit losa 
of the other, that the same potential is impressed on both, and that the sani< 
load current passes through both, (c) When the meter under test haa not 
been previously in circuit, sufflcient time should be allowed for the tempera 
ture of the potential circuit to become constant, preferably not less than 1( 
min.; this is important with direct-current meters, especiall)^ in the oane o 
rotating standards. In some types of the tatter, special i>rovi8ion is nuule fot 
rapid heating, (f) Ouard against the effect of stray nelds by loeatinc tbt 
standards and arranging the temporary test wiring in a judicious manner. 

Ml. Meter constantt. The following definitions of varioas xneten 
constants are taken from "Code for Electricity Meters."* 

Keffiat«r constMlt is the number by which the register readinoB must bt 
multiplied to obtain the registration. They are ordinarily used only oi 
largo-capacity meters and are marked on the register. 

Gear ratio la number of revolutions of the rotating element per revolu 
Uon of the first dial hand. 

Watt-hour constant is the registration reduced to watt-hours per revolu 
tion of the rotating clement. It has a definite value for each type and ratec 
capacity of meter. 

Watt-aecond constant is the registration reduced to watt aeoondi 
per revolution of the rotating element. It is equal to watt-hour constani 
multiplied by 3.600. 

Teit constant is the constant assigned by the manufacturer for uaeii 
the test formula for his meter. 

Sn. Testtnf f<vinulas. The accuracy of a watt-hour meter is the per 
centage of the total energy passed throiigh a meter which is registered on thi 
dials. Accuracy in percent. =» meter watt-hours X 100/true watt-hours. Thi 
value of one revolution having been assigned by the manufacturer, the metea 
watt-hours — KfcXR, where Xa — watt-hours per revolution or watt-hour oon 
stant and A =■ revolutions in S seconds. The corresponding power in 'watt 
is /'""(S.dOOXAX/irAX/'S-* meter watts and lOOXmeter watts/actual watts «i 
per cent, accuracy. This is the standard formula for watt-hour metera. 

lis. Manufacturers' formulas tor meter watts. When the tern 
constant K differs from the watt-hour constant, Kk, the formula is ch&ngec 
accordingly as follows: 



Manufacturer 



Columbia 

Duncan 

Fort Wayne 

General £lectric. 

Sangamo 

Westinghousc 



K in terms of Kk 



K^- 3,600 A'*. 
K- 60 Kk. 
K" 30 Aa. 
A- Kk. 

X- 3,600 Kk. 
A -3.600 Kk. 



Manufacturers* formula 
for meter watts 



W^RXK/S 
W-60XRXAAS 

iy«100XfiXAAS 
IF- 3.600 X/JXiCVS 
W^RXK/S 
W'RXK/S 



A*- watt-hour constant. A — test constant (marked on meter, usuidly oi 
disc), 72 — number of revolutions in S seconds, ^ — meter watts. 

SM. Average accuracy of watt-hour meters. The aecuraoy of a 
meter varies with the load, but it is often desirable to assign a value for th< 

• "Code for Electricity Meters." A. £. I. C. and N. £. L. A..' 1912~^ 
pp. 95 and 96. 



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UBASVRINO APPARATUS See. S-225 

sTcnM accaracy for all loads. Such a value obviously must be based od " 
as anitrary nile. The "Code for Electricity Meters" recommends the 
fdlowisc:* When feasible; test the meter at 10 ^r cent, and 100 per cent, 
oparity of meter and at the normal load. Multiply the accuracy at normal 
load by three, add (to this) the accuracies found at each of the other two 
loads ind divide the sum by five. This result is to be taken as the average 
moracy. The "normal load" shall be taken as the percentage of the total 
iitiiic <j the connected load indicated in the table in Far. lit. 

m. Tabla of Homial Loadi of Watt-hour Metanf 
Pn cent, of connected load which is equal to the "normal load" in calcula* 
tion of average accuracy (Par. 114) 

Retidence and apartment lighting 2S per cent. 

Elevator service 40 per cent. 

Factories (individual drive) ehurches and offices. ... 45 per cent. 

Factories (shaft drive) theatres, ^clubs, entrances, 
baUways and general store lighting 60 per cent. 

Saloons, restaurants, pumps, air compressors, ice 
machines and movinc picture theatres 70 per cent. 

Sign and window lighting and blowers 100 per cent. 

IM. Watt-hoar mater ipoelflektioiig. Probably the most extensive 
•ad satboritative q)eeifioations for the performance, installation, testing and 
naiatenanoe of watt-hour meters in the United States are those included in 
tte "Cod* for Beetrletty Meton" prepared by the Electrical Testing 
laboiatories ondertfae joint direction of the Meter Committees of the A. £. 
L (^.'s and the M. E. L. A. It ia the basis of the rules issued by most of those 
Hate public utility commissions which have adopted regulations covering 
At fubMct of electricity meters. While scientific accuracy and correct 
tKhueaJ principles are the basis of the code, the commercial phase of meter 
pnetice is not neglected. It covers the entire field of representative Amer- 
Kaa meter practice including definitions, standards, specincatioDS for meters 
•ad aoxiliaiy apparatus, installation tests and maintenance. 

W. Asiporo-hoor laeteri measure only quantity, that is, coulombs 
or ampere-hours, and therefore where they are used in the measurement of 
deetrieal energy, the iK>tential is assumed to remain constant at a "declared" 
nine, and the meter is calibrated or adjusted accordingly. Meters of this 
live may be divided into two general classes: .electrochemical (Par. SM) 
•ad electromotor (Par. 111). 

Ml. BUetrochomleal ampors-hour nuten are essentially vol- 
tameters, becaoae the quantity is measured by the amount of chemical 
daeompomtion of a substance caused by the passage of all or a part of the 
(•ad eomnt. In the Kdtson chanileal meter, now obaolete, two sine 
lilatn were immersed in a jar containing a sine sulphate solution and con- 
•Med ia parallel with a shunt which in turn was in series with the load. 
The energy consumption was obtained by measuring the decrease in weight 
•f the anode (positive) plate; 1.224 grams represented one ampere-hour. 

pt. Ilodanx tn>o* <rf aleetrochomleal uupwe-honr meton. The 
PjUopal modem tyi>es utilise the electrolyais of either water or mercury. 
rhe Isstlaii mirtitr is an example of the former in which the change of the 
ksglh of a eolamn of water, as it is decomposed, is a measure of the quantity 
<< eleetrieity. A little caustic soda is added to decrease the resistance and 
■ lartroC oU is floated on top of the water to prevent evaporation and faeili- 
*sie Rading. A scale at the side of the tube is calibrated to read kilowatt- 
Inui acconlinc to s "dedared" voltage. 

The Wright motor is the principal example of the maroury type. - 
n*taUie roerenry is earned into a mercurous nitrate solution from s platinum 
fsp aaode and deposited in a platinum cui> cathode, from which it flows 
mio a fine tube. The height of this column is a measure of the energy con- 
■mplian, a graduated scale being placed at the side of the tube. The 
'"etrndei are connected in parallel with a shunt, so that only a small portion 
"^ the load current passes through the solution. Provision is made for 

' Pige 99, I»I2 Edition. 
. t "Voit for Eleetrieity Meters;" A. E. I. C. and N. E. L. A.; 1912 ed., p. 

m. 



100 



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Sec. 3-230 



MSASVHTNO APPARATUS 



easily emptving the mercury from the tube into the anode receptacle wlieil 
the former becomes filled. This type of meter has been highly developed 
and inherent errors due to variation in temperature, concentration of ttkfl 
solution, level of mercury, effect of vibration, etc., are largely elimiiuited 
in the latest forms. 

550. The principal adYantagei of •leetrol7tio-t7p« unp«r«-bour 
liutruxnenta are tncir low first cost and their simplicity, which results in 
low maintenance cost. These are important items to power compnoiefl 
serving very small customers, especially where the rates are low; and may 
outweigh the disadvantages, the principal among which are eliminatioo oi 
the potential element ana relatively low accuracy. 

551. ■lectroznotor ampere-hour zneten are similar to watt-hour 
meters, except that the field is produced by permanent magnets instead of 
electromagnets. The rotating element is geared to a register which is cali- 
brated in watt-hours for a given assumed voltage. There are two general 
types, the electromagnetic and the mercury flotation. The former im 
not made or used very much in this country. 

The Chamberlain and Hookum meter is an example of the elcctromas-i 
netic type. ^ It employs a flat (pan-cake) armature winding mounted on an 
aluminum disc which also serves as the drag element. Connection Is made to 
the circuit through a commutator and brushes in the usual manner. The 
armature is connected to a tow-resistance shunt which is in series with the 
load. 

The mercury type meter is well represented by the Sanffamo motor 
which is practically the same as the Sangamo direct-current watt-hour meter 
(Par. IM), the electromagnet being replaced by permanent magneta. 

tSS. Maximum demand meters. Many methods of selling energy 
involve the maximum amount which is taken by the customer in any period 
of a prescribed length, that is, the maximum demaDd. 
Meters for measuring this demand variously utilise the 
expansion of air, the torquo of a watt-hour meter, or a 
special recording device in connection with a standard 
watt-hour meter. 

The Wright demand meter is a thermal inatrn- 
mont. It consists of a hermetically sealed U-shaped 

f;lass tube (Fig. 79), partly filled with a liquid. One 
eg A ifl connected near the top to a smaller graduated 
tuoe T. Around the top of the tube, B, is wound a re- 
sistance wire through which the current flows. Th« 
resultant heating of the air forces the liquid up the tube 
R and, if sufficient, over into the graduated tube. The 
air heats up gradually and the necesaary time l%g ia 
thus obtainea. According to the makers, if the over- 
load continues 5 min., 80 per cent, of the load will be 
indicated; 10 min., 95 per cent.; and 30 min. 100 per 
cent 

111. The Oeneral lleotric denujid metor utiliios 
the principle of the induction watt-hour meter. The 




torque of the moving element is opposed by three long 
spiral springs, in series, and a powerful drag on the 



Fia, 79. — Dia- 
gram, Wright de- 
mand meter. 

drag disc. This arrangement provides the necessary 
time lag. Two sweep-hands are provided on a dial. One is geared to tfao ! 
moving element, while the other is moved by the first one and left at tfaO; 
last position reached by it. This second pointer indicates therefore thfj 
maximum energy, until it is reset. The drag magnets and spiral sprinf^l 
being adjustable, the time lag can be adjusted through a considerable rang&^ 
In this t^pe of instrument, the demand is indicated at all times, as well aM; 
the maximum demand since the last setting. 

tS4. Recordinff maximum-demand meters. In the MinorallaO 
■leotric Co.'s "Printometer" the kilo watt- hours indicated on a watt-hour 
meter are printed on a paper tape at intervals of any desired length. ThS^ 
hourly intervals are also indicated. It is separately mounted and can b# 
electrically connected to any standard make of watt-hour meter. Thil 
device, while it indicates the time of maximum demand, is not an indicatin| 
instrument and considerable labor is involved in determining the maximuil 



170 



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USASVniNQ APPARATUS 



Sec. 8-235 



The "Mulcator" (Minerallac Co.). indioat«s tha raazimuiii 
with a flwfiep-haad. The "Oraphomotcr/' (Minerallao Co.)i 
prtxlucM a graphic record of the demand. 

CintTI-DEAWIKO ZHSTKXrMKNTS 

SM. OoTTA-dnkwinff or roeordinc ixutrumenti are nsentially indi- 
cating injitrutneoU ao arranged that a permanent, rontinuoiu record of the 
indieataoD is made on a chart. They are made for recording all electrical 
qvantitiea that can be meaaured with indicating instrumpnta: current^ poten- 
tial, power, frequency and power-factor. Here the fundamental pnnciplea 
are, la ^nerai, those of standard in<licatiog instruments, with the addition 
of a nutable reoordina mechanism. The two general classes are those in 
which the record or chart is made directly bv the moving element and 
Ukmk in which it is made by a separate mochanism. In all typen the chart 
ia driven by a clock mochanism which is entirely separate from the 
instrument proper. 

IM. XMrect roconliiur typs. Examples of this class are Bristol, Gen- 
eral Electric and E^terline meters. The distinguishing feature of the 
Brist<d instrument is the use of a circular chart. The direct-current am- 
meters and voltmeters employ a stationary coil or solenoid, the moving ele- 
ment being a soft-iron armature working against flat springs. The iilternat- 
ing-cnrrent instruments employ the electrodyDamcmeter principle, with 
one movable coil and one stationary coil. Suitable provision is made for 
mnltiplyinf the armature movement, and damping is obtained with a vann 
iauncTsed in oil. These instruments are extremely simple and relatively 
inexpensve. The sensi- 
tiveoeaa is aeriously af- 
fected by pen friction and 
wbere lugh sensibility is 
flBMntial, a smoked chart 
with a very light pointer 
is used instead of the usual 
paper chart with pen and 
ink. 

The principle of General 
EHectric alternating am- 
■keters is shown in Fig. 80, 
where AA are fixed coils 
foonected in series, and B 
is a soft-iron armature 
spon which the field acta 
and produces a torque, and 
shicn carries the pen. The 
chart is a continuous 
■traight one, moving from 
1 in. to 12 in. per hoar, as 
desired. The record is 
made in the form of a 
ttraight line on rectangular 
coordinates. The pen in 
tUa instrument carries an 
ittk-weli and ia self-inking. 



i 




Fio. 80. — Diagram, G. E. alternating graphio 
ammeters. 



_ Magnetic damping ia employed. The volt- 

Btetera and wattmeters are similar except that they utilise the electro- 
dynamometer principle, with fixed and moving coils. The greater friction 
mad eom^eation necessary to get the straight-line record necessitates a 
U^ torque and therefore a larger and more expensive construction. 

Gaterhne direct-current instruments are of the D'Arsonval moving-coil 
type. The ammeters are 50-miIlivolt voltmeters connected to shunts. 
Tbe ahemating-current instruments are of the movioR-coil or electrody- 
aamometer type. The record is a straight-line one, made with a pen inked 
by siphon action from a stationary well. These instruments are made in 
portable as well as in switchboard form. 

Sit. Where pen friction ii particularly objectionable, aa in low- 
nading millivoltmetera, the indicator is so arranged that it is in contact with 
^ chart for only an instant at a time. In one form of Bristol instru- 
OMita, a lever presses the end of the pointer against a amoked chart once 



171 



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Sec. 3-238 



MEASURING APPARATUS 




a minute, the pointer being perfectly free in the interim. The record is 
therefore a suoccaaion of dots. In other types of instruments, an inked. 
thread or ribbon is interposed between the pointer and the paper ehart. 
1S8. The Weitinffhouae recordlnff ixutrumenta are the princiiMl 

example, in American practice, of 
the claes where the reeordinic 
mechanism is separate from the 
instrument proper. The moving 
element, by means of contacts, 
operates a relay which in turn 
operates the recording mechan- 
ism. Thus the moving element 
does not have to produce a larce 
toroue, while ample power can Be 
appliea to the recoroing tncchaji- 
ism, and hence friction does not 
affect the sensitiveness of the 
instrument. The direct-current 
Instruments employ the D'Araon- 

F.o.81.-piagramW«,tinghou.e graphic ^IJe/iSilPeU^^"^^^^^^^^^ 

voiimeier. rjx^^ alternating-current instru- 

ments use the principle of the 
Kelvin balance. Fig. 81 shows the scheme as employed in a voltmeter. 

tS9. The Callender recorder made by the Cambridge Scientific Tnatru- 
ment Co. employe the princi- 
ple of a slide-wire bridge (Fig. 
82) in which the resistance of 
one arm, X, varies with the 
current, potential or power to 
be measured. As soon as the 
bridge is unbalanced, a D'Ar- 
sonval galvanometer operates 
a relay, r or r', which moves a 
contact, c, along theslidewire«, 
until balance is restored, when 
the relay circuit opens. This 
contact also carries the record- 
ing pen, which leaves an ink 
record on a rectilinear chart. 






? 




Fio 



Diagram^, Callender recorder. 



XND17CTAN0B MEASUBEMBNTB 

MO. Oeiural. Th« lelf -inductance, or coafflolent of ■elf-induc- 
tion, of a circuit is the constant by which the time-rate of change of the 
current in the cii^uit must be multiplied, to give the self-induced counter 
e.m.f. Similarly, the mutual induct&nca between two circuits ia the 
constant by which the time-rate of change of current in cither circuit must 
be multiplied to give the e.m.f. thereby induced in the other circuit. Self- 
inductance and mutual inductance depend upon the shape and dimenaiona 
of the circuits, the number of turns and the nature of the surrounding medium. 

S41. Standardi ni inductance are usually simple colla of copper wire 
suitably mounted on a non-conducting, non-magnetic frame. The turns 
are held rigidly in place by shellac, paraffine or other insulating medium. 
Inductance standards are made in single units like standard resistanoea, or 
in combinations, with plug connections, like a subdivided condenser or a 
resistance box. In the Ayrton-Perry variable standard there are two con- 
centric coils, one fixed and the other movable. When connected in aeries 
these coils form a variable inductance, the value of which at any relative 
position is read from a circular scale at the top. Additional ranee is secured 
by connecting sections of the two coils in series-parallel combinationa by 
means of plugs. 

lil. Methods. The most commonly employed methods of measuring 
inductance are (a) Wheatstone-bridgo methods, where the inductance is 
determined by comparison with a known inductance or known capacity; 
and (b) impedance methods where the inductance is determined by calcula- 
tion from meaaurements made with alternating current. 



172 



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MSASVRISa APPARATUS 



S«c. 3-243 



MS. la mM«trton»-brid(a mathodi a rarying current mtut ba em- 
planed. The twtential drops, with etesdy current, are proportional to the 
reastancee, whereas with a varying current the drdpa are proportional to 
the inductance, because fLdi/dU where L-i inductance and e^e.m.f. 
iaduoed by the current varying at the rate di/dt. 

MA. Wban the detaetor ii an ordinary D'Anonval nlTanomator 
the current may be varied by simply opening and closing the battery circuit, 
tbe galvanometer circuit being left cloeed; or a Meohmineter may be 
employed which rapidly reverses the current going into the bridge and 
■mnltaneonsly rectifies the galvanometer current, so that the latteru used 
M in ordinary bridge measurements. The current may also be rapidly 
iDtennpted with an inductionnioil interrupter 
with a telephone receiver as the detector. 

Ml. A mathod in which a itandard In- 
doctance la lUad is shown in Fig. 83. If a con- 
tinooua current is used, the bridge is first balanced 
with a steady current by adjusting n and r<, and 
again balanced with transient currents (battery 
wif opened and eloaed) by adjusting n and n; the 
bridge is then rebalanoed with t^e»ay current, and 
again for transient eunents, the process being re- 
peated until the bridge is perfectly balanced 

under both conditions. At complete balance Y\a 83 Inductance 

L -tft/n: where i -inductance being measured, measurements with 
and X,,- standard inductance. Z, will be in the standard inductance, 
same unite as L*. 

MS. Usa of Trednnd OfcUlAtor. Small inductances, as well a* large 
ooM, may be measured with special convenience, accuracy and rapidity by 
tUs method (Far. MS) if a source of high-frequency, sine-wave alternating 
earrent is available. A verv satisfactory apparatus for this purpose is a 
Tieeland oseiUator, * which aelivera an absolutely pure sine-wave having a 
frequency which can be varied from a few hundred to about 2,000 cycles 
per SFeond. _ It is operated from continuous current and is entireljr static, 
the alternating current being derived from a circuit in which oscillations are 
set up by the rapid shifting of a mercury arc back and forth between two 
anodes. A telephone can be used as tog detector, with a high degree of 
ability. 






Fio. 84. — Inductance measure- 
ments with a condenser. 



Flo. 85. — Inductance measure- 
ments with a condenser. 



MT. A mathod tulM »■ known oapaeity is shown in Fig. 84. It is a 
aiodified form of BlaswaU'l method in which the condenser is connected in 
parallel with i?, and two adjustments have to be made which are not inde- 
pendent of each other, one with steady currents and the other with transient 
rarrrats. The two adjustments have to be repeated until complete balance 
is obtained. In fig. 84, the bridge is balanced with steady current by 
adjoMing R, and then with transient currents by varying r without changing 
the first adjustment. At balance. 



..^'10- 



(henrys) 



(26) 



•Pktnral Rtriev, 1008, Vol. XXVIII, p. 286. 
173 



y Google 



Sec. 3-248 



MEASUBINO APPARATUS 



^ 



where £•> induotonoe of Zin henrys,r— ofanis in parallel with C.C' cspseity 
of condenser in micro-farada, R i> total ohnu of bridge arm to which oondenaer 
is connected and i2x~%hni8 of Z. 

I<8. A limllar method (Par. MT) ia indicated in Fig. 8S in which the 
adjuatmenta are independent of each other, the bridge being first balanced 
with a steady current and then with a transient current by adiusting r aa 
in Fig. 81. At balance, 

L-CrnO-« (henrys) (27) 

where L — inductance of Z in henryn, C~ capacity of the condenser in micro- 
farads and r » ohms in parallel with C. 





Fio. 86. — Inductance measure- 
ments — connections for three-volt- 
meter method. 



Flo. 87. — Inductance measure- 
ments — vector diagram for throe- 
volt-meter method. 



SM. ImMdanee method! of maMurtnc inductance are baaed on the 
law of the impedance of a circuit carrying sine-wave alternating current and 
containing only inductance and resistance, that is, 



E 
'] ' 



'' >/l 



I'R' 



Vfi»+(t2r/)»ori- -tl \2w/T)' <''«"y»J <28) 



where L = inductance in henrys, £<«drop in volts, f ^current in amperes* 
A « resistance in ohms, and /■= frequency in cycles per sec. Obviously, 
due allowance should be made for the voltmeter current where ita magnitude 
is sufficiently important. 

ISO. In the three-voltmeter method, the inductance to lie meaaured is 
connected in neries with a non-inductive resistance as shown in Fig. 86. 




-^^-%J 




Fio. 88. — Inductance measure- 
ments — connections for three-am- 
meter method. 



Fia. 89. — Inductance measure- 
ments — vector diagram for three-am- 
meter method. 



The current, /, is measured, also the total volts, and the volts across the 
inductance Z and the resistance R. From these readings a triangle is con- 
structed. Fig. 87. If R is known, the quantity 2ir/L7 can be calculated from 
the triangle. If R is unknown, 2t/L/ can be obtained by graphical construc- 
tion. / and / being known, L is obtained by calculation. 

Ml. The three-ammeter method is similar. The connections are 
shown in Fig 88, and from the three currents. Fig. 80 is constructed. The 
o.m.f., By can be measured directly or, if R is known, by calculation from 
the relation E^RIt. Hence L can be obtained from the quantity B/2w/L. 

ISt. In drouiti containing iron the inductance varies with the 
frequency and with the current ; hence ulternating current of known 
frequency and intensity must be used. In such cases a bridge method 
with a standard inductance is convenient. A vibration galvanometer, a 



174 



yGoogle 



MBASURim APPARATUS 



Sec. 3-253 



synehrono<u eonteetor or a aepnrately excited electrodynamometer oaD b« 
■9ed em the detector. The bndge ia first balanced for reoistance (that is, 
balanced for bridiee-arni drops in phase with the supply current) and then 
lor inductance (bridge-arm drops 90 deg., from the phase of the supply 
current). 

MS. Tbe mntoal inductance, M, betwe.en two colli may be 
maaatzred by aoTeral methodi, as follows: 



JL—^ff^^ 



LR 



V^^H 



Fio. 90. — Mutual inductance 
Baeaaurements with inductance of 
one coil known. 






Fio. 01. — Mutual inductaDce 
measurements with known seU 
induetanoe. 



(ft) Wli«n th« Iziduetanee, L, of on* eoU U known. The connections 
an afaown in Fig. 90. The bridge is balaaoed as in inductance measurements 
{or both sC«ady and transient currents. Then 

M and L are in Muna unita, n and n in ohms. 

(b) By Gompariaon with a known aelf-induetane*. Connect as in 
Fig. 01. First balance for steady currents; then balance for transient 
comnta by adjuating ri. Then 



11- -V 



nir.+r) 



(30) 



V—i — r«n 

/ l! a @ 

-=L *» r.. 



Fio. 92. — Mutual in- 
ductance measurements 
with known capacity. 



^R+rO' 
where r^reaistance of secondary or mutual, in- 
duetance Jf, and i2 » resistance of self-induct- 
ance, L. M is in same units as L. 

(e) By comjMUtlMnt with a known capacity. 
CoBaeeted as in Fig. 92. Balance as before for 
steady and transient currents by adjusting n 
sad n. 
Then 

U-CnnlO-> (henrys) (31) 
where Jf.> mutual inductance in henrys, C— 
capacity in microfarads. 

(d) By conoactint tha aaemidafy In tariai with a baUiitie calva- 
iMtiWittw and noting the quantity, ^ in coulombs, discharged into the gal- 
Tsaonteter when the primary circuit is closed through a known resistance, 
olR ohms, the steady value of the current being / amperes. Then M — QR/I 
in henrys. The quantity is determined from the galvanometer constant, or 
anre direetly, by eaiibrating the galvanometer with a standard condenser. 

CAFAOITT MBASVHBinim 
SM. Ocnaral. The electrostatic capacity of two conductors separated 
by a dielectric depends upon the surface area of the conductors, the distance 
between them, the character of the dielectric, the temperature and the 



are groups of conductors separated by insulation and 
<s|iccially constructed to have a known capacity. Commercial forms are 
■noally nude of sheets of tin foil separated by mica or paraffined paper, 
•hnaate layers of tin foil being connected to the same terminal. One box 
■ay contain one or more of these groups, with plug or other arrangements 
for coaaeetfav tbem in Tatious series or parallel oombinationa. 



176 



Jigili.edbyCoOgle 



Sec. S-256 



MSASVRtf/a APPARATUS 



tM. TIw oapadtj of a group of condenMn in uaiin U: 






2. 

C" 



When connected In parkllol, 

C-Ci+C. + C.+ c. 

SIT. 



(32) 
(33) 



In talvh-crade itandard condanMrt, the aim is to reduce tha 
abaorptioD, the ffielectric hysteresis and the ohtnio losses to a minimum. 
Commaretal itandardi are made with tin-foil and high-grade mica. 
bound together under high pressure. Primary ttandardl, however, 
are made with air as the dielectric, in which absorption and leakage are nil. 

SU. Mathoda. Electrostatic capacity measurements are made by bridse 
methods (Par. lit), with a ballistic galvanometer (Par. SM), by loss of 
charge (Par. tCt), and by impedance methods (Par. S6S). 

tM. A bride* mathod of measuring capacity is shown in Fig. 93. Tha 
ratio, n/n, or the standard condenser (if adjustable), is adjusted until tlie 
bridge is balanced; with an ordinary D'Anonval galvanometer this condition 
is iaoieated when there is no " kick ' ' as the reversing switch is changed from 
one position to the oUier. If interrupted currents or high-frequency alter- 
nating currents are used, with a telephone receiver, balance is indicated by 
silenoe in the receiver. Then Ct — Ciri/n. The resistance should be non- 
inductive, anti-capacity and relatively large — several hundred ohms. Ob- 
viously, maximum sensibility ia obtained when Ct and Ci are about equal. 
By employing a Vreeland oscillator (Par. S4f) and an adjustable air or oil 
condenser, small capacities can be very accurately measured by this method. 




r* 1 

-tltJ'I'l^ 

Fia. 03. — (Capacity measurements, 
bridge method. 




Fio. 04. — Capacity measurements, 
method of mixtures. 



SM. In tha balliitio (slTanomatar method, the deflection is noted 
when the unknown capacity is discharged through it, Immediately after 
having been charged at some known potential. A reading is then obtained 
with a standard condenser, the deflection being made about the same as 
before, by varying the capacity or the ohamng potential. The capadty 
ean tiien be computed from the relation <f/di""C£/Ci£i; where d,di, C, Ci, and 
£, Bi are the respective deflections, capacities and potentials. Thia method 
is belt suited to relatively large capacities, such as lead-covered, paper- 
insulated cables, etc. 

Ml. Tha Thomion method of mJxturaa is shown in Fig. 94, where n 
is a cable, transmission line or other capacity to be measured, and ct is a 
standard condenser. First the switches are closed at 1, 1, and the condensers 
ebarged to potentials corresponding to ri and n respectively. After complete 
charge (a cable may require several minutes), the switches are shiftea to 
2, 2 and the charges equalised. If, then, the switch at 3 is closed, the deflec- 
tion of the galvanometer will be proportional to the difference of the charges. 
This operation is repeated with various ratios n/n until there is no deflection. 
Then n — cin/n. 

lU. In the loai of oharga method. Fig. 06, the condenser to be 
measured is first completely charged by moving switch b to a, and then imme- 
diately discharged through a ballistic galvanometer by moving b to c. The 
oondenser is again charged and allowed to discharge through a known high 



176 



i.jv^iuuyic 



MBASURING APPARATUS 



Sec. 3-263 



J Rt h, ^ven number of seoonda, t, before being connected to the 
l»iTWU>iaster a aeoond tizae. The capacity in miorofarade is 

(microfarads) (34) 



R log lodi/di 2.303 

whien dio first deflection, dt — eecond deflection and £» resistance in meg- 
vhxam. This method is applicable only where the resistance of the condenser 
being measured is very high, such as porcelain insulators. 



^ 






IK ' e 



Hl|«l» 



-at 




Fic. 95. — Capacity measurements, 
loas of charge method. 



Fjq. 96. — Capacity measurements, 
impeoance method. 



MS. In ilM imp«danee metliod, the capacity is computed from the 
reactaooe as measured with an ammeter and a voltmeter, with alternating 
rarreat of known frequency as shown in Fig. 9G. Then 

C-2;^(10«) (microfarads) (35) 

wfaete C— capacity in microfarads, £ — volts, J — amperes, and /—frequency 
ia cycles per second. Unless the voltmeter is an electrostatic instrument it 
dioaid be disconnected when taking current readings. With small capacities, 
where / is small, care should be taken that the high inductance of a low 
reading ammeter does not introduce an error. The capacity given by this 
EDethod depends upon the wave form. Therefore the teat should be made 
Iron the circuits to which the apparatus being measured will be connected 
ia service. 

Mt. Tb« ipeelfle indaetlTa eapadty of materials is the ratio of the 
c^Muity of a condenser with the given material as a dielectric to that of the 
ama eoDdenser with air as a dielectric. In the case of solids in the form of 
■heets or plates, a condenaer ia readily made b^r attaching similar square or 
circular pieces of tin-foil of known area to opposite sides of the specimen and 
measuring the capacity by one of the methods described. Care should be 
Ukeo that there is no deflection when the condenser has no charge. Certain 
matoials in thin, sheet form may show a deflection, due to the galvanic 
I td the paste used to apply the tin-foil. 



C2^ 

' — • I 



fr^ 



Tia. 97. — Guard ring in specific induction capacity measurements. 

Ul. Th* "trlngs illect" (electrostatic field in the dielectric extending 
beyood the area corresponding to the electrodes) may be eliminated by using 
a guard ring, a, a, of^tixi*fou as^ shown i n Fig. 97. It ia very close to the 
ctectrade b and ia so connected in the circuit that only the charge on b is 



IM. The evad^ of an air condenser is C-il/4TeX9X10>,, where 
t^— capacity in miorofarads, A •* area in square centimeters and, ( * tliickness 
•f layer of air in eantimetera. 



M 



177 



JigilizedbyCoOgle 



Sec. 8-267 



MEASURING APPARATUS 



WAVX-rOSM BUASUBIMKNTB 

SC7. Metbods. Tho instantaneouB variationa of current and potentiml 
in a oircuit are measurable by step-b^-step mothodjs (Far. 268)^ and with ^e 
oacUIograph, (Par. 171.) Tbo former is applicable only where the current and 
the potential are strictly periodic and recurrent, as in a normal alt«rnatins- 
curront circuit. The oscillograph can be used under all conditions, but ia es- 
pecially applicable to measuremcntB of iransiont phenomena (Par. lU), such 
aa those which occur during switching operations on direct-current and al- 
ternating-current circuits. Where the wave form is to be analysed, tho former 
is the more convenient and accurate. 

IfS. A oonTenlent "step-by-itop" &rranffement is ahown in Fig. 98. 
The contact device consista of two slip-rings and a four-part commutator. 
One slip-ring is connected to one terminal of the source, the other to a volt- 
meter, and the commutator to a condenser. By means of this arrangement, 
the condenser after being charged is immediately discharged through the 
voltmeter. These impulses follow each other so rapidly that a steady de- 
flection is obtained, and by suitable adjustment of R and r nn continuous 
ourrent, the voltmeter may be made direct reading. The instantaneous 
values at any point on the wave are obtained by shifting the brushes around 
the shaft. The switch is closed at 1 for volt^e measurements and at 2 for 
current measurements. * 

The General Electric w&ve meter operates on 'this principle. The 
driving motor is an eight-pole synchronous motor connected to the source 
being measured and there are eight segments (one per pole), instead of only 
one. Suitable provision ia made for tracing the wave form on a photographia 
plate. 





Fxo. 98. — ^Wave-form measurements, 
**Step-by-8tep** method. 



Fig. 



99. — Wave-form measure- 
ments, aero method. 



169. In the sero method shown in Fig. 09, the e.m.f. of a battery B is 
opposed to the potential across c and tf, which are connected to the contact 
devices described above. The contact point, b, ia adjusted until O shows no 
deflection; then the length 6a is a measure of the e.m.f. G^ may be a portable 
galvanometer, or a telephone in conjunction with a slide wire and a contact 
stylus as used in the Sage ohmmeter -(Par. 189). 

170. The wave fonu of a hiffh-tension wave may be obtained by uaing 
the device shown in Fig. 102 and described in Par. 277. The indication of 
the electrostatic voltmeter is obtained at different angular positioua of the 
brushes on the synchronous commutator, from which the wave form may 
be plotted. 

171. The oeciUograph is a form of galvanometer in which the natxxral 
period of the moving system is ao small that the deflections will alwavs be 
proportional to the instantaneous value of the ourrent flowing through the 
coil. The indicator ia a beam of light from an arc lamp, reflected from an 
extremely small mirror attached to the moving system. The path of the 
beam is determined visualty or photographically. Recurrent or periodic 
waves may be rendered stationary and therefore visible by suitable optical 
systems as indicated below. Transient phenomena must be photographed 
by an instantaneous process. 

171. In the movinff-iron type of oaclU ograph, first propoeed by 

•See also Frederick Bedell. "Condenser Current Method for the Deter- 
mination of Alternating Wave Form," Electrical Worldt 1918, Vol. LXII.p. 378. 



ITS 



ji.odbyCoogle 



MEASURING APPARATUS 



Sec. S-273 



« * a veiy amaU piece of soft iron is suspended in ft strong macnetio 
StkL, thofl foroung a polarued magnet. Near this strip are plaoed two 
■naU coila, which carry the onrrent to be inrestii^ted. Because of its very 
nail period, this znagnet will follow every variation in the current. 

lis. Tha moTln^-coil t^pe of oieilloffraph developed by DuddoU 
eoDssts of a sin^e-turn coil formed by passing a phosphor-bronse strip 
Qwtr s puUey suspended by a spring, and between the ^ 

potea of a powerful electromagnet as shown in Fig. 100. S 

It hss a much lower inductance than the moving-iron % 

type and therefore a wider ran(^ of application. This 
4i)e is now in most general use and m this counti^ is 
proninently represented by the General Electric oscUlo- 
snph, a Tery simple, rugged and practical instrument. 
Thrre elemeots or vibrators are usually provided in the 
latter, and three waves may be taken simultaneously. 
The dectromagnets are wound for 110 volts, at which 
excitation the sensibility of the vibrators is of the order 
of 0.005 amp. per millimeter deflection. The moving . 
fTsCem is immcraed in a well, with a glass front, and filled 
with oil to dampen the ospillations. The natural fre- 
quency is of the order of 5,000 vibrations per second. 

04. Varloiu roceMiMr derieei are used to render 

tlis wave visible to the eye. One scheme employs a 

ntatiag mirror driven by a synchronous motor oon- 

sKted to the circuit being tested. In the General 

Beeteie oscillo^vph the beam of light from the arc, n, 

Rg. 101, is concentrated by a lens, 6, upon the mirror, 

I. erf the vibrator, which is oscillating about an axis per- 

peodjcolar to the beam. The mirror, m, is driven by 

s cam, d, which gives a comparatively slow forward 

fUoke and a quick backward stroke. When this mirror is stationary the 

unage of the reflected beam at c is a straight line the length of which is 
, piOfWTtional to twice the angular deflection of the vibrator. If the mirror 
i IB rotated forward* the image at « is spread out thus tracing a wave. TIw 
' VBTe is made to appear stationary by automatically cutting off the light on 

t^ return stroke of m by means of the shutter e. 



i 



=3t 

Fio. 100. — Ele- 
ment of movins 
ooil type of oecUlo- 
graph. 



namtOMillograph record* may be mode by tradna the ware 

, referred to above 



^^■^- _ U :s-! in th 



in. p« _ _ 

08 toansparent paper or tracing cloth placed en the screen. . . _ 

(Par. 174). For making pho- 
tograph records, or oscillo- 
IP'am.4, the visual attachment 
V I IS replaced by a light-proof 

cylinder containing the fflm 
1 fitting over an opening 
the oscillograph case 
through which the beam of 
t passes to the film. The 
is unrolled from one spool 
on to another and past the 
Fio. 101. — Visual attachment, G. E. opening by a motor-driven 

oeciUograph. mechanism; its speed is ad- 

justed to suit the condl- 
tioas. In the case of transient phenomena it is often found necessary 
to srnuige special devices to start the film automatically at the proper time 
is order to get the phenomena on the film. A record of elapsed time in di- 
v^et-current phenomena can be obtained by connecting one oithe elements to 
ssooree oi alternating current of known frequency, or by means of an electric- 
sBy driven tuning-fork of known frequency. A small mirror mounted on 
the end of one prong and so plaoed that it will reflect a part of the beam, 
«iD pre an excellent time record. The scalo of ordinates is obtained by 
c^bratioD on continuous current, the deflection of the spot of light oorre- 
^oik&nc to a known current, or voltage, being noted. 

tn. Standard wave form. It is desirable that commercial alter- 
sstii^^arrent wave forms be as near a sine curve as possible in order to 



*Bloodcl,A.E. Cfwiptef itMdus, 1893, Vol. CXVI, p. 603. 

179 



yCoogle 



Sec. S-277 



MBASURING APPARATUS 



^ 



reduce iron losecB, excitation currenta, ohargiag currents, etc., to ft minlm«i« 
The present A. I. E. E. atandard method of meaauring thft deviation from 
a sine curve is simply to measure the greatest difference between corre- 
sponding ordinates at any point along the axis of abscisse. It has been pro- 
posed* to replace this method by another in which the increase in condenser 
charging-current with the given wave, over the charging current with a 
pure nine-wave, will be determined. This is a simple and sensitive method 
of determining the presence of harmonica, since the charging current of a con- 
denser varies with the square of the frequency. The current for a given con- 
denser on a sine-wave can be calculated from the relation /"•£CX2ir/, where 
/■■current in amperes. £ — potential in volts. C* capacity in microfarads 
and /» cycles per second. 

ST7. In high-Toltftffe testinff it is partioularlsr important that the value 
of the maximum instantaneous voltage be available, because the stress 
to which insulation is subjected depends upon this value. When the wave 
is distorted, the maximum value and the ratio of the maximum to meao- 
efTective (amplitude or peak factor) have to be obtained from a plot of 
the wave. This may be taken with a wave meter or with an oscillograph, 
preferably connecteci to a t«at coil in the high-tension winding or to the 
secondary of a shunt-type instrument transfonper connected to the hi^h- 
tension circuit. 

A method which can be uaed dinetHs on the hiffhMt TOltecMt 
is indicated in Fig. 102, where C ia a series of condensers connected across 

the high-tension circuit. The end con- 
denser Ci is grounded and connected in 
parallel with a commutator driven by a 
synchronous motor. The bars on the 
commutator are very narrow and are 
one ptolar s^ace apart, so that contact is 
practically instantaneous. The brushes 
arc shifted untjl the voltmeter indication 
is a maximum. The multiplying ratio 
is obtained from the ratio (C-t-Ci)/Ci. 
The instrument may be calibrated by 
noting the indication corresponding to 
the mean effective value, which ia ob- 
tained with the motor stationary and 
the lirushes resting on the bars. This 
indication is compared with a spark gap 
or other standard. The method aiH 
sumea that the capacity of V is negligible 
in comparison with Ci. Obviously the condensers can be dispensed with by 
connecting directly to a teat coil on the high-tension winding. 




Fia. 102. — Wave meter for high 
voltage circuits. 



MKASXraSMKICTS 
of an alternating current is /■■nr/3. 



■^11,,,, 



'!niIP, 



m 



[-\iiisii!'MM'mmw'\ E 






rSKQUKirCT 

tTS. OmanA. The frequency 
where/— frequency in cycles per 
second, n — number of poles, and 
r — revolutions per second. It 
may therefore be determined by 
measuring the speed of the gen- 
erator supplying the circuit or 
the speed of a synchronous mo- 
tor operated from the circuit. 

179. frequency meten indi- 
cate the frequency directly. In Fio. 103. — Frequency meters — Reed type, 
the reed ^pe as made by Hart- 
man and nraun or Siemens and Halske, there are numerous steel strips of 
different lengths, each rigidly fastened at one end and free to vibrate at the 
other. The strips are placed in the field of an electromagnet which ia ener- 

• Davis, C. M. "A Pruprweil Wavt-shapc? Standard;" /'r.«-. A. I. F.. E, 
Feb., I9i;), p. 2.15. 

t Sharp, C. H. and Farmer, F. M. "MeasuremenU of Ntaximuni Values 
In High-voltage Testing;" Trons. A. I. E. E., 1912, Vol. XXXI, p. 1017. 



180 



y Google 



MEASURING APPARATUS 



Sec.S-280 



Died from the circuit to be meuured, u *hown in Fig. 103. The strips tuive 

afferent natural periocU, and the one with a period corresponding to the 

tltem&tions of the magnetic field will b« set in vibration. The ends are 

timed up and painted white ao that the particular reed in a row, which i« 

ribrating. «rill be in- 

diested by a white ,ttli<>'/ 

band or blur. Each ^* 



Red is carefully ad- 
ioited to an exact 
period by aitacMng 
minute weights. 
These meters are 
Bade in various 
nnies and with 
reeds adjusted from 
035 cycle to 2 cycles 
spartv 

SM. The West- 
Infhouse fr«- 
qiMiicj meter cod- 
Bote of two Toltmeter 
morement«, mechan- 
ically so iDtercon- 




V, 



-m 



Fio. 103a. — Circuits in WestingbouM frequency 
meters. 



oected th&t they tend to rotate the pointer in opposite directions. A non- 
iDdurtive resi^ance B is connected in series with one movement, Vi (Fig. 
103a) and sn inductance X is connected in scries with the other element^ V«. 
Tbe apparent resistance of the inductive movement varies with the fre- 
qoency and thus varies the amount of current tnken by it. Therefore 
each frequency wilt cause the pointer to talce up a different portion. 

161. The Weston freque&oy zneter is 
shown in Fig. 104, where 1, 1 and 2, 2 are fixed 
ooils, 90 deg. apart, and r, c is the movable 
element constating of a simple, soft-iron core 
mounted on a shaft, with no control of any 
kjnd. One coil, 2, 2, is connected in series 
with a non-inductive resistance, Rt, and the 
other coil, 1, 1, in series with an inductance, 
Xi. A second non-inductive resistance Rt is 
connected in fmrallel with 1, l,and Xi. A 





fia. 104. — Circuits in Weston frequency 
meters. 



Fio. 105, — Hiph seasibility 
frequency mdicator. 



•eotnd inductaace, Xt, is connected in parallel with 2, 2 and Rt. The nof t- 
iron eote takes up the position of the resultant field produced by the two 
coilt. When the frequency increases, the current decreav's in 1, 1 and 
increases in 2, 2, thus shifting the direction of the resultant field and the 
position of r, c to which the pointer in attached. The opposite effei-t takes 
pUee when the frequency is deerease<l. Tht; serie.** iuductanM*, X, serves 
merely to damp the higher harmonica. 
til. A very tensittve frequeney indicator is shown in Pig. 105. in 



181 



ibyv^iuoyie 



Sec. 8-283 



MEA8URTN0 APPARATUS 



which the principle of resonance (Sec. 2) in an electrical eirouit is emplosred. * 
In a 60-oycle instrument, one main drouit is adjusted for resonancfl 
at about 70 cycles, another at about 58 cycles and the third CTrcuit 
at about 36 cycles. The latter two are eonnected in parallel, and then in 
aeries with coil A; the first circuit is in aeries with coil A^, both coils b^iiK in 
series with the field F. With the centre of a &-in. (15 cm.) scale marked for 
60 cycles, half-scale deflection is obtained for a variation of only 5 cyclea 
either way. It is possible to adjust the instrument for a fuU-scato range ai 
only 1 eycle. 

SLIP MXASURXMKNT8 
t8>. Oenwal. The aUp of a rotating altemating^urrent machine in 
per cent, is the difference between its speed and the synchronous speed. 
divided by the synchronous speed. It may be determined by noting the 

differenco between the meaBurpd speed 
of the machine and the synchronous 
speed as calculated from the frequency 
and the number of poles. Thts 

method is obviously not accurate, 
because the result is a small difTerenco 
between two relatively large quanti- 
ties. It is therefore customary to 
measure the slip directly. 

284. Dooley'fl method of zn««a- 
urine tUp. One form of device for 
indicating the slip of an induction 
ia_ -.na Of • J _i motort is shown diagram ma tically in 

Fio. 106.— Shp measurmg device, yjg ^^ ^ g^^^ cylinder made S 

conducting material, and in two parts, 
each insulated from the other, is mounted in a frame. Four small bruahee, 
1, 2, 3, and 4, bear upon the cylinder as shown. The brushes, 3, 4, are 
connected through a resistance, r, across one phase of the supply circuit and 
the brushes, 1, 2, are connected to a low-reading continuous-current ammeter, 
/. Each time the brushes, 1, 2, bridge the insulating strip as the cylinder 
rotates, the circuit is completed in alternate directions 
through the ammeter. The cylinder should have as many 
segments as the motor has poles. The ammeter will in- 
dicate a constant current at synchronous speed, and an 
oscillating current for any speed above or below syn- 
chronism, because the impulses of current through the 
brushes, 1, 2, will occur at the same point on the wave 
at synchronous speed, and at constantly advancing or 
retarding points for other speeds. Thus, the apimcter 
will be reversed each time the motor loses one-half of a 
cycle, and will reach a maximum positive value each time 
the motor loses one complete cycle. If the motor loses n 
cycles per min., then the slip in per cent. ■• 1 O0n/(K)/, 
where /» frequency of the system in cycles per sec. 

S85. Strobosooplo method. The device indicated !n 
Fig. 107 does not require the measurement of frequency. 
A olack disc with white sectors, equal in number to the _ . M-*-. sh^f* 




rShaCi 




Fig. 107. — Stip 

measurements — 
8tr oboscopio 
method. 

-slip in terms ofs 



number of poles of the induction motor, is attached with 
wax to the induction-motor shaft. It is observed 
through another disc having an equal number of sector- 
shaped slits and carried on the shaft of a small self-start- 
ing synchronous motor, in turn fitted with a revolution 
counter which can be thrown in and out of gear at will. If 
n is the number of passages of the sectors, then (n/nj) /fir 

where n, »i the number of sectors, and nr » the number of revolutions recorded 
by the counter during the interval of observation. For large values of slip 
the observations can be simplified by using only one sector (ni — 1); then «■• 
the slip in revolutions, 
SM. A direct-reading sUp-measurlng device is shown in Fig. 108. 

* Pratt W. H. and Price D. R. "Resonant Circuit Frequency Indicator;*' 
Trans. A. I. E. E., 1912, Vol. XXXI. p. 1696. 
t Dooley, C. R. BUe. CltA Journal, 1904, Vol. I, p. 590. 



182 



jyle 



MRASUniNG APPAHATVa 



See. 8-287 




Fzo. 108. — Slip meaBuring device. 



is a earelully turned and hardened conical drum driven by the motor beinc 

iaited, throofth a flexible shaft, 3. The Long screw, H, moves a carriage, 

C, parallel to the surface of D. This carriage carries a wheel d, also care- 

fidbr tunked and hardened, which has a line edge and is kept in contact at 

■11 tinMB with the surface of D by means of a light spring. Thus It revolves 

with D. On the same shaft is a disc, sd, with alternate black and white 

sectors painted on it, the number of sectors being equal to the poles of the 

Bifltor oeinc tested. The 

diameter of d la made equal 

to that of the small end of D. 

At the eettins corresponding 

to the small end of Z), the 

■cale along which the carriage 

moves is marked zero. This 

eoneqMKids to synchronous 

Rjccd. As the speed of D 

wcreaaea, it is necessary to 

move d toward the large 

cad of D in order to keep 

the speed <rf d the Mme as at 

sfnchronou* speed. . This 

oistaDce is a measure of the 

riip. The synchronous speed 

of «f is inoxcated when it appears to stand sttll, when illuminated by an 

are lamp connected to the same circuit to which the motor is connected. 

ThnB, if D is 2 in. (5.1 cm.) in diameter at the small end, 2.5 in. (6.35 cm.) at 

the larce end and 5 in. (12.7 cm.) long, slips from to 20 per cent, can be 

neasured with a precision within 0.2 per cent. A more sensitive detector 

eoDBsta of a commutator in place of m, connected in series with a direct- 

eanent voltmeter and the circuit to which the motor is cooneoted. The 

iwUcation is % maximum at synchronous speed. 

tST, S^FnehroniBm indioatori. In order to connect any svnchronous 
wtarhinw in parallel with another machine or system, the two voltages must 
be made equal and the machine must be synchronised, that is, the Bi>eed 
so adjusted titiat corresponding instantaneous values on the two waves are 

reached at the same instant, 
when they will be in exact 
phase. Furthermore, with 
polyphase machines, the direc- 
tion of nhaso rotation must 
assuredly oe the same. This, 
however, is usually made right 
once for all when the machines 
are installed, the phases being 
so connected to the switches 
that the phase rotation will 
always be correct. 

SM. The lamp method of 
gvnohronislnc is the simplest. 
Fia. 109. — Connections Ita synchronising The principle of lamp svnchro- 
with lamps. nisers is shown in Fig. 109, 

where a, a\ are the sources be- 
ing eonneeted in parallel and t, t\ are transformers, the secondaries of 
wueh are connected in opposition through incandescent lamps, /, h. When 
Ibe two sources are in synchronism, the secondary e.m.fs. neutralise each 
other and the lamps will bo "dark." As the phase difference increases, 
the eorrent through the lamps will increase, reaching a maximum at 180 
deg. of phase difference. If the secondary of one transformer is reversed, 
the lamps will be brightest at synchronism and dark at 180 deg. of phase 
diflerenoe. The former connection is preferable because the point of total 
"darkness" is more easily detected than the point of maximum brightness.** 
A voltmeter may be substituted for the lamps by connecting it so that 
lynehronum is indicated when the reading is a maximum. The disadvantage 
cf this method is that it does not indicate which frequency is the higher. 
Srnehrootsm iodicators (Par. M7) are instruments which not only over- 
cone this objecticm, but indicate the point of s3mchroni8m more accurately. 




183 



hy»^iUUyiC 



Sec S-289 



MBASVRINO APPARATUS 



) 



U9. Th« prtnctpl* of the WattinchoUM unchroniMr U Ehown ii 
Fig. 110, where a rotating field ia produced by the coila. M and iV, conxieotM 
to the buACfl through the reactance P and the resiatance Q, respectively. Aj 
iron vane A, free to rotate, is mounted in tbia rotating field and xnagnetiMC 
by the coil C, which in turn is connected acroaa 
the incoming machine. As the vane is attracted 
or repelled by the rotating field from Af and \, 
it wiU take up a position where this field is sero 
at the same instant that the field from C is zero. 
Hence the position at any instant indicates the 
difference in phase. When the two frequencies 
arc different, thin position is constantly changing 
and the pointer will rotate "fast" or "slow, 
coming to rest at the sero-field position when the 
frequencies are equal. In a larger type, the split- 
phase winding ia placed on the movable memner, 
similar to the arrangement shown in Fig. HI. 

200. The Bchame of the Weeton STnchro- 
scopo is shown in Fig. 112. There is no iron in 



Inn Anukton 




^m 



■nlqltanU 



SAB 




FlO. 



FlQ. 



To lutooiing 

Machine 
111. — Circuita in G. 
E. synchroscope. 



110. — Circuits in Westingbouse ayn- 
phroniser. 
the instrument and the moving element is not allowed to rotate. The ele- 
ments are practically the same as in an electrodynamometer wattmeter. 
The fixed coils, F, F, are connected in series with the resistance R and to the 
buses. The moving coil, M, is connected in series with a condenser C and 
the incoming machine. The two circuits are adjusted to exactly 90 dec. 




Fio. 112. — Circuits in Weston synchroscope, 
difference in phase. At synchronism there is no torque and M us held at the 
sero position by the control spring. If the frequencies are the same, but 
there is a phase difference, a torque will be exerted and M will more to a 
position of balance at the right or left ("fast" or "slow"). If the fre- 
quencies are different, the torque will continually vary and the pointer will 
oscillate over the dial. A synchruniiing lamp illuminates the scale simul- 
taneously and the direction of apparent rotation mdioatea the faster machine. 



18i 



MBASUR2N0 APPARATUS Sec. 8-291 

IM. TIm 0«iMral Utctrie lyii^iroMMipe operates on the ume principle 
IS the WestinchouBe instrument (Fig. 111). The BpUt^haae windinff, C, B, 
ii maanVed on the movable element, E, the two ooiu being connected to the 
wm r^i i g maehine tiirough slip-rings. 

XAaHKTIC BUAaxmixxHTa 

MS. OanarmL The (trenfth of a macnatlo field, X, U meuured in 
fiMKof mmsnetio force per aquera centimeter, or in gausses. In a long 
alnici>t satenaid it is 4rA//lCW, where / ■- current in amperes and N/l — tuma 
per unit lencth. Macnatle induetlon or flux danalty, (B, is measured 
■aliiica of macnetio induction per square centimeter, or in gaussee. When 
Ike anfaatanee in which the field exists is non-magnetio, 3 — 3C and the ratio 
■/X. cr permeafaiJittr, is » — 1. When the substance is magnetic, 3 becomea 
nuch greater than X, due to the decieaaed mognetio resistsnoe; in general it 
nnes with 9C. 

tM. Tha nonnal induetlon or (B^ enrre of a manietic material is the 
carfc platted between the strength of the magnetic field existing in tha 
■atarial.3e. and the magnetic indnction. (B, produced by that field, when the 
Biateiial ia in a neutral or normal condition. A permeability eurre ia 
plotted between the permeability fi and (B, or between ii and X. 

Bt. Tha hTStareaU eurra is a curve plotted between (B and K, for 
naooi Taluea of X from a maximum Talue in the poaitive direction to a 
iMiimnni -raloe in the negatiTe direction, and back again, or through a 
•ODpfete eyeie of Talues. The ends of a hyatereais loop will Ue in the normal 
iadaietson enrre. 

m. MayiaMe maaaurementi mar,ba divided into two elaiMf, (1) 
those in which the strength of a magnetic field ia determined (such aa the 
•srth's field, the field due to a conductor carrying a current, the field in the 
air mi of a iiiag;net, etc.) and (2) thoee made to determine the projjlertiea 
of Bsgnetie materiaJ. 

IN. Flald-s^oncthmeasureinanta may be made by induction methods, 
vith aa oscilUiting bar magnet (Par. n>),orwithabi8muthBpiral (Far.tOO). 
Ia the induction method a coil of known tuma and area is so arranged that 
it eta be made to eat the field in a known area in a direction perpendicular 
to the field. The e.jnj. generated in the coil, and henee the field producing 
it. ii determined from the quantity of electricity discharged throiicb a ballistia 
pWanometer ooiinected to the coil terminals. 

Ia measuring the field strength in air gaps, the coil is so arranged that it 
on be moved quickly across the entire gap, or through a definite distance, by 
wans of a spring or weight suddenly released. When there is sufficient space, 
a more accurate and convenient.method is to rotate the coil through 180 deg. 
Twy weak fields, anch aa the earth's field and that due to conductors, may be 
XMasured in this manner by using a sufficiently large coil. 

W. Vonnnla for Held itranxth. The field strength in. lines per square 
••alimeter ia 

^_ 10Vka (gaberts per cm.) (3® 

xan 
*ben d— deflection, jt.> constant of galvanometer in coulombs per scale 
^vision, Aa>total resistance in ^Ivanometer circuit, n» turns in coil, a*" 
Bean area of coil in aquare centimeters, x — linear distance moved in oenti- 
■astcn or, when the coil ia turned through 180 deg., x — 2. 

M. Tha Oranot flnzmater is a portable instrument with which mag- 
artie lax may be read directly on a scale. It is essentially a ballistic galva- 
peotttcrwith the moving element replaced by a torsionlcss suspension so that 
It KBains deflected. The inatrumpnt is connected to an exploring coil 
ekjch is placed in the air cap to be' measured. . The flux is measured bv 
*e1iBg the deflection when tne magnetising circuit is either opened or cloeea. 
, M, la tha eaeiUstlnc-macnet method, a small simple bar magnet 

^- ■ * ■ . 1-A-.J ^11. A1...A.. ftl.- A : t. J. ;l a: a1 -L 



iiW^iiiliJud by nntiriated nlk fibres. The magnet is set to vibrating through 
■■ ave of about 6 dec. and the period of oaeilTation determined. The aver- 
W <a atbatt tbrae obaervationa should be taken. The field strength is 



K-^'jf^- (gUberU per cm.) (37) 



18S 



.ligilizedbyCoOgle 



Sec. 8-300 



MEASURING APPARATUS 



where K — moment of inertia computed from the maM and dimenrions, . 
macnetic moment, and T"- period of oscillation. M may be determix; 
with a magnetometer, or by calibration in a known field (Helmholtr coi| 
This method is onlv Biiitabfe for weak fields, such as the earth's field, 
mounted in a wooaen box with a glass front, it will be protected from 
currents and can be conveniently moved about when making magnet 
surveys. 

SOO. Bismuth-ipiral method. The resistance of bismuth wire inerea 
when placed in a magnetic field. This property is utilized by noting tM 
increase in resistance of a flat spiral coil of bismuth wire when placed in tU 
field to be measured, the leading-in wires being arranged non-inductivcra 
The device is oallbratad with known field strengths. It is particular^ 
suitable for exploring small air gaps such as those in motors and generators. * 

101. HeMureznent of maffnotio proportles. The magnetic propertied 
of iron and steel which are of most commercial importance are nornaa] 
Induction or jperme ability, hystereils loss and total lotaai with alteiv 
nating magnetiiing forces of commercial frequencies. 

tOS. Normal-Induction data. The various methods are distinguished 

5rincipally by the method employed to measure (B, for in all methods 3C. ia 
etermined from the magnetiiing coil. (B can be measured directly aa in tho 
balliitio methoda or indirectly with penneametars. 

SOS. Balllitic methodi are usually employed in the more accurate meaa- 
urements. The best-known methods are the rinf method, the divided 
bar or Uopkinson, and the double-bar double-^oka methodi. In all of 
these methods the flux is measured with a ballistic galvanometer connected 
to a test coil which is cut by the flux when the exciting current is reversed. 

504. The line method, devised by Rowland, is one of the earlieat 
metbofts of measuring the permeability and the hysteresis of iron and ateeL 

The connections are shown diagram- 
matically in Fig. 113, where T is the 
test specimen. The latter is an annuiar 
ring, either solid or built up of punch- 
ings of sheet metal, with a 'diameter 
preferably 8 or 10 times the radial 
thickness. After covering with a thin 
layer of insulation, a teat coil of very 
fine double-silk-covered wire is wound 
on a portion of the ring. The mag- 
netiring coil is wound over the teat 
coil, and distributed uniformly over the 
entire ring; it is usually comprised of 
double-cotton-covered wire, of suffi- 
cient size to carry the maximum cur- 
rent withoutraising the temperature of 
the iron appreciably. 

505. The divided-bar method devised by Hopkinson avoids the necee- 
nty of winding each specimen separately, permits the use of a more con- 
venient test piece, and avoids the errors in ring specimens.* The devioe 
eonsista of a test piece, BC (Fig. 114), in the form of a bar about 15 in. (38.1 
cm.) long and 0.5 in. ^1.27 cm.) 
diameter, which is divided at A 
and inserted in a massive frame, 
F. The secondary coil, S, is bo B 
arranged that it will be thrown 
clear of the yoke by a spring 
when the part, AB, of the test 
bar is suddenly withdrawn. In 
calculating 3C, the length of the 
magnetic circuit is taken aa that 
between the inside faces of the 
yoke, the reluctance of the yoke 
being considered negligible. This 
introduces an indeterminable 




Fia. 113. 



-Permeability tests — ring 
method. 




FlQ. 



114. — Permeability testa — divided- 
bar method. 



• Lloyd, M.G. "Errors in Magnetic Testing with Tting Specimens;" Bureau 
of Standards, BuUetin, 1908, Vol. V, No. 3: p. 435. 



196 



y Google 



MEASURING APPARATUS 



Sec. S-306 



•Ror and, therefore, tho method can be suitable only for rough meaauremonts. 
Tbe leakage error due to flux through the coil, but not through the bar, can 
he deCermmed by preliminary test with a non-magnetic bar. The formula 
far X aod (B are JC - 4rNI/l0t and (B = 10*dkR/aTi, where A' - total tuma of 
Bciung roil, /» exciting current in amperes, /■■ length of magnetising coil 
IB cm. (A^/// — ampere-tums per cm.). d = deflection, ^i- total resistance of 
teit ooU circuit, it * galvaiiometer constant, ac^area of specimen in square 
feotimetcr and n « turns in test coil. 

MC. Th« double-bar, double-yoke method is the one recommended 
hf the Ameiieazi Society for Tefltin^ MateiiaU. It wae devised by 




Fio. 115. — Permeability tests, double-yoke method. 



C W. Burrows* and is the standard method used at the Bureau of Stand- 
ards for both aolid and sheet specimens. Not only is the precision high, 
bat the method is also rapid and convenient when the observer is experi- 
enced. The esaentiai feature is the distribution of the magnetising wind- 
lag in sections, w^bicb permits the independent adjustment of the magnet- 
iSBg force in various parts of the magnetic circuit. Thus the efFcL't of 
noa-uniform reluctance at joints, etc., can be overcome and the induction 
Bade uniform throughout the entire magnetic circuit. Exploring coils are 
l^aecd at various positions so that the uniformity of the induction can be 



r^ F* n 



^ 



m 






N, 



-^w^ywiw 






To PotentIoinoter(or MllllToUoieter) 
Pig. 1 1ft. — Connection diagram for double-yoke method. 

tntcd. The echeme is shown in Fig. Hi) where b, & are two bars (standard 
ue. 1 em. diameter, 35 cm. long) one to be tested and the other an auxiliary 
htr (rf amilar material. Y, y are yokes of Norway iron about 15 cm. long 
aad shoot 4 or 5 cm. diameter, into which the bare are clamped. The mag- 
■Ktomotive-force is applied in three sections: one coil, Nt, is placed over the 
*<at ipcdmen; another, ^«, over the auxiliary rod; and the third, A/y, 
M divided into four parts, one near each joint. The corresponding exploring 
nib an m. «« and nf. These coils all have the same number of turns, that 
ii> af>»,* the two parte of n/ in series. They are so connected to a switch 
^atR«or n^ may be connected through the ballistic galvanometer in oppo- 
■tion to Ri. thus providing a sero method of determining the condition of 
aaiformity of flux. The scheme of connections is shown in Fi^. 116. _ The 
"^Hnetiaing coils are connected to special mercury-cup reversing switches 
K> made that they can be operated simultaneously like the keys of a piano. 



'BttTTOwa, C. W. Traiu. A. 8. T. M„ 1909. Vol. XI. p. 81. 



187 



yGoogle 



Sec. 8-307 



MEASURING APPARATUS 



) 



MT. Proo«dur* in double-bar doubto-foka mathod. The metiuM 

of procedure is as follows: After demagDetUing (Par. Sll), the current i] 
A'l u adjusted to the value of X required. The current in ail masnetisinj 
coils is then simultaneously reversed several times to get the specimen in t 
cyclic rendition, the current in JVa and N i hcing adjusted during the proces 
until the Hux is uniform as indicated by aero deflection when na and r^ tkn 
successively opposed to nt. The galvanometer is connected to n and tlu 
deflection noted when the current in the various mognetinng coils ia r« 
versed simultaneously- Then 

,„ 4t.\V , .,^ , , ,„^ 

X - ■ (gilberts per cm.) (3g 

® - -iiHr -{-A-)^ (gausses) (39. 

The units are the same as in Par. SOS. The quantity in the parentbeaU fi 
the correction factor for the space ontween the nurface of the bar and thi 
test coil. A — area of bar and a ■■area of test coil. Ordinarily this corree> 
tion ia very small because the brass tube is made very thin and the teal 
coil is wound under the magnetising coil. 

SOS. Permeametars are commercial instruments for ^e rapid testini 
of iron and steel for permeability. The Thompson permeameter emiSloyi 
the tractive force exerted between the polo of h magnetised bar and a pieo« 
of steel in direct contart with the pole. This force in dynes is/^^-Ci^/Sv. 
where (B <« induction in bar in lines per square centimeter and avarea ot 
bar in square centimeters. Kocpsel and Ficout permeameters are induc- 
tion-type instruments. 

SOS. B. P. Thompson's iMnneanutar is shown schematically in Fiic. 
117, where AB is the test specimen in the form of a rod which pass es Uiroucli 
a hole in the top of a heavy yoke, F. The surfaces of the end of the rod and 
the yoke at F are carefully machined. The force necessary to move the rod 
is measured with a spring balance at H. The induction is 

CB - 156.9 \/''+5C (gausses) <40) 

where (B" induction in lines per square centimeter (gausses) P «pi^ in grams 
and a i* area in square centimeters. 





Fig. 117. — Thompson permeameter. Fig. 118. — Koepsel permeameter. 



SIO. Tha Koepsel permeameter, as made by Siemens Halske, is 
shown schematically in Fig. 118, where JJ ia & massive yoke divided at the 
centre so as to admit a moving coil e to which a pointer is attached, the 
arrangement being similar to standard D'Arsonval-type direct-current instru- 
ments. This pointer moves over a scale graduated directly in lines per square 
centimeter. The magnetic circuit is completed through the test piece 7*. 
firmly clamped between the ends df the yoke in the usual manner. Tne value 
of (B corresponding to various magnetising currents in C is indicated directly 
by the deflection with a known small current through c. Separate coils are 
placed on the yoke pieces, J J, by means of which the reluctance of the various 

taps is approximately compensated. But even with these coils, there is a 
ux leakage, so that correction or "shearing" curves have to be used. These 
curves, obtained by test with standardised specimens, are furnished with the 
instrument, as are also standardised test specimens with which the device 
ean be checked from time to time. 



18S 



yGoogle 



MBASURim APPARATUS 



Sec. 8-311 



ni. Tb» prtaieiMi adTmntecM of tnkctioo jMrmmunetan ant their 
r^ednoB and MipUcity, whjch are important featurea in shop testing where 
madity m eaaential and onjy comparative data are required. 

i.*^i-.ir*lTl/*f"! PermeMaeter is a double-yoke, single-bar instrument 
^ 5? »t_ reluctance in the junction between test spenimens and the 
S IIB -ZH"! .?"r~ iK "'"Pe'^'od f°r; The scheme is indicated in 
krf.»?Lr^ '■ A '" i''°/!'u° y°^™- ^?* «l"are-bar teat specimen T 
« damped between the ends of the yokes as shown. 
The two aoiiliaiy magnetiaing coils on Fi, Fi are 
fst eonmected in such a manner that their magneto- 
•Mrtive forces are in series. There is then supposed 
tobe no flux in the test bar, its magnetising coil 
beinzout of circuit. The two coils on ?'i, Fi are then 
jranoeted in opposition and the current in the test- 
Bar eoil adjusted until the flux in Ft, Fi is the same 
•a bdore. as indicated by a balliaUc galvanometer , 
•r aone other mitable method. The conditiona in ' 
*■< teat imt an then supposed to be the same aain 
a lens, uniformly magnetised bar. The magneto- 
Bodye force of the test-bar coil simply overcomes 
^ rdnctance of the test bar and 3C is calculated 
bom the current atid the constants of the coil as be- 
fcre, <S being measured with a test ccril idaeed over 
the teat bar. 



T 

m 



m. 



41 



Fio. 



119. — Picout per- 
meameter. 



Ml. BjsteraaU enrrai are obtained by any of 
tte methods described above, for permeability tests, 
Bwfaieh a eoil is used to measure the flux. In 
•tert-indieating permeametera such as the Koepsel type, S is noted for 
nnouB values of X. first descending from a positive maximum value of JC 
<o the negative maximum, and then ascending in the opposite direction. 

U4. BalUatic stap-by-itep method of datermlnlng hyitereiU. 
*«•« Hjh precision is desired the ballistic "step-by-step" method is 
""d-. Ttaa method is earri^ out as follows: The current in the magnetising 
; enmt J» adjusted to a valne corresponding to maximum (B. It is then 
, wversea a few times to get the specimen in a cyclic state. By means of 
nitable switching arrangements, some resistance is suddenly cut into the 
""mt. thus reducing SC to a new value, which is carefully noted. The 
enresponding ehiuge in (B is determined with a ballistic galvanometer in 
the usual manner. This process is continued, step by step, until sero current 
B leached, when the circuit is reversed and the resistance cut out, step by 
fm, imtil the same maximum value of 3C is reached in the opposite direction. 
Tke whole process is then repeated and the other side of the loop obtained, 
la tUs method, the errors wiU be cumulative, but can be eliminated by going 
Wk each time to the original maximum 3C; furthermore, it is then a simple 
attter to insure that the conditions remain constant, by occasionally 
rhRldng the value of (B corresponding to maximum X. 

_ Knowing the value of (B at the start, the values corresponding to the var- 
ms steps in the step-bynitep method are obtained by adding algebraically 
the Tsnooa changes in (B to this initial value. The resulting values of & 
sad £ suitably plotted on eroea-section paper form the hyitweiis loop. 

Ut. HysUTMU low mMaurementa. The area of the hysteresis loop, 
■Mewed in the units of the ordinates of the curve (by planimeter or other- 
•iw) and divided by *r, gives the hystereaia loss in ergs per cubic centimeter 
W cyde, between flux deiudtiea +(B max. and - ffi max. This method of 
■Msuring hystereaia loss is much too slow and expensive for commercial 
eposes, and several methods have been devised by means of which 
Bfsteiesis lossee can be measured directly, by electrical or mechanical 



IK. loUnaon'i matliod of sMagmliir b/it«raiia lou. An example 
cf in rlectrieal method of measuring hysteresis loss is one used by L. T. 
lobiasoiL* It was designed primarily to reduce to a minimum the time and 

. 'Batmson, L. T. "Commercial Testing of Sheet Iron for Hysteresis 
I«r fhBMu A. I. E. E., 1911. Vol. XXX. 741. 



189 



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Sec. 3-317 



MEASURING APPARATUS 



expenae in preparing the sample, as well as the time spent in testing. Tli 
specimen is a bundle of strips 0.5 in. (1.27 cm.) X 10 m. (26.4 cm.), weijcl 
ing 1 lb. (0.45 kg.). It is placed in a simple straight solenoid, with a sens 
tive wattmeter (reflecting electrodynamometer) in series with the magnetii 
ing coil. A separate winding is provided for the wattmeter potential cci 
thus simplifying the correction factor for wattmeter loss. The induction : 
determined from the indication of a voltmeter, which is also connected to 
separate winding at the centre of the specimen. The flux which it indicate 
is much higher than that at the ends, but experiment has shown that tfc 
ratio of the maximum to the average is 1.3 to 1. Due allowance is therefoi 
made, when adjusting the magnctiziDg current to such a value that tfa 
voltmeter deflection will correspond to the required average flux-denaitj 
Measurements are made at 10 cycles, or less, in order to reduce the CKld] 
eurrent loss to a point where it can be eliminated by means of empiriei 
eorreotiona without serious error. The precision obtained is about ± 
per cent. 

S17. In the Bolden and the Iwlxiff hyttMresU met«n, the lou \ 
determined mechanically. In the Holden meter the test specimen, 
ring of laminations about 1 cm. X 2 cm. (0.4X0.79 in.) cro8»-eecUon, an 
9 cm. (3.55 in.) diameter, is placc$d between the poles of a pair of revolvin 
magnets. The torque exerted on the specimen ia resisted by a spiral aprini 
The deflection of this spring which is necessary to bring the specimen bao 
to the sero position ia a measure of the loss in ergs per cycle. 

The Bwlnff apparatus is operated on a similar principle, except that th 
specimen is rotated instead oi the magnets. The specimen is a bundle c 
strip I in. (1.6 cm.) square and 3 in. (7.6 cm.) long. 

818. Core-lou meaiurements. The total loss in iron or steel sut 
jected to an alternating magnetic field lb most accurately measured with ; 
wattmeter. In making preciBion measurements, the Hopkinson rinK-specime 
can be used, but the Epstein apparatus is more convenient ana has bee 
adopted by the American Society for Testing Materials. * Fig. 120 shows th 
scheme diagrammatically. 

The specimen is arranged In the form of a rectangle. The magnetiaick 

winding is divided into four solenoidi 
^ each being wound on a form into whici 
f\\/\V>/\ I one aide of the rectangular specimei 
'^ < is placed. The form is non-magneti( 

^ non-conducting and has the follo«-in 
^ dimensions: inside cross-section* 4 en 
c (1.57 in.) X 4 cm.; thickness of wal 
J) not oyer 0.3 cm. (0.12 in.)j|^ windini 




^^smm 



length, 42 cm. (16.5 in.). Each liml 
Fio. 120. — Core-loss measurements of the specimen consists of 2.5 ki 
— Epstein method. ., (5.5 lb.) of strips 3 cm. (1.18 in.) wid 

and 50 cm. (10.7 in.) long. Two o 
the bundles are made up of strips cut in the direction of rolling and two a 
right angles to the direction of rolling. The strips are held together witl 
tape wound tightly around the bundle. The bundles form butt joints a 
the corners with tough paper 0.01 cm. (0.CX)4 in.) thick between. They er 
held fi.rmly in position by clamps placed at the corners. 

The magnetlxlnr winding on each solenoid consists of 150 turns um 
formly distributed over the 42 cm. (16.5 in.) winding-length, and has a resist 
ance of between 0.075 and 0.125 ohm. A secondary winding is uniforml] 
wound underneath the first; it also contains 150 turns in each solenoid. aiM 
energises the poteatial circuit of the wattmeter and also the voltmeter witl 
which the induction is measured. The resistance should not exceed 0.21 
ohro per solenoid. With a sine-wave e.m.f. impressed on the magnetiiiai 
winding, the maximum induction is 

^ E 41D 10* . , ,.-, 

®"-47^rrrir " <«*"»***^ ^^^' 

where 5 — volts indicated by voltmeter, I " length of specimen, D " specif 
gravity (7.5 for alloy or hish-reBistance steels and 7.7 for standard or low* 

'Standard Magnetic TesU of Iron and Steel; Tram. A. S. T. M., 19U: 
Vol. XI: p. 110. 



100 



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ilSASVRISG APPARATUS S«C. *-319 

Mi* « n i T steeb). /-form factor of macnetixiiic eleetromotiTe force (I. II for 
■■ ■■ve). iV — total Kcoodary turns, n — eyetoa |>er •econd. ilikI ikf — total 
BMsia cr»izi«. The wattmeter sivee the total loaa in the iron, plus tliat in 
fie Becondarjr circuit. The latter a calculated from the reeistanee and the 
i^taee, and deducted from the wattmeter readinc. 

SM. For comparatiTe conunareial maammnanta of ea>* loaH*, 
aaaple smple volenoid may be uoed.* The wattmeter indicataona are atan- 
ivdiaed irith a standard sample. The accuracy obtained is quite aufficieat 
. i:r meet factory purposes. 

IMl S«parmtlon of •ddj-enrrant and bTitaraaia Igmsi in the core 
, ii asaally accomplished by takinc adrantace of the tact that with a given 
. nloe of SmM, the hysteresis loss varies directly with the frequency and the 
eddy-current loes with square of the frequency. The specimen is arraaaed 
■ la a eore-loas test and the loss noted at two frequencies, the indueUoa 
b«a$ kept the same in the two eases. By means of two simultaneous 
•potions, with two unknown quantities, both losses can be calculated. 

ttl. PracaaUona in macmatle ta«Wny. Where the induction is meas- 
««d by means of a stationary test coil surrounding the specimen, the spaca 
teveen the coil and the test n>ecimen should be as small as poesible. This 
cia ordinarily be made ao small that the leakage error is negligible. 

Before induction noeasurements are made, the specimen should be eare- 
hily demagnetised. This is best done by first magnetising to a Talua 
•tfl above the maximum at which measurements will be made; the current 
it then gradually reduced to aero, betn^ r^ndly rerenwd meanwhile. Alter- 
•sting current of 25-eyele frequency is convenient where much work is to 
be (ione.t 

Is loes measurements, the temjieratnre of the specimen should be car» 
UI7 noted, because this affects the eddy-current loss. The exciting winding 
^)sld therefore be sufficiently large to avoid heating of the specimen, la 
precision work, the apparatus is placed in an oil bath. 

la tests of sheet materials, the strips shotild not be too narrow, because 
cf the hardening at the edges due to cutting. This effect is negligible with 
tvkhh of 2 in. (.5 cm.). Care should be taken that burrs are removed from 
At tt^fa and that the only insulation between sheets is the natural seal* 
or oxide. The test specimen should be composed of strips eui from the sheets 
a both direetions. 

The remdjngn of a baUlsUe ratranomatar should be kept at about tba 
suns magnitude by varying the resistance in series with it. The observe 
li<nsl ennr is thus kept about constant. 

BIBLIOaKAPRT 

tax. Bdaetad list of rafarane* UtaratiiT* on electric and magnetic 
Beamrementa. 

GaAT. A. — "Absolute Measurements in Electricity and Magnetism.'* 
Tlie Macmillan Company, New York. 

Kexd. LmAK C. — ''American Meter Practlee." McGraw-Hill Book 
Company Ina., New Torfc. 

FLzuno. J. A. — Handbook for the dectrieal Laboratory and Testing 
Room. D. Van Nostrand Compaq New York. 

Swaaay axo FajimtENnEU). — "Testing of Electromagnetic Machinery." 
The Mscmillan Company, New York. 

FisHE*, W. C. — "The Potentiometer and lu AdjuncU." D. Van Noa- 
ttsad Company, New York. 

DC Bob, B. — "The Magnetic Circuit." Longmans, Green A Company, 
Hew Yofk. 

G P. PcTXAM Soxs. — Reports of the Standards Committee of the British 
Aaoeistion for the Advancement of Science; Cambridge University Press, 
New York. 

* Robinson, L. T. "Commercial Testing of Sheet Iron for Hysteresis 
Low. ■ Tnn: A. I. E. E., 1911. Vol. XXX. p. 747. 

t Borrows, C. W. "Best Method of Demacnetuing Iron in Magnetic 
Teni]i(;'- Bureau of Standards Bulletin, 1907, Vol. IV, No. 2, p. 205. 

DigilizedbyCjOOgle 



\ 



Sec. J-323 MBAsuRixa apparatus 

SoLOUAN, H. G. — "Electrioity Metera." J. B. Lippincott Company, Phili 
delpbia, Pa. 

Gbrhardi, C. H. W. — "Electricity Meters." D. Vsn Nostrmod Compun 
New York. 

Bedell, F. — "Direct- nnd Alternsting-current Manual." D. Van Not 
trand Company, New York. 

Pabb, O. D. a. — "Elpctrical Engineering Meaaunng loetruniente.** £ 
Vhd Nostrand Company, New Vort. 

Fleuinq, J. A. — Magnetic Induction in Iron and Other Materials." I 
Van Nostrand Company, New York. 

Pakb, G. D. A.^"Practical Electrical Testins in Physics and Bleetria 
Engineering." Ixingmana. Green & Company, New York. 

Carhart and Pattehbon.— "Electrical MeasurementB." Allyn Bacoi 
Boston, Mass. 

Sharp, C. II. — "Electricity Meters." Intematiodal Congreaa of the Appli 
cation of Electricity, Turin, 1911. 

Franklin and Ebtt. — "Elements of Electrical Engineering." The Mac 
millan Co., New Yore. 

Nichols, E. L. — "Laboratory Manual of Physics and Applied Electricity. 
The Macmillaa Company, New York. 

Shepard and Jones. — "The Watt-hour Meter." Technical Publishia 
Company, San Francisco, California. 

FrrcH, T. T. and Huber, C. J. — "A Comparison of American Oirect-cni 
rent Switchboard Voltmeters and Ammeters. Bulletin Bureau of Stsbndardi 
Vol. VII, No. 3, page 407. (Reprint No. 163.) 

Franklin and Wiluamson. — "Altematiog Currenu." The Macmillai 
Company, New York. 

Kehpb, H. R. — Handbook of Electrical Testing: Spon Cbamberiaii 
New York. 

Electrical Meterman's Handbook; National Electric Iiight AaaociaUon 
New York. 

Janskt, C. M. — "Electrical Meters." McGraw-Hill Book Company Ina 
New York. 

Roller, F. W. — "Electric and Magnetic Measurements." McGraw-Hil 
Book Company Ino., New Torfc. 

Karapetoff; V. — "Experimental Electrical Engineering." John Wile] 
Son.1, New York. 

NoRTHRUP, E. F. — "Methods of Measuring Electrical Reaiatanoe.' 
McGraw-Hill Book Company Inc., New York. 

Annual Reports, Meter Committee; National Electric light AasociatioD 
New York. 

Code for Electricity Meters; Association of Edison Illuminating Companie 
and National Electric Light Association, New York. 

Brooks, H. B. — "Electrical Instruments and Meters in Europe.*' BuUetii 
66, Bureau of Foreign j&nd Domestic Commerce, U. S. Dept. of Commerce 

Fitch, T. T. and Hvbbr, C. J. — "A Comparative Study of American Con 
tinuous Current Watt-hour Meters." Bulletin Bureau of Standards, D. S 
Dept. of Commerce, Vol, X, page 161. (Reprint No. 207.) 

MECHANICAL POWER BIEASURKMENTS 

BT r. MALCOLM FABMKB, M.S. 

TOBQUl M1A8UUIMUTT8 

SIS. Torque b bait measured with dynamom at a n , of which there an 
two classes, absorption and transmission.* ^ Absorption dynamometen 
absorb the total power dplivcrcd by the machine being tested,^ while trans- 
mission dynamometers absorb only that part represented by friction in ttM 
dynamometer itself. 

S14. Tha Frony brake is the most common type of abiorptlon dyna- 
mometar. It is simply a brake applied to the surface of a pulley on thi 
shaft of the machine being tested, together with suitable means for vary- 

' Carpenter and Diedrirhs. "Experimental Ennneering" (Wiln 
Sons, 1012). J. A. Moyer. "Power Plant Testing" (McGraw-Hill Boot 
Co,lae., 1»1S). 

193 

Digitized by VjOOQIC 



MBASURINO APPARATUS 



Sec. 3-325 



Idc the fiietion prodneed. The torque developed by the maohine to orer- 
eooM the friction ia determined from the force required to prevent rotation 
rf the bnJce. 

SU. ThB principal fomu of Frony brakaa are shown Bchematically 
b Rss- 121. 122, 123 and 124. In fie. 121 the load is applied by tightening 




FiQ. 121.— Prony brake. 

the brake baad at a, and the oorreoponding torque is measured by noting 
the force required at the end of a lever-arm of known length in order to pre- 
vent rotation. This force is usually measured with ordinary weiehing 
•alee or a firing balance. In Figs. 122, 123 and 124, the brake band is a 
bdt or rope applied directly to the surface of the pulley, and the force is 
Beasmed at the pulley surface b^ the various methods indicated. The 1 cad 
is apphed by tightening the brake band as in Fig. 
^::^_ 124, or adding weights as in Figs. 122 and 123. 

y^Tp^> <M. A Mlf-regolatlii^ brake for small torques* 

^ ^J.\^ \^ can be made by attaching copper rivets to the 

leather belt in IHg. 122, the rivets per unit of sur- 
face ranging from sero at one end of the working 
surface to a maximum at the 
other end. For very small 




Flos. 122, 123, 




and 124. — Prony brake. 



leniaa a roand belt in a grooved pulley and with small steel wire wound 
qmUy around it, sero turns per inch at one end to maximum turns at the 
•tier, makes a simple and very satisfactory brake. 

BT. FtarmnUu fw oaletilation of torque (Tom dynamomater 
OMasiirainenta. The torque, T, in the various forms of Prony brakes (Par. 
>U) is determined as follows: In Ilg. 121, T—F,L, whereF,-force measured 
U sad of brake-ann, Z(=> length of brake-arm or distance from centre of 
Aaft to point at which the force is measured. In Figs. 122 and 123, T°> 
(f.-/^£. where ^.— weight attached to end of brake-band, F, - reading 
<< 4d^ balance, L — brake-arm — radius of pulley plus one-half the thick- 
"■ of belt or rope. In Fig. 124, T-F,L, where F,- force weighed on 
«ha£-br^ce-arm»ndiua of pulley plus one-half the thickness of belt or 



' E M. Sobdbe. 
IV, ». 118. 



"A Self-regolating Brake.' 



im 



Bledric Journal, 1907, Vol. 

DigiiizMbjV^iUUl^le 



Sec. S-328 



MEASURINO APPARATUS 



rope. If P and L are niMaured in pounda and feet reapeetivety, T will 
in lb. ft. 

IIS. Diaatpatlon of heat In frietion brakai. The energy diasipated 
the brake appears in the form of heat. In small brakes natural ooolinc 
sufficient, but in large brakes special provisions have to be made to diaaipi 
the heat. Water-cooling is the most common method, one scheme e: 
ploying a flanged pulley. About 100 sq. in. of rubbing surface of bra 
should be allowed with air cooling, or about 60 sq. in. with water ooolii 
per horse-power. 

IM. For Tsiy larre torqusi, other forma of absorption brake* • 
UMd. In the Alden brake, a rotating oast-iron disc rubs against tij 
copper discs which are held stationary. The friction is adjusted by varyi' 
the pleasure of the cooling water in the chamber surrounding the eop^ 
discs. The tendency of the copper disc member to rotate ia measured wi 
a lever as in the Prony brake. 

The WaiUnchouaa turbine brake employs the principle of the wa( 
turbine and is capable of absorbing several thousand horse-power at vei 
high speeds. 

In the magnetic brake, a metallic disc on the shaft of the machine beii 
tested is rotated between the poles of magnets mounted on a yoke which 
free to move. The puU due to the eddy currents induced in the discs ia mea 
uied in the usual manner by counteracting the tendency of the yoke 
revolve. 

IM. The prinelpal forma of transmlnion dynamometer* are tl 
lever, the torsion and the cradle types. An example of the lever type 



n 1 1 [ 1 1 1 1 1 [ 1 1 1 J 1 1 1 1 1 1 1 1 1 i I n 1 1 1 1 1 1 ft 1 1 1 1 1 




Fio. 125. — Transmission dynamometer. 



shown in Fig. 125. where P is the force applied to the dynamometer, all 
P* is the force being delivered. When the downward force, JT, is balance 
by the weight W, the following formula holds, 

F_ l/2(l+>')Jrr ^^j 

a 
where /i* coefficient of friction determined experimentally. 

111. Zn tonlon dynamometan, the deflection of a thaft or spiral aprini 
which mechanically oonaecta the driving and driven machines, is used t 
measure the torque^ The spring or shaft can be calibrated staticAlly b, 
noting the angular twist correeponding to a known weight at the end of 
known lever-arm perpendicular to the axis. When in use the angle can b 
measured by various electrical and optical methods. In one method th 
angular diqAaoement between two points on the shaft is determined by mean 
of two discs <A insulating material, in the periphery of each of which is m 
a very thin piece of metal. The two pieces of metal are connected electric 
ally through the shaft. A light, thin metal brush rests on the pcriphet; 
*A each disc, and the two brushes are connected together through a batter 
and an indicator such as a bell, or a telephone. At no load, one brush 1 
moved until the electrical circuit is completed onoe every revolution. Tb 
angle through which either brush has to be moved as the load is increased, i 
order to keep the oirouit closed, is then measured. 



194 



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MBASVRTSa APPARATUS Sec. 3-^32 

Ml. TIm enuU* AjaMauuattmr is a oonvenient and aoounte dsTica 
«ycfa IB extenoiTely UMsd for routine meacurementfl of tha order of 100 h.p, 
V leM. An electric generator ia mounted on a " cradle " supported on trun- 
MDiH and mechanically connected to the machine being trated. The pull 
Borted between the armature and field tenda to rotate the field. ThU 
toraoe ia counterfoalanced and measured with weights moved along an arm 
in the usual manner. 

BPKXO mAaUUMXNTB 

ns. BeTolntloiu are measured with speed counters and tachometers. 
■paad or rvrolntlon eonnters are attached directly to the shaft to be mess- 
snd and record the total revolutions from the instant that the mechanism 
is connected. They usually consist of an arrangement of worm and ^ears. 
the total revolntiooa being uiown by a graduated dial moving under a pointer, 
or by a cyclometer dial on which the total revolutions are indicated numer- 
ically at eseh revolntion. In order to obtain the speed, the intervening time 
mst be obaerved aiiiniltaneously. 

tM. Taefaomatan or ipead Indicators indicate the speed directly and 
thus inelade the time element. The principal types are centrifugal, liquid, 
reed and eleetfieal. In the eentrifugal type, a revolving; weight on the end 
of a lever moves under the action of centrifugal force m proportion to the 
•peed, as in a fly-ball governor. This movement is indicated by a pointer 
wUeh ramrea over a graduated scale. In the portable or hand-type, the 
tsebometer shaft ia beta in contact with the end of the shaft being measured, 
sad is the stationary type, the instrument is either geared or oelted. In 
thefiaiud tachometer of the Veeder type, a small centrifugal pump is driven 
by a belt consisting of a light cord or string. This pump discharges a col- 
ored liquid into a vertical tube, the height of the column being a measure of 
the speed. 

M$*d taehonutarg are similar to reed-type frequency indicators (Far. 
tn), the reeds being set in resonant vibration correaponding to the speed of 
(he machine, by various means. The instrument may be set on the bed- 
irame of the machine where any slight vibration due to the unbalancing of 
the reciprocating or revolving member will set the corresponding reed in 
vibration. Some forms are belted to the revolving shaft and the vibrations 
imparted by a mechanical device. Beetrieal taohomatar* may be either 
reed imtraments operated electrically from small alternators geared or belted 
to the machine being measured, or ordinary voltmeters connected to small 
permaaent-macnet, direct-current generators driven by the machine being 
waled. 

ttf. Cliroao^rmpllg are speed-recording instruments in which agrapbieal 
record ot speed is made. In the usual forms, the record-paper is placed on 
tke surface of a dmm which is driven at a certain definite and exact speed by 
dock-work or weights, combined with a speed-control device so that 1 in. 
en tke paper represents a definite time. The pens which make the record 
are attached to the armatures of electromagnets. With the pens in con^ct 
■ith the paper and making a straight line, an impulse of current cauaes the 
pea to make a alight lateral motion and therefore a sharp indication in the 
lenrd. This impulae can be sent automatically by a suitable oontact- 
Bieekanism on the shaft oi the machine or by a key operated by hand. The 
tiae per revolution is then determined directly from the distance between 
narka 

THERMOMETRY, PTROMETRY AND HEAT 

CONDUCTIVITY 

BT O. K. BUXOnS, SCO. 

Ain> 

PAUL D. rOOTK, A.M. 

THXBMOmTBT 

W, Tamparataro leale. The standard scale of temperature from 100 

seat, to —36 dag. cent, is based on the hydrogen gas thermometer. 

—35 deg. c«nt. the scale is usually referred to the helium or hydrogen 

^nneter while in the range 100 to 1.600 deg. cent, the nitrogen the^ 

■■OBMcr is used. Still higher temperatures are based on the Wlen-Planek 

■Mkn-BoltBliaan r»dl«tloii laws. Uttiinately measurements of 

195 D,c„!,.Mb,<^iUUyiC 



&; 



) 



Sec S-337 measuring apparatus 

temperature should be expressed in some one standard soale sueh as tli« 
thermodynamic or ideal gas scale. The hydrogen and nitrogen gas ther- 
mometers differ from this scale by various small amounta. The scale defined 
by the radiation lawa is the thermodynamic scale, asaumiog these laws to 
have a sound theoretical basia. For the past 25 years it has been possible 
to express temperatures to 0.002 deg. cent, in the range to 100 d^. o^t., 
but outside of this interval the accuracy is far from being what is desired. 
Only recently for example, has the certainty of the suIfurboUing-point been 
closer than 0.5 deg. and of the gold melting-point 5 de^. cent. At the present 
time the International Bureau and the several national laboratones are 
interchanging communications vith ^e object of eetablishing an intemn- 
tional temperature scale. 

tST. Mercurial thermometers. Primary mercury thermometers are 
constructed of the very best thermometrio gfssses such as verre dur, Jena 
IQiit, Jena 5Qi^i, and the scales defined by the differential expansion of these 
glasses and the mercury have been compared with the gas thermometer so 
that their (5orrections are fairly well established. (See Circular No. 8 of 
the Bureau of Standards.) 

SS8. Laboratory and industrial meroury-in-glass thermometstv 
(range - S6 to + S60 deg. cent.) are calibrated by direct oompaxiaon with 
standards. Two points which frequently occasion trouble in Uie use of 
mercury thermometers are (a) correction for emsr^eni stem, (b) oorree- 
tion for thermometric lair< 

S89. Correction for emergent stem. In general the calibration cor- 
rections are determined for total immersion of the thermometer. When 
used with the stem emergent into space either hotter or colder than the tem- 
perature of the bulb, a stem correction must be applied to the observod 
reading of the thermometer in addition to the calibration oorrection. This 
stem-correction may amount to more than 20 deg. cent, for measurexnents 
made with a mereurial thermometer at 400 deg. cent. (760 deg. fahr.). The 
stem correction may be computcKl from the formula: Stem Correction « 
KXn(T^ — (^) where X^faotor for relative expansion of mercury in glass; 
0.00015 to 0.00016 for centigrade thermometers. O.000OS3 to 0.000089 for 
fahrenheit thermometers; n~ number of degrees emergent from the bath; 
T ■■ temperature of bath ; < — mean temperature of emergent stem. 

faampls: Suppose that the observed temperature was 100 deg. cent, 
and the thermometer was immersed to the 20-de^. mark on the scale, so that 
80 deg. of the mercury column projected out into the ur, and the mean 
temperature of the emergent column was found to be 25 deg. cent.; then— 
stem cor.-0.00025XS0X(100-25)-0.9 deg. cent. As the stem was at a 
lower temperature than the bulb, the thermometer read too low, so that this 
correction must be added making the correct temp. «* 100.9 d^. cent^ Ths 
mean temperature of the emergent stem may be approximately meaaured. by 
a small auxiliary thermometer, bv a Faden thermometer, or by surroundins 
the stem with a water jacket and observing the temperature of this bath. 

S40. Correction for thermometaic lav (Bur. of Standards, Reprint 
No. 171)» When a thermometer is immersed in any medium it does not take 
up the temperature of the medium immediately, but approaches it asymptot- 
ically. This effect may be minimised by stirring the bath. With vigorous 
stirring in the case of a liquid bath, the thermometer reading should be cor- 
rect to within 1 per c^nt. of the original difference in temperature of the ther* 
mometer and bath after 10 to 60 sec. exposure. In absoiat^y quiet air this 
degree of accuracy mi|Eht require 20 min. Fanning the thermometer nu|(ht 
reduce the time to 1 nun. With caution, corrections for lag may be neglected 
in ordinary laboratory work. 

141. High-temperature thermometerti Although mereury boils at 
357 deg. cent, under atmospheric pressure, by filling the space above the mez^ 
oury with COi or Ni under sufficient pressure, certain mereurv-in-glasa ther- 
mometers may be used at a maximum temperature of about 500 d^. 
cent. Glasses used are Jena 16"i to 450 deg. cent, Jena 59^^^ to 520 deg. 
cent., and special grades of combustion tubing to 660 deg. cent. Care 
must be exereised that the thermometer is not overheated. If the long 
portion of the stem is cold, the stem (x>rreotion may amount to 40 dog. 
oent. and hence while the mereury stood at 500 deg. cent, the true temp«a- 
ture of the bulb would be 540 deg. cent. A few moments at that tempera- 



llBASURIira APPARATUS Sec. S-342 

tore misht ebance the ioe point 20 deg. cent, in the caae of Jena SS>" or any 
ipereui7-iD-slaaa thermometer except one constructed of high-grade oombua- 
laoD tobins- 

StS. l«w-t*niperatiiT« thermometen. For the measurement of 
temperatures bdow the range of the merciuy thermometer ( — 35 deg. cent.), 
there ar« Available alcohol (—70 deg. cent.), toluene (—90 deg. cent.), and 
peuoleuin-ether or pentane (—200 deg. cent.) Uquid-in-glaas tnermometen, 
eeppep-eonstantan and other thermocouple*, and electrio resistance ther- 
mometers. With these types of liquid-in-glass thermometers the same pre- 
caationa apply as with mercury, and in addition apeaial care must be taken 
to p rere m t uie liquid from sticking to the sides of the glass. On atcount of 
Tiaeaaity of the liquid at low temperatures the thermometer must be slowly. 
cooied to the temperatore of the bath, cooling first the bulb and tiien the 
■tern. 

MS. Caloriinatrle marrary tharmomatan are of two types, the 
ordinary mercurr thermometer with a total stem length of 10 to 15 deg. 
cent., craduated in 0.05-d«i. to 0.03-deg. intervals, and the Baokmann 
tharinom^tar arranged so that part of the mercury may be removed from 
the bdlb in order to utilise the snort scale (5 or 6 deg. cent, graduated in 
ai>l-des. intervals) for differential work at various temperatures. In addi- 
tion to the stem corrections the Beokmann type requires a setting 
eorrsetion depending upon the amount of mercury remaining in the bulb. 
Cslcrinketrie tnermometers may be in error by 1 per cent, of the indicated 
lamperatare scale differences, and consequently should be calibrated. Thn 
highrst aoenracy attainable is from 0.5 to 0.1 per cent. For greater preciaion, 
tbemoooaplea or resistanoe thermometeia are available. 

■44. AnsxmaJing of tliannoinatan. Every thermometer, particularly 
if intsoMied for use above 100 deg. cent., should undergo suitable annealing. 
Thonmsh annealing requires from 4 to 10 days at a temperature of 460 deg. 
cent, or as mnch higher as the glass will safely stand, and the annealing may 
wsD be followed by a period of slow cooling extending over several days. 
AHeraate heating aind cooling is also beneficisii. 

PTBOMXTBT 

Ml. Tbamutalaetrie pyrometiT. In pyrometers of this type tempera- 
tases are meaaured by the magnitude of the electromotive forces set up be* 
taeen wires of different materials when one junction is exposed to the 
temperature to be measured and the other junction (or junctions) is kept at 
aoiae known temperature. 

MC Katagial of ConpU. The LaOhatalier eouple (Ft, 90Pt-10Rh) 
isia caneral the most satufactory couple in the raure 300 to 1,500 deg. cent.. 



aithonxh (Pt, 90Pt-10Ir) is frequently used. For temperatures below 
IJOOOd^i. cent. (Cu. eOCu-40Ni), (Ni-Cu), (Ni, 90Ni-10Cr), and other 
aBoys a e i t e satisfactorily in technical work. From 500 deg. cent, to the 



temperatures, eopper-conatantan and iron-constantan are materials 

f re que ntly uaed. At 1,000 deg. cent, (cold junction— deg. cent.) the 
LeChatriier couple develops an e.m.f. of 0.5 millivolts. Many base-metal 
I iwnJia will develop an e.m.f. of several times this magnitude. 

MT. rarmnlaa and calibration. (Ft, Pt-Rh) and (Pt, Pt-Ir) 
'"TpV* have a temperature-e.m.f . relation of the form . 

e-a+bt+cf (43) 

from 300 to 1.200 deg. cent.; and 

«~pl+gl' (44) 

fraa O te 100 deg. cent., where ( is the temperature centigrade and a, b, e, p, q, 
m eapoisal eonatants. Three calibration paints serve to determine 
a, t, c Those moat satisfactory are the melting- or freesing-pointa of 
ne or lead, antimony (Kahlbaum) or aluminum, and copper. Ordinary 
hasi iiM liil eonples may have transition jwints in the temperature-e.m.(. 
civTc so that in general a calibration must be made at a larger number of 
tsBtperatnree, when the best curve may be drawn through the plotted points. 
SM. QalraiMniiaten used to measure the e.m.f. develop>ed bv a couple 
shoald preferably have a resistance high in comparison with that of the 
eoaplcL Tbe relation between the true e.m.t. of the couple B and that indi- 
I catM by a olyanomater W is 



197 



i.jv^iuuyie 



Sec. 3-349 



MBASURINQ APPARATUS 



E- 



«'(«+r+rO 



««: 



) 



where /Z, r, K are the reaistaoceB of the galvanometer, thermocouple and leadi 

respectively. 

349. Gold-Junction oorrectiona. If a thermocouple u calibrated witk 
cold junctiona at deg. cent, and used with cold junctions at t« deg. cent.. 
one must add to the e.m.f. actually developed, the value of the e.m.f. devel- 
oped when the hot junction is at U deg. cent, and the cold juncti6ns are de^ 
cent., to obtain the correct value of the e.m.f. corresponding totempera.- 
tures shown by the calibration. If the indicator is graduated to read tem- 
perature directly, instead of e.m.f., the cold-junction correction has the form 
p deg. cent. —Factor Xfo. For the LeChatelier couple this factor ia about 
0.6 in the range 300 to 700 deg. cent, and 0.6 from 700 to 1,400 deg. cent. 
B&w-metal couples show factors varying from 0.2 to 1.2 depending upou th« 
particular alloy used. 

As an example, suppose the indicated temperature , (cold junction «« 40 
deg. cent.; calibration temperature ««0 deg. cent.) by the LeChatelier couple 
is 1,000 deg. cent. Then p«0.5X40-20 deg. True temp. -1.000+20^ 
1,020 deg. cent. 

300. Certain prvoauttons should be taken in the use of thermocioupltta. 
The hot junction is usually formed by welding the dianmilar metala m lua 
oxyhydrogen flame. Other junctions may ne soldered or thorouehly 
securad with binding screws. The entire couple should be annealed al; aa 
high a temperature as it will safely stand in order to render it as homogeneous 
as possible. The couple must be protected from furnace vapors or dii-ect 
contact with liquid baths, and the two leads must be insulated from each 
other. 

SSI. Xlectrical resistance pyrometry. This method of high-temperar- 
ture measurement ordinarily niakes use of the variation in the eleotrical 
resistance oH platinum ancf is capable of great sensibility. In one of ita 
simplest forms the pjrrometer consists of a coil of platinum wire woundl on 
mica, and encased in a protecting tube of porcelain. On account of the dis- 
tillation of platinum, high- resistance coils of small wire are not used much 
above 900 deg. cent. However, coils constructed of 0.6-mm. wire may serve 
satisfaetorily to 1,200 deg. cent. 

383. Three-lead type— Wheatatone bridge method. For the pur- 
poee of eliminating the resistance of the leads to the coil« a third wire is 





Fio. 126. — Three-lead resist- 
ance thermometw. 



Fig. 127. — Four-lead resist- 
ance thermometer. 



frequently introduced as in Fig. 126. The coil P forms one arm of a dial-] 
type bridge, of which the others are n, rt and A, whence from Uie principle' 
<n the bridge, if the galvanometer <7 remains undeflected, < 

(46) 

ri ig uBually made equal to rt and W i* coiMtructed as nearly as poeiibia 
identical with an', ao under theee circunutsncea P — A regardleH of the tcm- 



p_ MR + W) _^ 



198 



i.jv^iuuyic 



MEASURING APPARATUS 



Sec. 8-353 



pentora or reaiataiioe of ibe lead*. This type of thermometar may also be 
and with a differential galTanometer. 

MS. ronr-Uad type — Wheatstooa lHld<« nMthod. The compeiuat- 
ioc leads are inaertea in one arm of the bridge R and the thermometer 
Uik in the other, aa shown in fig. 127. This type may be used with a sLide- 
wire bridse. 

IM. Voor-Iaad potonttal-tarminal type (Fig. 128). The resistance of 
llw eoil is mieasured by sending the same current from^ a storage battery 
throogh the thermometer and a known resistance in series, and measuring 
the potential drop by means of a potentiometer, first across the known resist- 
aoec and then acrose the thermometer coil. Two of the thermometer ter- 
fflinala are current leads and two are potential leads. The current ordinarily 
ased is of the magnitude 0.003 to 0.05 amp., and should be the same as that 
osed daring the odibration of the iostrament, to eliminate the errors due to 
the heating effect of this eurrent. 








Fie. I28.^Four-lead resistance thermometer — potential terminal type. 



IH. 7«rnuilag. Tbe relation between temperature and resistance of the 
platinum coil is of the form 

Ri-Rt(.\+at-U*) (47) 

la ttneral it is more convenient to refer to an arbitrary scale known as the 
platinum temperature, and to correct this scale by a certain difference foT- 
■ala. If pt denotes the platiQum temperature corresponding to a resistance 
<, we have the relation 

100(Jt-g «) 

where i2us and R% are the resistances atlOO deg. cent, and dec. cent, respec- 
tiTdy. The relation between the centigrade temperature ( and the platinum 
temperature pC is as follows: 



»-jX- 



'(t^-0 



(49) 



100 

m. Calibrfttton. For the calibration of a thermometer, the ooil of 
>Ucb is of the highest purity platinum, resistance measurements are made at 
three temperatures, as imlows: the ice point, the steam point and the boiling 
point of sulphur. Substitutiag the values thus obtained in formula for 
p (Par. SU) the value of pt corresponding to the sulphur point is known. 
Ucning to the formula for I (Par. MS), the value of t should be found a 
ttiBitaat of the magnitude 1.49 ± 0.01, whence from the_ two formulas a 
tshle of R and t may be computed. Such a calibration will indicate tempera- 
tares in the range —50 to 1,200 deg. cent, as closely as they are known in 
(•raw of the gas scale. If < is found considerably greater tban 1 .49 due to 
iBipority of uie platinum, there is advantage in using a fourth calibration 
post, nch as the silver freesing-point as a check. 

ttf. Aiiape^MHty The Teilstance tharmomater is especially adapted 
«> ^ nwsuia ment of small temperature changes such as occur in oalor- 



199 



jv^iueivie 



,y, 



\ 



Sec. S-3S8 MBAauRiNO apparatus 

imetiVi to the determination of freenoc-pointa, etc., uid to spenal pfayaioi 
and tcermochemical inveatixationa where an acouracy of one or two pmrl 
in 10,000 may be attained (see Bur. of Standards, Reprint No. S8 and N< 
124). In the technical industriee thia type of thermometer with one of Ul 
many forms of indicators available ia highly satisfactory. 

S5S. Badifttlon. The temperature of bodies ma^ be eetimated from th 
radiant energy which they send out in the form of visible light or of the lonn 
infra-red raya which may be detected by their thermal effects. Since tii 
intensity of radiation increaaea very rapidly with a riae in temperature, j 
would appear that a system of pyrometry baaed on the intensity of the li«h 
or total radiation from a hot body would be an ideal and simple one. How 
ever, different subatancea at the same temperature show vastly diCTeren 
intenaitiea at a given wave length, or in other worda, the ftbiorbiiif or amis 
llTs powen may vary with the aubstance, with the wave lensth. and ala 
with the temperature. 

tM. Blkck-body radiation. A aubatance which abaorba all the radis 
tion of any wave length falling upon it is known aa a black body. Buch i 
body will emit the maximum intensity of radiation for any given temi^eratuit 
and wave length. No such material exista, but a very close approximatioi 
ia obtained by heating the walla of a hollow opaque encloaure aa uniformly ai 
possible and obaernng the radiation coming from the inaide through a vei] 
small opening in the wall. 

>M. Stefan-Boltsmuin law. The relation between the total enern 
radiated by a black body and its temperature ia expreeaed by the equatioi 
J^v(r*—Tt'), where J is the energy of all wave lengttia emitted per squan 
centimeter of aurface, T and Tz the abaolute temperaturea of the radiatoi 
and receiver respectively, and v a constant of about the value 5.8 X 10~>> watti 
cm.~* deg.'*. In general Tq^ is negligible in comparison with T* so that th( 
above relation becomes J — rT*. Although the total energy emitted by anj 
substance is not that emitted by a black body at the same temperature, it mai 
be considered as some fractional part of that from the ideal radiator, thu 
fraction « being known as the total emissivity- If iS denotes the apparen 
absolute temperature, i.e., the temperature on the black-body acale corro 
spending to an amount of energy equivalent to that emitted by the non 
blaok suDStance at a true temperature T deg. absolute, the relation betweei 
its total emissivity c and the quantities S and T is: 

Log c -4(log S-log D . (50) 

>U. Badlatlon pyrometry. The quantity of heat a body receives b] 
radiation from another body depends upon certain conditiona r^ative t< 
each of the two bodies, namely (a) temi>erature, (b) area of aurface', (c) d^ 
tance apart, (d) emiaaive and abaorbing powers. A pyrometer may be 8< 
conatructed that conditiona (b) and (c; compensate one another, at leas' 
within certain prescribed limits, ao that for all technical purposes the radia 
tion received by the instrument depends only upon the temperature of tbi 
radiating source and its emissivity. The p^meter is calibrated by sightin« 
upon a black body, the temperature of which may be obtained by thermo. 
couples. Specially oonstructed furnaces for this purpose are available ia al] 
testing laboratories. 

Ml. Fery mirror telaieope pyrometer. (Fig. 129.) Radiation of al 
wave lengtha is brought to a focus by means of a oonoave gold mirror it upoi 
the hot junotion of a minute ther- 
mooouple located at I*. The cold TO Indicator 
iunetions of the couple are suit- 
ably screened from the direct 
radiation of the hot body. The 
concentration of beat at the hot 
junction develops an e.m.f. which „E 
may be measured by a potentio- ^ ' 
meter or galvanometer. In prac- 
tice the galvanometer is usually 

calibrated to road temperature i 1 5 

directly. The relation between ^ .«/» kk j. ^. 

the e.m.f. and the temperature ^'°- 129.— F«ry radiation pyrometer. 

may be expressed by the equation 

B^aT*, or in log form, loc£—t+6log 7, where 7* is the absolute tempera- 

DigilizedbyV^iUUyiC 




MSASURINQ APPARATUS 



Sec.S-363 



tBnudaortand&ueempirioal conrtmnU. In general 5 approximateB the 
Tfthie 4, but znay bxve a rao^ varying from 3.5 to 4.5 depending upon the 
coDStmetion of toe individual inatrumeut. The pyrometer should Be sharply 
(oeaaed upon the radiating source and for this purpose an ingenious device 
ii moonted in tiie instniment by means of which straight lines appear broken 
BBtil the mirror is adjusted by the thumb screw S to the proper position. 
Vaster has transformed the F4ry telescope into a fixed-foous pyrometer bjr 
phdng the thermocouple and a small front.dii4>hnigm at the oonjugate foci 
of the gold mirror. 

•n. Thwlnc pfrometer. In the Thwing pyrometer the reflecting 
■imr is replaced by an aluminum cone which by multiple reflections eon- 
esotrmtea the radiation at its apex on one or more small thermoeouplea in 
■ries with a portable galvanometer. The instrument requires no focusing, 
the froat di^ihragm acting as a soxxrce. The object sighted upon must be 
higs enough to eover.the projection of the cone through this diaphragm. 

Mt. Freeantlons in the tias of radUtton pyromstan. The mirrors 
or reflecting devices must be kept bright and free from dust. In the case of 
the F6ry p^ometer, errors amounting to 100 deg. cent, have been observed* 
doc to ordinary accumulation of dirt upon the large gold mirror. 

Many radiation instruments re<}uire several minutes of ezjKMure to the 
radiating source to indicate a maximum reading due to the slow heating of 
the hot junction, 'while others require less than 20 sec. The maximum in- 
dieatioa diould be accepted. Care must be taken that the source is large 
n»mU to completely ''fill" the aperture of the pyrometer. It is usually 
inipiaiUe to focus upon the back of a furnace through a very small peep- 
bote and obtain reliable results; in such cases the hole must be enlarged so 
that it does not eut into the cone of rays entering the instrument, or the 
pynmeter may be focused upon the hole itself. In the latter case the hole 
■nat be large enough to cover the thermocouple in the F6ry pyrometer or 
tke front diaphragms of the Thwing and Foster pyrometen. Variations in 
leom temperature in general affect the hot and cold junctions nearly alike, 
se that very little error is introduced in the reading of a radiation instrument 
from this cause- 
Mi. XmisslTttr eoirsetloiu for radiation pyrometers. In the case 
fli sighting upon peep-holes in furnaces, kilns, etc., the total-radiation py- 
moeters incucato approximately true temperatures. When sighting upon 
efaieets in the open, certain corrections must be applied. These oorrectiona 
m but roughly known. The following table (Par. IM) shows the true tem- 
peiatares corresponding to the pyrometer indications when sighting upon 
■Biten iron (t — 0.28), molten copper (0.16^, copper oxide (0.60), u-ott 
adde (0.86), and nickd oxide. The data is obtained from the work of Thwing, 
"* I ana several experiments of the authors. 

S66. Total KmisslTlty Oorreetlons 



Observed tem- 


True temperature, deg. cent. 


pcratore, 
dsg. cent. 


Molten 
iron- 


Molten 
copper 


"i^' 


Iron 
oxide 


Nickel 
oxide 


60O 




1,130 
1,290 


720 

830 

945 

1,060 

1,170 


630 

736 

840 

945 

1,050 

1,155 

1,260 


710 


700 




800 


800 


1,200 
1,340 
1,475 
1,610 
1,7S0 


895 


MO 




985 


IMO 




1,075 


1,100 




1,165 


1,200 






1,256 











MT. man's law. Wien's laws relate to the distribution of the energy 
°< the biaek body in the spectrum. The law chiefly concerned in optical 
Ufiu amUj expresses the relative intensity of the energy emitted at any 
Pno wave length X and temperature in the following manner: . 

i-eix-»«~Vxr.) 



(6U 



201 



yGoOgk 



Sec. S-368 



MBASURtNO APPARATUS 



where J u the energy correepondinc to the wave length X and the sbaolute 
tempenture T of the radiator, s the base of the natural (Napierian) ayatem 
of logarithmii, and ci and n empirical Constanta, a may be talcen aa 
14,SCfO when X is measured in nucrons, i.e., n (Sec. 1). n depends upon 
the energy units. If iSj^ is the apparent absolute temperature correspondinfi to 
the wave length X of a non-black body at a true absolute temperature 7*. 
it follows that 

^-i-C^og-J'-'-'^x <*« 

where Aj^ u the Absorptivity "emisaivity — umty minus roflectinc power of 
the'radiator at the particulaf wave length X and temperature T. 

168. Optical p^om^try. Optical pyrometers are based upon the 
photometric principle of matching the intensity of visible monochromatie 
radiation emitted by a substance, with that of the same wave length or 
color from a standard reproducible source such as the amylacetate lamp, or 
a oonstant source such as an electric lamj). The instruments are calibrated 
by comparison with the intensity of radiation from a black body, the primary 
standard to which all measurementa are referred. 

569. T4tj absorption pTrometar. (Fig. 130.) The apparatus con- 
sists essentially of a telescope carry inf^ a small oil or gasoline lamp L, The 
image of the name of this lamp is projected on a silver strip at M adjusted 
to tne focal point of the ocular and objective system. By means of the 
black-glass absorbing wedges lo, 10, the intensity from the source may l>e 
varied until a match 

of the photometric 
field (see small Fig.) 
is obtained. A red- 
glass screen is used in 
the ocular so that 
fairly monochromatic 
light of this color 
(0.65 or 0.63m) is com- 

Eared. The relation 
etween the thickness 
of the wedges x, read 
on a scale, and the ab- 
solute temperature T is 
»+P-Q/r, where P 
and Q are constants 
determinable by two 
calibration points. The instrument must be focused upon the radiating 
source but no corrections for distance need be applied. The IiaChatalier 

Eyrometer, the first optical pyrometer developed, is similar in principle 
ut is not of constant aperture and important corrections must be made 
with change of focus. The Shcnra pyroscope has a direct-reading tem- 
perature scale controlled by a diaphragm before the standard oil lamp. 
In all of these instruments the purity of the gasoUne, oil, or even the 
amylacetate used in the companson lamias is of little importance. Con- 
siderable impurity may be introduced without affecting the calibration 
perceptibly. 

570. Wanner pyromotar. (Fi^. 131.) The comparison light is a six- 
volt incandescent lamp illuminating a glass matt surface; monochromatic 
red light is produced by means of a direct-vision spectroscope P and a screen 
cutting out all but a narrow band in the red (X»0.056m) and the photo- 
metric comparison is made by adjusting to equiU brightness both halves of 
the photometric field by means of a polarising arrangement. The slit St 
is illuminated by the incandescent lam^ while light from the furnace enters 
Si. After passing through a Rochon prism and a biprism, the light from the 
two slits polarizod in planes at 90 deg. to each other reaches the Niool prism 
N. Rotation of this analyzer serves to extinguish one field and brighten 
the other simultaneously, until a match is effected. A reference angle ia 
chcuen, usually about 30 deg., corresponding to the ajiparent temperature 
of a section of an amylacetate flame. The instrument is set at this normal 
point and sighted upon the ground-glass screen of the flame gage. The 




Fia. 130. — FAry optical ps^rometer. 



202 



hy»^TUUyiC 



MMAavtam APPABATva 8ecS-37i 

brii^iiMa of the elactrie lamp ia then vkried by alterins the ouneot throuth 
it nntU the h&lYee of the photometric field are matched. Maintaining thja 
current eonitant, the pyrometer is ready for calibration or for temperature 
mMauements. The instrument follows the law 

log-Un,.-o+^ (S3) 

where ^ ie the angtUar reading of the analyser, T the absolute temperature 
aad a and b empirical constants. The relation between log-tan y and \/T 
m linear. Two calibration points serve to determine a ana b, when a table 
or plot may be made of 9 vs. I deg. cent. (7^ — 273). Frequent adjustments 
iboQld be made of the current throi2^ the electric lamp necessary to obtain 
s match mt the normal |>oint when sighted on the amylaeetate lamp. The 
■le t tri e lamp bums at a high temperature (about 1,800 deg. eent.) asd eon- 
•cqnently deterioratee rapidly. For the highest aeeuraey this adjustment 
fhoold be made before and after a series of temperature readings; in indus- 
trial plant* once a day or once a week will answer depending upon the 
\ of use. 

Xi P B Alt 



Si| 



eW KMsa sg iJi i aM ag MBjaMMgE 







Fio. 131. — Wanner pyrometer. 

STL. Ttaa SdiBAteo pffoaMter is as Improved form of the Wanner 
(Par. >T0). The delicate optical parts are encased in a strong metal sheath, 
aad the addition is made of a direct-reading temperature scale, besides 
asiiiy adjustments for convenience of operation. 

tn. KoTM and Bolbom-Kurlbauxn pyrometan. The filament of a 
•nsQ dectric lamp is placed at the focal point of an objective and ocular 
lomuiig an ordinary telescope, which superposes the image of the furnace 
opoa tne lamp. The tip of the filament is brought to a photometric match 
by varying tne current. Red glass, Jena 2,745, or preferably F 4,512, 
mounted at the ocular furnishes a high quality of monochromatic light. 
Tke relation between the current through the lamp and the temperature 
kas the form 

»•-o-^M-^c«^ (64) 

Three standardisation points are necessary to determine the constants a, 
i, e. The lamps should not be used at temperaturee higher than 1,500 
di(. cent, (for the highest accuracy 1,300 deg. cent.) on account of deteriora- 
tacm of the filament. By proper care they may be used for hundreds of 
hova without appreciably ijtering the calibration. For temperatures 
Ugker than 1,500 deg. eent. black absorption glasses (Jena F 3,815) or 
laetor discs are used to cut down the intensity of -light from the furnace. 
The relation between the observed temperature and the true temperature 
follow* from Wien's law: 

W(i-x,).?^M^(lJ^) 

*l>sra ilx >■ fM absorption coefficient of the glass or sector, a- 14,500, log 
<»0.4343. X is the mean wave length of the red glass, Ti the absolute 
tsnperatnre observed when sighted through the disc or glass and Tt the 
sbaclate temperature of the furnace. All lamps should be aged before using 
by hsatiiw at 1,800 deg. cent, for a period of 20 hr. 

tn. ImlagiTltjr ooireetloiu for optical pyromatars. Optical pyrom- 
gjBi win indicate true temperatures when sighted upon a black Dody. 
^ek-body conditions are approximated in practice by a peep-hole in the 
■ds of a furnace or kiln, or a closed porcelain tube thrust into molten metals 
or salts. When sighting upon objects in the open, certain corrections must 
** sppUed. Tba relation between the emiarivity (monochromatic light) 

303 

DigilizedbyV^iUUyiC 



Sec. 3-374 



MSASURIffa APPARATUS 



(f-k^-ahre^"'"^^ 



of a substance and its observed and true temperature follows from WSen's 
law: 

(56) 

where T ia the true absolute temperature of the substanoe, Sj^ the apparent 
abaolute temperature aa measured by an optical pyrometer using light d 
wave length X measured in microns, and Ax is the abaorption or emissirxty 
at the wave length X and temperature T. The following table (Par. ST4) 
presents the emissivities of various substances determined for red Iigh< 
U- 0.65,1). 

•T4. Tkble of ImiwriTlUei Tor Bad Ucht (X-0.6Sm) 



Sttbatance 



Substanoe 



(o) Silver 

WO""' HkJidd:: 

Platinum 

Palladium 

(«) Copper ^"ilj:; 

Nickel 

(c) Tungaten l jIsoo"^." 
(c) Tantalum | ||Jgg ; ■ 
W Carbon { ^Jggg ; ; 



0.07 
0.13 
0.22 
0.33 
0.33 
0.11 
O.IS 
0.33 
0.46 
0.66 
0.60 
0.48 
0.86 
0.79 



Cuprous oxide. 

Iron oxide 

Porcelain 

Lime. 



(c) Molybdenum j j ^' ' 



(d) Iron 



solid 



/ 1,100. 
\ 1,600. 

liquid! 21200. 



(<) Nickel oxide (iJqo; 



0.70 

0.8S 

0. 25 too. SO 

0.10to0.40 

0.44 

0.37 

0.62 

0.40 

0.10 

0.53 , 

0.06 

0.85 



(f) 



Solid 



Liquid 



(f) 



Solid Liquid 



Cu. 
Ag. 
Au. 
Pd. 
Pt.. 
Ir.. 
Rh. 
Ni.. 
Co. 
Fe.. 
Mn. 
Ti. 
Zr.. 
Th. 
Yt. 
Er.. 
Be. 



0.10 
0.04 
0.14 
0.33 
0.33 
0.30 
0.29 
0.36 
0.36 
0.37 
O.SB 
0.63 
0.32 
0.36 
0.35 
0.55 
0.61 



0.15 
0.07 
0.22 
0.37 
0.38 



0.30 
0.37 
0.37 
0.37 
0.59 
0.65 
0.30 
0.40 
0.35 
0.38 
0.61 



Cb 

V 

Cr 

Mo 

W 

U 

NiO.... 
Co»0« . . 
FeiO«.., 
MnK)<. 
TiOi.... 
ThO.. . . 
YtiO... 
BeO.... 
CbO.. . . 
VK)t..-. 
CrjOi. . , 
UiO.... 



0.49 
0.35 
0.39 
0.43 
0.39 
0.54 
0.S9 
0.77 
0.63 



0.40 
0.32 
0.30 
0.40 



0.52 
0.67 
0.61 
0.37 
0.71 
0.69 
0.60 
0.30 



0.34 
0.88 
0.63 
0.53 
0.47 
0.51 
0.60 



0.31 



Authority (a) Stubbs; (6) Stubbs and Prideaux; (c) Mendenhall and For- 
aythe; (if) Bidwell; («) Burgess and Foote; (/) Burgess and Waltenberg. 

ITS. Curve of amlulvity correetioni. Fig. 132 shows the correc- 
tions to apply to the pyrometer readings for a number of values of A, using 
s deg, cent, as abscissas and (1 — a) deg. cent, as ordinates. To obtain the 
true temperature correaponding to an observed temperature < deg. cent., 
add to B the value of the ordinate at the particular emissivity A and abscissa 
s. As an example, let A » 0.30, a » 2,000 deg. cent. ; true temperature ■> 
2,000+320-2.320 deg. cent. 

ST6. Becordlng pyrometry. Among the different methods for th« 
measurement of nign temperatures, several may be made continuously i«. 



204 



DigilizedbyV^iOUyie 



UBASURINO JWPARATVS 



Sec. 8-377 



_ Form of Mmjieratara reoordiiig appsmtiu niitsble for laboratory 
iacrestisatioa have boon in existence for years. Of late a number of manu- 
faetnrers have prodneed recorders which serve most satisfactorily in the 
^fykwM— I industries. 

tTT. AppUembllltjr of raeordinc Byromateri. The foUowins pyrom- 
eters have been made recording: (a) constant-volume gas thermometer; 
(k) thermoelectric pyrometer; (c) electrical resistance thermometer; (d) 
total radiation pyrometer; (e) transpiration pyrometer. The optical pyrom- 
Mer d the Morse type could be made semi-recording, but the other optical 
aad diaoontinuons tyvtu of pyrometers oouM be made recording only with 
Tsrj great difficulty. 



BOO 

no 

lanft 


















F 1 




















M 


y 




/ 




















/ 


i 


/ 






1 ""' 

1- 

r 

S«oo 

■0 

MO 

» 
















/ 


A- 


i 






/ 














/ 


/ 


r 




/ 














/ 




/ 




/ 


/ 












J 


/ 


/ 


A 


"■} 


/ 




/ 










/ 


/ 




y 


/ 


,/ 


/ 










/ 


y 


/ 


y 


^A 


y 


/ 










/ 


r 


/ 


y 


> 


/ 








^ 




/ 


> 




y 


^ 


X 


A-y 


^ 


•^ 






y^ 


< 




^ 


k-'" 


^ 




4- a 


1 







■^ 




--' 






— 


— ' 




^ 


»__ 


— 







ooouaonooitfouooiaionnonwzttoaoossoo 

OpUoal PjiDmeter Beadlaga Ceat. 
BaaLlBht(A.aaB/t) 
no. 132. — Correction curves for optical pyrometera. 

tn. TypM of cnzTM vA rMXtrdlnc PTromtten. The simplest and 
Bolt noiveraal q)plicatiao of reoordets ia to obtain the time-temperature 
csm U vs. f) wbisre time and temperature, or some quantities proportional 
tothtn, appmr as the coordinates. This type of curve is especially valuable 
•B a coatuinoas record of the temperatures of a furnace or kiln during a 
pnloBged run. Sometimes it ia also used to detect recalesoence points in 
•tad, wiiieb appear as flexures or indentations on the plot, when the furnace 
■ataiainc ^^ sample is uniformly heated or cooled. Oocaaionslly the 
■•mptntare-rate curve (« vs. dt/it) is employed for this purpose, and 
nry eoaanCDly in metaUography Uie inverse xate curve (9 vs. dl/dt) is 
■M. The inTcne-tste curve ia obtained by noting the time intervals 
. wiiij to ood (or heat) the specimen by equal decrements of temperature. 
''tk«ae methods accidental variation in the temperature of the furnace is 
"»rd«d. This is desirable in case the chanses m the temperature of the 
'viics or contenta are desired, but when the transformations which are 
iiUv pbw within the lanvla itialf are being inveatigated, such fluctuations 



aoe 



i.jv^iueiyie 



Sec. 8-379 



MBA8UR1N0 APPARATUS 



should be eUminated. Thii may be done by taldnc the diffarentU 
temperature ourva (t vs. t — 8'), or recordinit the temperature of the BKm|( 
in terms of the suooeaaive differences in temperature between the sample i 
another body called the neutral, possessing no transformation points, i 

S laced within the furnace close to the sample. The relations involved in 1 
ifferential-temperature curve are usually better interpreted by means i 
the derived-differentia] curve, or the temperature difference between t] 
sample and the neutral for equal temperature decrements vs. $, The foil 
of curve thus obtained is similar to the inverse rate curve. 

179. Btendard tamparaturai. From a consideration of determinatioa 
msde since 1900, and selecting only temperatures in the location of whjel 
two or more independent observers nave participated, and which are suitabb 
for use as check points in physical and chemical operations, the foUowini 
table is presented (Par. SM). Temperatures above 1,550 deg. cent, are baaM 
on ci» 14,500. Boiling-points are given for a pressure of 760 mm. Hg. 



SM. 



Tftbia of Btemdard TamparatuTM; Tharmodynunle Scale 

(dag. oant) 



Substance 



Phenomenon 



Tempera- 
ture 



Uncer- 
tainty 



Reprodu- 
cibility 



Hydrogen 

Oxygen 

Carbon dioxide. 

Mercury 

Water 

NaiSO«-|-10HiO. 

Water 

Naphthalene. . . 

Tin 

Beniophenone. . 

Cadmium 

Lead 

Zino 

Sulphur 

Antimony 

Ag>.Cui 

NaCl 

Silver 

Gold 

Copper 

Palladium 

Platinum 

AlumiDa 

Tungsten 

Carbon arc 

Sun 



Boiling 

Boiling 

Sublimation in in- 
ert liquid. 

Freesing 

Freesing 

Transformation to 
anhyd. salt. 

Boiling 

Boiling 

Fleeting 

Boiling 

.Freesing 

Freesing 

Freesing 

Boiling 

Freesing 

Euteetic f reese 

Freesing 

Freesing 

Freesing 

Freesing 

Freesing 

Melting 

Melting 

Melting 

Pos. crater 

Surface 



-262.7 
-182.9 
-78.34 

-37.7 

32.383 

100 

217.96 

231.85 

305.90 

320.92 

327.4 

419.4 

444.8 

630.0 

779 

800 

960.9 

lOOS 

1083 

1549 

1755 

2050 

3000 

3600 

6000 



0.2 
0.1 
0.1 

0.1 



0.002 



0.02 

0.1 

0.05 

0.1 

0.1 

0.1 

0.1 

0.5 

1 

2 

1.0 

2 

2 

10 

15 

30 

100 

ISO 

500 



0.05 
0.03 
0.03 

0.05 

O.OOI 

0.001 

0.001 

0.01 

0.05 

0.02 

0.03 

0.06 

0.16 

0.03 

0.3 

1 

1 

0.6 

1 

1 

3 

6 

20 

25 

50 

100 



Oxygen boiling-point*.. . 

Carbon dioxide, sublimation 
point. 

Water, boiling-point. 

Naphthalene, boiling-point. 

Bensophenone, boiling- 
point. 

Sulphur, boilinc-point 



-182.9 -1-0.013 (p-760) 
- 78.34-1-0.017 (p-760) 



-f0.037 <p-760) 
217.96+0.068 (p-76p) 



I- 100 

< ■ . .. 

(- 305.90 + 0.063 (p-760) 



t- 



444.6 +0.0912(p-760)- 
(p-760)« 



0.000042 



Of the boiling substances, bensophenone and oxygen ate the only onea t* 
the purity of which special attention need be given, but the metals used fo 
freesing- or melting-points must be of the highest purity. 

* p denotes pressure in mm. of Hg. 



206 



y Google 



j MSA8VRINO APPARATUS SeC. S-381 

asAT oowDVOTmrr 

Ml. B««t OondaeUTity. Thra« proc««M ntot by mauu of which 
I knt laay b« tnuiaferred from ooe body to another, b^ radiatioD, by con- 
: Metion and by conduotion. All of these factors enter into the computation 
rf the heat loaeea from a fnmaee, bat frequently the loee by convection and 
Tulimtion may be made email or neKlimUe in comparison with the loee by eoo- 
iattkm. The quantity of heat wHieh flows through a plate ot area A and 
thiekneea e in m time t la ezpresaed, 

0-*(»i-»«).ilJ/« (87) 

^ when •■ and 0t ar« the temi>eratures upon each side of the plate (a plate 
Ihenietir ally infinite in extent) audi is known as the thermal oonduotlnty. 
kis defbwd by the quantity of heat which flows per unit time throush unit 
■lea ef a plate of unit tbioknees, harinc unit difference of temperature 
betwsen its faces. Numerically k is usually expressed as the quantity of 
ksat in small calories which is transmitted per second throush a pUte 1 cm. 
tUck, per square centimeter of its surface, when the difference in temperature 
between the two faces is 1 deg. cent. Q then refers to g-cal., I to dec. 
ctatigiade, A to sauare centimeters and ( to seconds, k fa found to vary with 
the temperature of the plate and is ezpreseed approximately by the equation 
k,-k,(l+aO (68) 

where I is tha temperature centigrade and a a constant. As an example be 
it lequinMl to find the quantity of heat lost iwr hour by conduotion through a 
Mction 100 cm. bylOO em. of a fire4>rick furnace wall 20 em. thick, the con- 
itcimtT being 0.00028 eal./(cm..eeo.-degree) and constant with temperature, 
the ianae temperature of the fumaoe bung 1,600 deg. cent, and the outside 
no dsg. cent. 

Q-0.OOQ28 ^^p 100X100X3.800 = 606,000 g.-cat 

BDUOOBAFBT 

m. Balactad list of referenoei to literature on thermometry, py- 
i leiaetry and heat conductivity. 

I ' Thtfmometry." Circular No. 8; Bur. Standards, Washington, D. C. 
Pyrametiy. Measurement of High Temperatures." Burgess and Le- 
CteMier, 3d Edition, 1912, John Wiley & Sons, N. Y. 

"Charaeteristiea of Radiation Pyrometers." Burgess and Foote. Bur. 
Staadards Scientific Paper (in preee). 
"Heat Cosidnctivity.'' Ingeraoll and Zobel, Oinn Co., 1013. 

FUEL AND GAS AITALTSIS 

BT r. MALOOLH rARKSB, M.B. 

MS. Tha pmpoM of tbii Motion is to indicate very briefly the more 
important featurea in connection with fuel and gas analysis. For further 
iwormation. the reader is referred to the numerous publications on fuel and 
•■ analyaia. See Par. MS. 

H*. Coal for ■teaminc or produeer purpose* is uinally inhieeted 
aaly to a iirosimate or sncmearinc analyds, which includes the d»- 
tennination of the heating value and the percentagee by weight of moisture, 
fiasd carbon, volatile matter, sulphur and ash. When a complete or 
sltunate analysis is made, the components of the volatile matter are also 
detemdned. 

M>. Tb* details of BMillpalation in eoal analyses have a marked 
tflcct on the result and since many of the determinations are made in a man- 
ner more or less arbitrary, care should be taken to conform to standard 
netice. The American Chemical Society and the American Society for 
Testing Materials are jointly preparing standard specifications, and until 
r are completed their interim reports are the basis of the most generally 
1 practice in this country. * 

* The latest report is given in Tkt Journal of Indutrial and gnginterittt 
Cbmatrv, Jane, 1813, p. 617. The proposed speeificationa are given in 
r detail. 



307 



i.jv^iuuyic 



Sec. 3-386 



MEASURING APPARATUS 



SBft. The MinpUng of eoftl U of the utmost importance. The gr^a.teat 
care is neccBsary la order to obtain a sample which is truly repreaentatiTS 
of all of tho coal in the lot which the sample ia to represent. Id gener&l, & 
largo sample of 100 to 200 lb. should be made up of small quantities taken 
from various parts of the entire lot. This ia gradually reduced to m 2^b. 
sample about pea mie, by oruahing. mixing and quartering. * 

8ST. Heating Talutti of fuels are determined with c*lorlmet«r», or 

instruments in which the heat evolved by the combustion of a sample of thm 
fuel is absorbed by water, tho weight and rise in temperature of which are 
observed. There are two general classes, the non-continuous olaaa in 
which only a small quantity of the fuel (solid or liquid) Ib burned at one time, 
and the continuous class where the fuel (liquid or gaseous) flows continu- 
ously through the calorimeter. 

S88. The Bertheiot or bomb tjp9 cslorlmeter of the nos-eoatli&iiotig 
class is most generally used for hiKh-grado commercial work. Vl«. 133 
shows the arrangement of parts in an Atwater- Mahler calorimeter, whibb 
is similar to the Mahler, Emenson, Hempel and other well-known bomb 



oalorlmeters. Th9 "bomb" is the strong steel vessel, 
fitting screw-top and lined with 
platinum, gold, nickel, enamel 
or other non-corrosive material. 
A valve is provided at tho top 
for supplying ^ oxygen. The 
sample la placed in the crucible, 
C, and ignited by the very fine 
iron wire, /, which is heated to 
incandescence by an electric 
current through W and W. The 
bomb is placed in the calorim- 
eter vessel proper, Q, which is 
filled with water. Heat insula- 
tion is provided by placing the 
calorimeter in two other vessels, 
T and V, separated by air spaces. 
The water is agitated by the 
stirrer, S, and its temperature 
measured with a thermometer, t. 
The procedure In operation 
is hneny as follows: About 1 g. 
of coal is carefully weighed in 
the crucible, which ia placed in 
the bomb with the fine iron 
wire carefully arranged in con- 
tact with tho coal. After the 
top ia screwed on the bomb is 
filled with oxyKen at a pressure 
of 300 lb. to 4d0 Ib. per sq. in., 
and placed in the calorimeter 
tank, which contains a known 
weight of water After the ini- 
tial " radiation " rate is obtained, 
the specimen is ignited and the 
riso in temperature of the water 
observed. When the rate of 



B, with closely 




^ A X..J-L .-:.XX :■■---: v x.\^.x 



Fxo. 133. — Atwater-Mahler fuel 
calorimeter. 



change of temperature becomes constant, the final "radiation" rats is 
obtained. The heating value per pound is calculated from the weight of the 
specimen, the weight of the water and tho rise in temperature. Correction 
is mado for the heat capacity of the calorimeter (" water equivalent"), the 
"radiation" during the combustion interval, the heat from the electrie 
energy used in heating the wire and the heat of combustion of the latter. 
The temperature range is only a few degrees centigrade and is usually 

* Excellent detailed instructions are given in Bulletin No. 339, U. S. 
Geological Survey, and in later bulletins of the Bureau of Mines on eoal 
sampling. Also see books and technical articles on coal specificationa. 



DKjillir-.,|hy\^iL>0^ie 



MBASURINO APPARATUS 



Sec. S-389 



■euurad with differential mercury thermometers, read to O.OOl deg. with 
tbe lid of a'microacope. 

nt. TIm MMntikl detallj of procedure for » nroilinkta analriii 
inufoUowv: (1) Tlie whole aample is placed in a shallow pan and air-dried 
ia > special oren at 10 deg. or 15 deg. eent. above room temperature uotil 
tie weight is pntetioally constant (from 2 to 4 hr.) The loss in weight is the 
nuliM mouturo or " air-dry" lou. The sample is then ground in a 
aoffee mill until it will pass through a 20-mesh sieve;* it is next quartered 
and then about 100 g. are ground in a moHar or ball tmll to 80 or 100 mesh. 

(2) Total molatara is obtained by heating 1 g. of the final sample in an 
siMn porcelain or platinum crucible in an oven at 104 to 107 deg. cent., and 
sotiag the loss in weight. 

(3) Volatile znattar is obtained by heating 1 g. in a special, covered 
plttianm crucible at a bright red heat in a Bunsen flame for 7 min. The 
tetsl loss in weight is equal to the volatile matter plus the moisture. 

W Ash is determined by burning 1 g. of the sample in an open crucible 
astil the w^ht ia constant (1 to 2 hr.). The highest temperature of the 
Baosen flame is utilised. Sometimee a small stream of oxygen at low pre»- 
■nisinieeted into tbe orueible to hasten combustion. 

(S) Ilzod oarbon is determined by calculation, that is, fixed carbon <• 
100— (moiatiire + Tolatile matter + ash), all expressed in i>er cent. 

(0 Sii^>har ia determioed as follows: 1 g. of the coal is mixed with suit- 
uwdiemieaJs (such as magnesium oxide and sodium carbonate) and burned. 
The raadoe is exteacted with water, filtered, and the sulphur precipitated 
frrai the solution with barium chloride, coming down as barium sulphate. 
■Wn the weight of Uiie precipitate, the percentage of sulphur in the original 
Msiile is calculated. 

•. Th« Jnnkor calorimeter is the best known example of the con- 
JOn elML It ia mod extensively for gaa fuels and can also be used for 
ftiui fuels. Fig. 134 ahows the calorimeter set up for gas testing. The 




Wator 



W////////////r//////////W///M//////////M///M/M///////////////^^^^ 



Flo. 134.^^unker gaa calorimeter. 

|U Ion throngh tlie meter li and a pressure regulator A to a special Bunsen 
Bvner inside of the calorimeter C The combustion chamber is surrounded 
sr • chamber throusli which water flows at a constant rate. The heating 
™<K ia B.t.n. per cubic foot of gas is calculated from the rate of gas con- 
■" — ' , rate of flow of the water and the difference between the average 



*» dsw ipseeo per linear ineh. 
M 20» 



DigilizedbyLiOOQlc 



Sec. 3-391 



MEASURTIfa APPARATUS 



..i^i 



inlet and average outlet water temperatureB. For liquid fuels, a weichini; 
device and a special burner are provided. 

S91. Other typei of CAlorimeteri of the dlMontlnuoui elftss differ 
eBsentially from tne Berthelot only in the method of supplying the ozysen. 
la calorimeters of the Carpenter and the Favre and Silberman type, oxycen 
gas is supplied at atmospheric pressure. In instruments of the Farr class, 
the oxygen is supplied by chemicals with which the sample is mixed. 

S9S. Fuel oili are, in addition to the foregoing, Par. S90, frequently 
tested for flaih-pbint, or temperature where the vapor given off will ig- 
nite but will not continue to burn; flre-point, or temperature wlters 
combustion will continue if the vapors are ignited; TilCOtlty; ChiU-potn^, 
or congealing temperature; per cent, of aaphaltum. 

595. Report! of proximate analjiei and heating value (in B.i.u. per 

pound) usually give the results calculated on at least two bases, "as reoei'ved" 
and "dry." The former are of most interest to the users of the fuel, but. the 
results must be reduced to the latter basis when comparisons are to be niAde. 
S94. fuel or illumlnatiu gatei are analysed for the following oon- 
ponenta in per cent, by Toluzne; carbon dioxide <COt)< carbon mon- 
oxide (CO), oxygen (Os), methane (CHO. ethylena (CsHi), hydrtk^en 
(Hs) and nitrogen (N). CO, COs, Os and CfHi are usually determined by 
passing a known volume of the gas through a series of reagents, one at a time, 
each of which will absorb one, and only one, of 
the coinponents. The diminution of the 
volume is noted after each absorption. Hi 
and CH* are obtained by combustion in a 
glass tube with a known volume of air, the 
products of combustion being measured by 
absorption as in the case of the other constit- 
uents, and the original volume calculated. N . 
is obtained by difference. 

S9f. Oriat apparatui. The various 
forms of apparatus which employ the ab- 
sorption method are based on the principle 
of the Orsat apparatus shown in Fig. 135. 
A given quantity of gas, usually 100 c.c, is 
drawn into the measuring tube. T, by means , 
of the water bottle, B, and carefully measured. 
The gas is then forced into the COt reagent 
bottle, d, drawn back into T and the decrease 
in volume noted. The process is repeated 
with each of the tubes, c, b and a, giving the 
percentages of Oa, CO, and Hs respectively. 
The usual reagents are caustic potash solu- 
tion for COi, aramonjactd cuprous chloride 
solution for CO and alkaline pyrogallic acid 
solution^ tor Ot. Ht being obtained by 
combustion. 

596. Flue gases are analysed for carbon dioxide (COi). carbon mon- 
oxide (CO), oxygen (Os), hydrogen (Hx) and nitrogen (N). in the manner 
indicated for fuel or illuminating gas. 

997. OOs recorders are instruments which automatically and continu- 
ously remove samples of flue gas and indicate with a pointer or record on s 
clock-driven chart the percentage of CC)i in each sample. Various principles 
are employed, among which are the variation in the refraction index with the 
percentage of COs, the variation in density compared with air as a standaxd. 
and the variation in the position of a float with the volume remaining after 
the COt has been removed ^^-ith caustic potash, the usual reagent. 

S98. Selected list of reference literature on fuel and gas analysts. 

Lcwxs, V. B. — "Liquid and Gaseous Fuels." D. Van Nostrand Co., New 
York. 

Gill, A. H. — "Gas and Fuel Analysis for En^neers.** John Wiley A Sona. 
New York. 

Kejishaw, J. B. C— "The Calorific Value of Fuels." D. Van Noetrand Co., 
New York. 




Fio. 135. — Orsat apparatus. 



210 



yGoogle 



UBASURtHa APPARATUS 



Sec. 3-309 



SoMBamiBB. B. E. — "Coal, lu Composition, Analynii. Utiliiation and 
Valuation." McGraw-Hill Book Co. Inc., New York. 

MoTKS, J. A. — "Purchaainx Coal by Specification." Jour. Engineering 
Soocty of Pennsylvania, Aug., 1613. 

fvH Technolo^ Publications, U. S. Bureau of Mines (Formerly U. S. 
Grolocical Surrey). 

Bulletin No. 12. Apparatus and Methods for the Sampling and 
Analysis of Furnace Gases, 1911. 

Bulletin No. 23. Steaming Tests of Coal, 1912. 

Bulletin No. 63. Sampling Coal Deliveries and Types of Government 
Spedficationa, 1913. 

Technical Paper 3. Specifications for Fuel Oil for the Government, 1911. 

Technical Paper 8. Methods of Analysing Coal and Coke, 1912. 

Technical Paper 26. Methods of Determining Sulphur in Fuels, 
Especially Petroleum Products, 1912. 

Technical Paper 49. Flash-point of Oils, Methods and Apparatus, 1913. 
BaOetiiis. University of Illinois Experiment Station; 

No. 15. How to Bum Illinois Coal without Smoke, 1908. 

No. 31. Fuel TesU with House Heating Boilers, 1909. 

No. 37. Unit Coal and Composition of Coal Ash, 1909. 

No. 38. Weathering of Coal, 1909. 

No. 46. Spontaneous Combustion of Coal, 1911. 



WATER, GAS, AIR AND STEAM METERS 
BT asanrAiJ) j. s. piaoTT 

WARB MBTEBS 
C lMafflc a tf on, Water meters are of three classes: weighing, volu- 
: and velocity. 

4M. Water iralch«n are not affected by variations in temperature and 
•uov, approximately, 2 per cent, error. AU weighers must be fed with 
agravityflow. The various methods employed by concerns manufacturing 
vaier weighera are described in Par. 401 to 404. 

401. Worthlnfton weigher. In this device two counterweights are 
iBOonted on trunnions, water flowing into one tank while the other empties. 
As the water risee the centre of gravity of the tank and water is shifted, finally 




^a 



Fio. 138. — Wortbington recording liquid weigher. 

nacUag a point where the tank upsets and empties. This movement auto- 
i^ieal^ throws the water deflector over to fill the other tank. See Fig. 136. 
TMs deriee will, ol course, weigh only in units corresponding to the weight 
oatained in one tankful; the number of trips of the tanks being auto- 



211 



uyCoogle 



Sec. 8-402 



MBASVRINO APPARATUS 



) 



matically taken by a counter and multiplied by the tank unit weight. The 
accuracy approximates 2 per cent. See Par. 400. 

40t. The Richardson weigher, Fi^. 137, uses a single weighing taxUi 
mounted on knife-edged scale beams directly counterbalanced. The over- 
balancing of the weighing tank trips the feed valve from the upper reservoii 
and opens the discharge. By a system 
utilising two toggles and dead-centres, 
the upper valve does not open till the 
outlet valve is again entirely closed. 
See Par. 400. 

40S. Th« Wilcox weigher operates 
as a single tank with a syphon outlet. 
The bell float and standpipe (which ia 
open top and bottom), arc down nor- 
mally, so that the standpipe seals the 
opening in the diaphragm between up- 
per and lower tanks. Water accumu- 
lates in the upper section until it 
overflows the top of the standpipe and 
runs down into the lower compartment, 
trapping nir in the bell and inner legs of 
the two siphons, and raising the Dell. 
As the water rises, the trappeaair is com- 
pressed until finally it breaks through the 
trip seal and starts the main siphon. 
The release of air pressure allows the 
bell and standpipe to drop, and the cycle 
begins again. See Par. 400. 

404. Volumetric metere include 
measuring- tank meters (other than 
weighers), piston meters and disc meters. 
Vanations in temperature affect all 
these types, bo that they must be cali- 
brated for the average temperature on 
which they are to be used. Accuracy 
of piston and disc meters should be 
marred by only 1.0 to 1.5 per cent, aver- 
age error, provided they are properly used 
and not worn. Wear of piston meters 
or disc meters, causing leakage, may in- 
crease the percentage of average error 
to 5 or 10 per cent. The various types 
of volumetric meters are described in Par. 406 to 408. 

40f . Space occupied bj Bichardson weigher. 

8IS5B8 AND DIMENSIONS (IN.) 




Fig. 137. — Richardson weigher. 



"o 

1 


.0 


•3 


A 


B 


C 


D 


H 


J 


K 


L 


M 


N 





P 


Q 


R 


S 


T 


■<sl 


J 


200 


25 


25 


38.5 


22 


35 


2115 


19 


33 


187.25 


^1 


151.5 19 


20 
30 


13 
20 


1.065 


M 


500 


711 


36.5 54 


30.5 


36.5 


2823 


23 


43.6 


28J10 


32 


232.2523 


2,800 


P 


1000 


140 


55.25 75 


60 


54 


3835 


35 


36.5 


4110 


48 


354 35 


42 


30 


•.400 


R 


1500 


210 


55.25 76 


60 


54 


3835 


35 


36.5 


41,10 


48 


3514 35 


42 


30 


6.goo 


S 


2600|350 


«9 96 


76.2569 


48|48 


48 24 


5615 


61 


344 


M 


48 


37 


10,400 


T 


3000420 


SB B6 


7t.25'6» 


4848 


48 24 


56'l5 


61 


4 


34 


48 


37 


11,000 



212 



vGoogk 



UEASURINO APPARATUS 



Sec. 8-408 




Fie. 138. — Hammond water meter. 

313 Dglzed by Google 



Sec. 3-406 



MSASURINO APPARATUS 



406. The Hammond meaaurinc-tank m«t«r, Fig. 138, consista of two 
tanks, Bi and Ba. into one of which the inflowing water la directed by the 
baffle G, while the other is emptying through the valve />i. When the if ater 
level in Bi rises high enough to lift float ii, latch Hi releases, the weight of 
water on valve Di throws the wrist plate over, opening Di and closing LH, and 
changing the deflector to fill Bi. The action is very rapid at the release 
period, preventing Iom of water during the change period. A gage, A^, ia 
includea for accurately setting the meter. This device, as witn all the 
volumetric meters, is afTected by change of temperature. For variatioos of 
approximately 50 cleg. fahr. (28 cie^. cent.) the error is not great, the average 
being 2 per cent, to 3 per cent. It is operated on gravity flow. 

407. Disc meteri of the general type in Fig. 139, operate by the gyration 
of a disc in a spherical chamber. The stem attached to the disc describea a 
circular path and operates the counter. These meters arc used on cloved 
lines under pressure. 




Fig, 139. — Worthington disc meter. 



DUc meters ti. pUton meters. Disc meters are used chiefly for small 
lines, up to about 3 in. diameter. Piston meters for siies from 2 in. to 8 in. 
For larger flows, tank, Ventuii or turbine meters are generally employed. 

40S. Piston meters of the general type shown in Fig. 140, operate like a 
duplex steam pump, the movement of the pistons measuring 00" definite 
volumes of water per stroke. The strokes are recorded by the counters 
usually in units of cubic feet. These meters are used on closed lines under 
pressure, and necessitate, for their operation, a pressure diop of from 2 to 
6 lb. per sq. in., depending on the flow. 

409. The Venturl meter is widely used, both for large and small flow, on 
pumping sexvioe and boiler feed. It occupies practically no space outside of 



214 



DKjihic-.ihy^^iUUyHJ 



UBASURiya APPAkATVS 



Sec. 3-409 




S 

V 

a 

a 
o 

J 

a 



a 



31& 



V Google 



Sec. 3-410 



MEASURTKO APPARATUS 



the pipe line; has no moving patts in the meter proper, and operates o 
closed pi essure lines. The accuracy is from 1.0 to l.o per cent, if used o 
reasonably steady fiow. If used on lapidly fluctuating flow it becomes ver 
inaccurate. If kept clean, the accuracy is substantially constant during tb 
life of the meter. 

A iGsht pressure drop, 0.25 to 3 lb., occurs through the meter, dependinc I 
siie on the flow. For theory of the Venturi tube, see Sec. 10. 

410. Th* Pitot meter is not satisfactory for general aerrioe, as the he* 
differences are much less than those developed in the Venturi, consequent! 
the registering apparatus is much more delicate and sensitive to leakage in tb 
pressure lines leading from the main to the recording instrument.^ It is als 
very sensitive to edaies in the pipe lines in which the Pitot tube is inserte< 
For the theory of the Pitot tube, see Sec. 10. 

411. The turbin* mater, Fig. 141, is used to some extent for Isise-ai 
lines and large flow. It operates like a hydraulic turbine, and ae the met« 




SECTION THROUGH VERTICAL CENTRE UNE 
Fio. 141. — Worthington turbine meter. 

opposes practically no friction or pressure loss to flow, the speed of the met) 
is substantially proportional to the flow. It is called a "velocity meter," bi 
strictly speaking, this meter is volumetric; it is affected in accuracy by ten 
perature changes. The accuracy is practically the same aa the weighers ai 
tank meters (Far. 400). 

411. Weiri, usually of the V-notch type, are in considerable use, in ooi 
nection with indicating and recording mechanisms for water measuremen 
(See Sec. 10.) In the Ma type, a float in a chamber above the weir, operat 
a grooved drum in such a fashion that the recording and integrating appar 
tus move over equal increments of space for equal increments of flow. 

In the Hoppei type, a conoidal float is suspended by a coil spring, and ia i 
shaped that the descent of the float by the weight of water forced over by tl 
rise of the weir, is proportioned to the flow. Very good accuracy is claim* 
for these weir meters, from 0.5 to 1<3 per cent, over all ranges of flo' 
Temperature changes are approximately compensated for in both types, I 
the behavior of the float and the conoidal chamber reepeotively. 



216 



Di,jiliLf.lhyV^il.)UVIC 



UBASURINO APPARATUS See. 3-413 

OAB MXTIM AMD AIK MITUM 

4U. Tha matan •Tailabla for (u and air meaauramant ara: (s) 
bcDowa-trpe, for low praasure chiefly; (b). Thomu electrio, for high or low 
pnarare: (c) Ventori-tube and Fitot tube and types for high or Tow pt«s- 
snraa; (d) wet tyjies for low preasure; (e) rotaries. 

414. Tlia ballowi typa "dry' ' matar has usually a pair of leather bellows 
oparating two diaphragms, after the manner of a piston in a reciprocating 
envne. The valve operation is exactly like that of a two-cylinder double 
acting engine with quartering cranks. The movement of the diaphragms 
neaaurea off volumes of gas. The pressure and the temperature must be 
kept reasonably constant, as the accuracy of the meter is affected by both. 
The etror may range from 3 percent, "alow" to 2 percent, "fast." 

4U. Tito wat nMtar is now used chie6y for large gaa-works service, and 
ila operation is somewhat like that of a rotary en^e. The average error 
is nsnally from 3 per cent, slow to 2 per cent. fast. The obtainable accuracy 
with large wet meters is within 0.1 per cent. 

4M. The Tbomas elaetric gsi mater consists of an electrio resistance 
heater coil in the gas main, a wattmeter and two screen-resistance thermom- 
eters. An amount of current is passed through the heater such that the 
tfiflerenee of temperature of the gas before and after passing the heater is a 
definite amount as measured by the screen thermometers, which automatic- 
ally average the temperature. 

The relation between tite temperature, watts input and flow is then 

W - ""'^^ (lb. gas per min.) (59) 

vliere t » tempera tore difference, inlet and outlet, deg. fahr.; • m epecifio 
heat at eooatant pressure of air or gas measured; B * watts input. The 
Tbomas meter is used as a substitute for the huge wet meters formerl>r em- 
pioyed at gas houses for the main-flow measurement. Its accuracy is higher 
thdJt ^at of any other device now in use for air or gas flow, the error being 
litHB ±0.05 to ±0.2 per cent. In email siies it is too expensive to compete 
with other types of meter, but in large sises it is much less expensive in pro- 
porticHi, and luss the additional advantages of indicating and recording as well 
as integrating. In commercial service it is generally equipped with an auto- 
natie regulator arranged to keep a constant temperature difference between 
iaiet and outlet; the electric instnimenta can then be graduated directly in 
pounds or cubic feet, as the flow is directly proportional to the watts input. 

417. Tantari iiMt«ra are in some use for large gas-flow measuremente: 
the device is accurate, but the formula for its use is complicated and no satis- 
betory direct-reading indicating or recording device has yet been introduced. 

The formula for air and gas service is 



IT-Cilt 




Ob. gas or air per sec.) (60) 
Where il»npatream area, sq. ft,; Ai — throat area, sq. ft.; P — tt|>- 
icream p l ea su re, lb. per sq. ft.; Pi ..throat pressure, lb. per sq. ft.; -r — ratio 
wp. beat at constant pressure to sp. heat at constant volume; — 1.4()8 for air, 
— I.2Mfor natural gas; ii — density, lb. per cu. ft. at upstream section; 
^•0.98. coeiBcient oifiow; g -grsvitation constant, 32.2. 

For differences of pressure less than 20 in. of water, the hydraulic formula 
■ay be employed without error in excess of 1 per cent. 

fl-l&3 -^ 1— T^/ (cu. f t. per aec.) (61) 



Vl-^D 



217 



yGoOglq 



Sec.S-418 USASVRINO AfFABJ-TUS 

when Q— on. ft. per wo. (, — W/ti); k— differanoe of preMuie, upstream •nd 
thnwt in in. of water [-(Pi->i)(12/02.36)l. 
418. Th* Pltot-tub« {annul* for cm and air 

Q - 218.44£<2>^^'\/^(au. ft. gas or air per bt.HOZ) 

where g— flow faetor of tlie tube exp r ewed as a deoimal; «f»int«nial diam. of 
tube (in.); Ta-abeoiutefahr. temperature of measurement base; P— abso- 
lute pressure of measurement base, lb. per aq. in. ; O > sp, grav. of (u referred 
to air; if air is measured, O— 1; i>— absolute static preasure of flowing gaa in 
meter, lb. per eq. in.; T— absolute temperatura fahr. of flowing ns; A — 
velocity head of flowing gas (in. of water) ; Q - cu. ft. of gas per hr. at r and P. 

The Talue of S is 0.8630 for smooth tubes, 2-in. to 6-in. diameter, with the 
Fitot tube placed exactly in the centre of the pipe. The velocity is a mnzi- 
mum at the centre of a idpe, decreasing to • minimum at the i»i)e surfsice. 
This accounts for the fact that B is less than unity when the Fitot tube Is at 
the centre of the pipe. The ooe£Scient of flow for the Ventuii meter approxi- 
mstea from 0.97 to 0.98 for proiMtly designed meters. 

41t. BotazT meters of several makes are on the market; one (ra» is 
■l>ows in Fig. 142, intended for comprsssed-air service. Air enters th» «haiB> 




Fio. 142. — Krentsberg air meter. 

ber at C and impels the Sap pistons D and E toward ths outlet ride. As the 
pistonsA JC, and£, are cloaed on the return aide, the preesure area is grsstest 
on the under side, causing the meter to turn. 

STKAM UTIBS 

<M. Steam meters. Most of the steam-flow meters such as the St. John 
Sargent, Uallwachs, Oehre, Eckhardt and General Electric, can be used oa 
eomnressed-alr service if desired. See Par. 419. Steam meters are di- 
vided into area meters (Par. 421 and 4X2) and velocity meters (Par. 4SS and 
424). Preesure and quality variation affect the accuracy of all area and vel- 
odty meters, so that the meters are only correct for the calibration oonditioiM 
of pressure sad quality, unices fitted with compensating devices. 

421. '|Ar«a" iteain msters. In this class are those in which a diao or 
cup partially doeee an opening through which steam is psselng. The shape 
of the passage or of the cup is so arranged that as it rises from sero position. 
the free area for passage of steam is increased. As demand for steam is in- 
creased, the increase of pressure drop past the disc or cup, causes it to move 
further up the passage, enlarpng the area till the pressure drop is reduced 
and the mac amin in equilibrium. The movement of the disc Is communi- 
eated to an indicator and chart graduated in lb. per hr. flow. The paaaage is 
so designed that the movement of the (Use or cup is directly proportional 
to the flow, giving an equal increment reading. 

422. The Sargent mater is an example of the area type. It has a conical 
cup seating over a conical scat. As the stream flow la Increased, the cup 
rises, expostni; more area for Sow between cup and tef.%. As the weight a< the 
eup and stem is the only load, the pressure diSerenoe is constant. A pressure 
compensator in ilk» f9n>> 9( • Bourdon tube «an7in( tb« imUwtias iwidle. it 

>W DigiliavlbjV^iUUyiC 



MEASURING APPARATUS 



Sec. S-423 



utached to the bottom of the stem, and the coznbiued rise and tranalation of 
tbe needle, due to the Bourdon tube and the cup, is read off on a eeriee of 
■cigfat-fiow curves placed behind the needle. The accuracy will be about 
2 per eeat. if very well adjusted. The pressure compensation is likely 
tofedaoe the total error, which will average between ±2 and ±3 per cent, in 
ttdiiiary service. 

Its. PTMSure indicfttinff derlcas for lue with Telocity iteun nutcrs. 
All the Telocity meters, Venturi, Fitot and orifioe types, require some form 
of Knsitive differential gage which will accurately measure a small differ- 
«ee between two high initi&l pressures. 

Thenmc^t indicating apparatus consists of a glass water — or mercury — 
L tabe. To this claas belong the Gebhardt, Genre and General Electric 

Oi. Th« Gebhardt >teun meter, Fie. 143 is given as an example of the 
fofe-flav type of velocity meter and reads directly by a water column on a 
durt graduated in lb. per 
oifi- or per hr., and for a 
mnplete range of pressures. 
To read the meter correctly, 
ii u necessary to know the 
PfMBurea and qualitv. By 
Beu» of a small condensing 
cumber this meter is made 
■atable for uae with super- 
Kated steam. Accuracy of 
^Gebhardt met«r (also the 
G. £. type TSs and Gehre) is 
tl per cent, on careful hand- 
bor. but more usually ±1.5 
to 2 per cent, in ordinary ser- 
^ without constant pree- 
Mire and quality check. 

The Thoma« electric 
be used for 



BMuminf steam very ac- 
cvUely, but it cannot be 
toounercially employed as 
Uie amount of current re- 
<|und becomes excessive ^on 
•"count of the high specific 
fettof steam) and especially 
lor wet steam where mois- 
tsre must be evaporated. 

tti- Bteam-meter coits. 
At the present time there 
ve arailable at least two in- 
woting meters, one suitable 
|w Roeral toting, and one 
'or the boiler or engine room 
« permanent instruments. 
Of the recording instruments, 
ftjle one or two are fairly 
■■Olfactory in oi>eration, the 




Fio. 143. — Gebhardt steam meter. 



price of all is much too high for general adoption. There is notlung about 
tW instruments which should prevent their manufacture and sale in the 
nine oanner and at about the same price as high-grade recording gages. 

PRECISION Of MEAST7REHENTS 

BT WILLIAK J. DRI8KO 

tM. Clutiflestion of nukturementa. For convenience of treatment 
la nauurementa are claaaified aa either direct or indirect. A direct 
'^Miiirement conaiste in determininf the nunurle which ezpreflsea the 
■acnitude of the quantity in terma of aome arbitrary unit. Tbua lengtha 
^^cnnined by means of a graduated acale, time by a clock, volume of a liquid 
°T*(raduated flaak, etc., are illuatrationa. 

"•anminanta ar« indirect when the numeric ia obtained by aome 
*^iitatu>Q "^flr^t^g uae of aome functional relation ezpreaaed by a formula, 

219 J a 



Sec. 8-427 MEASURING APPARATUS 

9,g.i the density of a sphere expressed by the reUtion d>»3£/{^TD*), where 
M is the masa obtoiiwd by means of an equal-arm balance and D the diam- 
eter measured by a micrometer cali[>er; or the horse-power of an engine, 
h.p. *p.l.a.n./33,000, where p is the racan-effeotive pressure found by inea»- 
urement, I the length of stroke, a the area of the piston found by measuring 
its diameter and n the number of strokes per minute found by countins 
them. Iq general these expressions take the form, 

X^Fia,b,e ... A, B, C . . . ) 
where ab, e . . . represent measured quantities, while A, B, C . . . rep- 
resent conatantfl (like 33,000 and r in the above formuln) and F repre- 
sent that there is some functional relation between measurements, eonstanta 
and the indirectly measured quantity X. 

AST. Etsit m«Mur«m«nt hai * deflnlta prsoislon. Thus the length 
of a building might be reliable to the nearest quarter inch, the current in a 
certain circuit to the nearest tenth of an ampere, or the time of vibration of 
a pendulum to the nearest hundredth of a second. To determine this 
reliability it is necessary to make a very careful study of all the instruments 
used, the care with which they are made, graduated, calibrated, adjusted 
for change of temperature or of position, etc., etc. It furthermore is nec^ea- 
fiary to know not only the skill of the observer, but also whether any constant 
errors may be due to his "personal equation." If for instance one desires 
to calibrate a voltmeter at 110 volts by means of a standard Weston cell, 
the following points must be considered: How closely must the electro- 
motive force at standard temperature be determined? How closely must the 
temperature coefficient be determined? If the temperature of the cell when 
usea is determined by means of a mercury thermometer, how closely must 
the thermometer be calibrated and read? How closely must the resistance 
of the voltmeter be known and is it necessary to take any precautions re- 
garding its temperature; and lastly, what must be the precision of the variable 
resistance used for the balance? After an examination of all these probable 
sources of error the final question is, What is the most probable value of the 
combined effect of all these separate deviations or errors? (See Par. 1-6.) 

458. The ff«n«ral problam. Given the functional relation, 

jr-F(a. 6. c . . .) (63) 

the problem in general is as follows: First case if a, b, e . . . can be 
measured each with a definite degree of precision, what is the best repre- 
sentative value of the resultant precision in JC?^ Second case: if it is de- 
sired to determine X to a certEun definite precision, how precisely must 
each of the components be measured so that the combined effect of all the 
deviations may not produce a resultant deviation in X greater than the 
assigned limit? 

Unless it is possible to assign some numerical esUmate to the precision 
attained in determining any measured quantity, X, the result is of little 
practical value. Hours of valuable time are often wasted in determining 
some unimportant component of an indirect measurement with excessive 
precision, while at the other extreme we often find final results absolutely 
worthless as the result of failure to measure some imi>ortant component 
with the necessary precision. 

459. Detormination of precliion in final raault with known pre- 
diion In the msaiured components. Referring to Eq. 63, let So, Si, St 
... be the numerical deviations or precision measures of the direct measure- 
ments a, b, c . , . i Aa, Ab, Ae be the deviations in X due to the 
deviations in the separate components, and A the combined effect of 
the separate effects Aa. Aft, A« . . . . Then A/X is the fractional deviation or 
precision measure of X and 8a/a, tb/b, Sa/c * • . are the fractional de- 
viations of the components a, b, e . . . and 100 times the fractional 
deviation is the percentage deviation. We first find the separate effect 
of each of these deviations d«, th, 3« ... on X and then find the 
combined effect of these separate effects. The change in X due to a alight 

■ change in a (b, e . . . remaining constant) is found oy diff^eniiating the 
function with respect to a, i.e., 

aV" 

A.-^«« (64) 

and a similar slight change in any component k would give 

Digilizedbyi^OOgle 

220 



UBASUBINO AFPARATU8 See.S--430 

It can be ahown that the moat probable ralue of the reaultant effect, A, of 
the aBpazate eflecta, A«, At, A< ; . . ia 

A-Va.'+A4»+4,«+ . . . (66) 

Xcmmple. The value of the acceleration due to gravity is to be deter- 
mined by mrana of a pendulum wfaoee length and time of vibration are to be 
mcaaured and used in the formula «t'//<*. Here X ia g, a is I, h ia t and 
via a Eonatant. Measurements gave i=' 101.42 cm., reliable to 0.05 cm. and 
— I.0QB4 sec., reliable to 0.0008 gee. How i>reciae is the value of g when 
conpated from this data? Differentiating with respect to I, we have, Aii- 
fII/P — 0.0/ 1 .OX 0.05 - 0.50 cm. per see. per sec. Differentiating with respect 
to « we get. A»--T>/X2X«i/««-9.9X100X2X0.0008/1.0-1.6 cm. per 
see. per see. This means that a deviation of 0.05 cm. in the length of 
ttie pendulum ^affects g by only 0.5 cm. per sec. per sec. while a deviation 
ef O.0OOS aee. in the value of ( affects the value of g b y 1.6 cm . pe r sec, p er 
see. The combined or resultant effect would be A ■> VAi' + Ai» - v'O.S>+ l.S 
• 1.7 em. per see. per sec. and we might write the final result as — 981.S 
± 1.7 cm. per see. per see. which means that the value of g, as determined, 
■I probably reliable to the nearest 1.7 em. per sec. per sec. It should be 
BMsd UB UM above computation for Ai, Ai and A that not more than two 
igona ai« naed in any of the quantities, i.e., v'-9.9, (-1.0, f-100, etc., 
the laaaoii being that deviation measures always represent doubtful places. 
Hcaee, ainee more than two doubtful places would be useless, (Acre U no 
Mad of ewtr lutpint mart Hum tvo figure* in taeh quantity enterinn into a com- 
jadrntiotk of a diwiaticn measure. 

4M. Determination of naeanary pradalon in maamirad eomponanta 
to — eui e deatred preeUion in final reiult. The second or converse 
proble m ia as foUowa: JT is to lie measured to a certain degree of leliability 
npi— ed by A — some definite number. What are the allowable deviations 
*•.«••«*. . .in each of the measured components a,b,e. . . such 
that the eombined effeet. A, of their separate effects, Aa, At, A< . . . 
shaB not cseeed the preaeribed limit? From the law of errors (£q. 66) an 
iafinite munber of solutions is possible. The bett solution would be that 
oec which, with the least effort on the part of the investigator, would give 
the SBsigiMMl precision. The eaeietl solution and the one that has been found 
aatiifaetory. at least as a preliminaiy adjustment of deviations among the 
varioofl components, is to assume that each of the components may produce 
aa equal effect on the final result, t.e,, tolet Aa—A»~A(— , . .A.. From 
this and Eq. 68 it follows that 

A.-A4-A,- . . .A.--^ (67) 

Vn 

■here a rapreaenta the number of measured components. The allowable 

deviation in any component can then be determined from £)q. 65 and Eq. 67. 

""■"■■'•. It is desired to find tiie heat developed by an electric heater. 



within three parts in a thoosand (0.3 per cent.), by measuring the current 
osed, the voltage at the terminals and the time that the current u flowing. If 
thepraaaara ia about 110 volts, the current about 0.8 amp. and the time 



1 amp. 

10 min., how precisely must each oomponent be measured? The formula is 
B^I.BJ, when ff is in joules, or 0-0.8X110X600 joules- 52,800 joules. 
If 17 ia to be reliable to three parts per thousand, it must then be determined 
to the nearest 15^.4 joules, or keeping two figures only, to the nearest 160 
Joalea. fibwa then are three components, n - 3 and wo have 

Ar— Aw-Ai— — T=-— 7r--94ioules. Differentiating, we get, 
V» V3 

4,-»4-«rf/ .-. tj. jjg^-0.0014 amp. 
A,-*l-W« .-. ,j,-g^g^-0.19voIU 

*-•*-"* ■•••-aslTIo-"'"- 

TUi means that if we assume equal effects and wish to kaow the heat to the 
aasRst 160 joules, the current must be measured to the nearest 0.0014 amp., 
*ro roliaae to the nearart 0.19 volts and the time to the neareat 1.1 sec. It 



221 



i.jv^iueiyie 



Sec. 3-431 MEASURING APPARATUS 

would be very euy to reach thu precision in the time meMurement if a good 
itop watch were used; in fact this interval oould be determined to within 0^ 
sec. and therefore the time might be treated as a constant, in which ease n 
would be two instead of three and therefore it would not be necessary to 
measure / and B quite so accurately as indicated above. 

481. Two dasftei of formulaB in Indirect meMurementt. The two 
methoda ihown above for the direct (Par. 418) and the indirect (Par. 4>9) 
methods respectively are perfectly general; consequently by their use any 
problem may be solved provided all deviation or precision measures are ex- 

Sressed as actual numeric^ deviations and not as fractional or ^rcentage 
eviations. It is found in practice that nearly all formula used in indirect 
measurements fall in one or the other of two general groups. Those of the 
first class include all those functions which contain sums or differencee of 
terms, each of which may involve either measured components, or con- 
stants, or both. The general form would be 

X-Aa'±B6«±Cc''± . . . (6S) 

where At B,C . , . are constants and a, b, e . . . are measured quantitie* 
entering to the i'*, m'*, and »■* powers reepectivdy. Ezamplea of formula of 
this sort are the expressions for the electromotive force of a standard Clark 
cell, £-1.4340 [1-0.00078 ((°-15°)J, or the reelstanee of a etandard 10- 
ohm coil, A « loU +0.00388 (^-15°)]. 

Those of the second class include all those funotions which invcJve 
products, quotients or powers of the measured components and conatanta 
and do not involve either trigonometric or logarithmetio functiona. The 
general type would be 

y-Ao'-5-e- ... (69) 

where A, n» m, and k are constants (positive, negative, fractional orintMraS). 
An ezanqjle of formuUe of this \y^ is the expression for the modulus of elas- 
ticity for bending, given as £ — fFi*/4a b<i*, where W is the load at the 
centre, I is the length between supports, a is the deflection, b the breadth and 
d the depth of the beam; the formula given above for density (Par. 41$) 
is another example. 

4S1. Percentafe method of computing preolaloa. Problems of 
the second class (Par. 4S1) may be solveamuch more easilv by the fractional 
or percentage method than by the general method, as will appear frem the 



following. T^ing the general form of the function as 

JC-^.a-b-c* . . . (70) 

and differentiating with respect to each of the variables, and then dividing 
each of theee results by the general formula gives, 

Aa l&a Ah mib Ac if^e ._ . 

X a X X e 
This shows that a fractional deviation ta/a in a produces a fractional devii^ 
tion in X which is n times as great, or in per cent, it means that if a is un- 
reliable by 1 per cent., X will be unreliable n times 1 per cent, and it im 
to be noted that the remaining factors in the formula have no effect whatever 
upon tikis relation. This enables us to state at once the separate effect of 
any percentage deviation of a given component and by using the relation 

^ ^(i'r+'gr^"(5^ • • • • '•"> 

or its equivalent, 
A 
X 

we can therefore ezpreaa the final resultant effect as a percentage deviation. 
iU. The peroenten method 1* lUuitratad by the toUowlnc prob- 
lem. Meaaurementa lor the modulus of elaatieity uaing the above fornnils 
are a( follows. The weight is 10 kg., reliable to the nearest gram; the lencl^ 
is 1.000 mm., reliable to 0.6 mm. ; the deflection is 6.983 mm., reliable to 0.007 
mm; the breadth is 4.676 mm., reliable to 0.006 mm.; and the depth is 16.000 
mm., reliable to 0.008 mm. The problem is to determine the reliability of 
the QioduluB when calculated from the formula 5— W-P/A a.6.(f*. The fint 
step b to express all the deviations in per oent> Inspection shorn th»t W 

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UBASURINO APPARATUS SeC. S-434 

• reliable to 0.01 i>er cent, 1 to 0.05 per eent., a to 0.10 per cent., fc to 0.10 
)veent. and d to 0.05 per cent, and by £q. 71 we get 100 Au/£-0.01 per 
itat; 10O/U/S»0.15 par cent.; 100 Aa/£-0.1 per cent; 100 Ctb/B- 
1.10 per cent.; aad 100Ad/£-0.15per cent. Substituting theae values in 
■l h«r Eg. 78 or Eg. 73 we get tor th e percentage reliability of E: 100 A/£- 
V0.01'+0.15« + 0.10>+0.10«+0.1S»-0.28 per cent., i.e., tlie combined effect 
dr an tlie deristiona amounts to 0.25 per cent, in the value of the modulus. 
TVaa X* 23,420^ 56 kg. per equaze millimetor. 

iM. Tlia eonrorM problem in the percantaca method would be aa 
isBowB. It ia deaired to measure the modulus to 1 per cent. ; how precisely 
■■St each of the above 6ve components (Par. 488) be measured, and, aeo- 
aadly, ean any of them be measured with negligible precision? An inspection 
at tbs aboTe measurements, or a knowledge of measurements, would show 
•feat tlie wvisht might be measured so precisely as to be regarded as a oon- 
stsnt, and henoe n>-4; then we should have, assuming equal effects, At/B" 
A«'X-At/£-Aw/£- A/£\/4-l/100v/4- 1/200-0.5 per cent. Applying 
Ei|. 71 we find toe percentage deviations to be as follows: 100 iI/t—0.5/3** 
•LlTpar eent: 100 4V<>-0.5 per cent.; 100 <i/6-0.5per cent.; 100 Wf** 
flLVJ — 0.17 per cent. 

witti a little experience one can write the result of either the direct or the 
ai i a tgt s e problem, by the percentage method, from inspection* or at moet 
with a anull amount of calculation. It should be noted that the equal-effect 
■athod often girea only a first approziniation to the beat result, for it oCtea 
h tree that one or more components can be measured with negligible preci- 
doa if equal effects are assumed, in which case a second solution must be 
■ade treating each components as constants. 

Mi. Tazt-tRNiki or raf aranoa worki on itradalon of nuMuramenta. 

HouiAic, S. W. — "Predaion of Measurements." John Wiley ft Sons, 
Tcrk.1804. 

GooDwm, H. M. — "Preeiaion of Measurements and Graphical Methods." 
M«Graw-HilI BotA Co. loe.. New Todc 1918. 

PiuiBB, A. de F. — "The Theory of Measurements." McGraw-Hill Book 
Ca. lac. Natr York. 1912 

BaBraarr. D. P. — "The Method of Least Squares." Massachusetts Insti- 
W( of Tedmolocy, 1000. 

iimmaoMAM, M. — "Method of Least Squares." John Wiley & Sons, New 
lotk. 



338 

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SECTION 4 



I 



PROPERTIES OF MATERIALS 
BT FRANK F. FOWLS, S.B. 

Ctmtmltmt Sltctrical Sngineer, Member American InetiM* of Sleclrieal 
Enginetre 

COITTIITTB 

COHOUCTOK MATXBUL8 

Gencnl 1 Bronie 132 

Wire GagBS 10 Miscellaneous Metal* 138 

Ovper 81 Resistor Materials 148 

Ammiaum 79 Carbon and Graphite 153 

Copper-dad Steel 100 Skin Effect 160 

Irao and Steel 114 Bibliocraphy 167 

MAOHXTIC MATXBIALB 

Chsrififtion 168 Sheet Ga^ ^ 213 

Composition and Properties 172 Commercial Sheets 217 

Core Loans 206 Magnet Steel 225 

Bibliography, 232 

ZB8ULATIHO KATXBIAU 

dsasifieation 233 Rubber and Its Derivatives 330 

Disenasion of Properties 238 Varnishes and Compounds 346 

SaGd Natural Materials 254 Insulating Oils 358 

TttriSed Materials 273 Gases 366 

Rteoos Materials 281 Thermal Conductivities 369 

Maided Compositions 309 Bibliography 370 

STKUCTinUIi MATXBIALS 

Cnt Iron 371 Non-Ferrous Metals and Alloys 399 

Vroocht Iron 378 Concrete, Brick and Stone 400 

ttcel 383 Timber 410 

Steel Wire and Cable 895 Rope and Belting 428 

Bibliography, 431 

PBOPntTBS or THX BUUCXHTS, «3S 



226 

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SECTION 4 



CONDUCTOR MATERIALS 
OKNSBAL 

1. Conductor! and non-oonduetors. All materials poaseM, in somo 

degree, the property of electric conductivity and the question whether a 
given material shall be classed as a conductor or a non-conductor ia entirely 
one of degree. Certain materials are readily classified in these two general 
groups; metals, for iaatance, are easily classed as conductors, wbereaa such 
substances as mica, Elasn, rubber and mineral oil are classed as non-cozft- 
ductors. Certain other materials are not easily classified, because their 
properties undergo extreme cfaanKee with their degrees of purity, treatment 
and temperature. In general, all materials which are used commercially 
for conducting electricity can be classed as conductors; and those materiaJa 
used commercially for obstructing the flow of electricity can be classed aa 
non-conductors, a better term being int^Uaiors or dielectriea. ^ubstancea 
which are neither good conductors nor good insulators can be termed semi- 
conductors. 

1. Solid conduction, or the property of conduction through bodies in 
the solid state, is explained in Sec. 2. This type of conduction is the 
only one considered at length in this section (Sec. 4), 

S. Liquid conduction, while it refers mainly to the conduction o 
slectrolytot (Sec. 10), also includes liquids of elements in the pure stata 
as distinguished from chemical solutions, acid or basic. The property of 
liauid conduction is treated at length in Sec. 19. on " Electrochemistry*' 
(also see Sec. 20, on "Batteries"). 

4. Oaaaont conduction, or the oonduoting power of gases, iisually 
in a rarefied state, is also outside the scope of Sec. 4 and is taken up in 
Sec. 19. 

5. The theoiy of conduction is briefly explained in Sco. 2. The 
electron theory, or modern view of conduction phenomena, is treated more 
fully in Sec. 22. 

•. Bffect of temparatura. The resistivity of all metals becomes 
greater aa the teinperature rises. These materials are said to have positiTe 
temperature coefncienta of resistance. Carbon and electrolytes, on the 
opposite hand, have negative temperature cocflicients; that is, their resistiirity 
becomes less as the temperature rises. There are certain alloys, such as 
manganin, which have very small temperature coefficients, but such 
materials form the exception. It has also been found, in the esse of copper. 
that the temperature cocflScient of resistance varies directly as the percent- 
age of conductivity with respect to the annealed oopper standard (Par. 41). 

7. Temperature coefficient of reiistaace. The resistance of any 
conduct<M*, over at least a limited range, can be expressed by the linear equa- 
tion, 

Rt ^ Ro(l + ant) (ohms) (1) 

where Ri is the resistance at any temperature U R* ia the resistance at 
dog. cent, and en is the temperature coefficient per deg. from and at soro deg. 
At some other reference temperature fi, the resistance is 

A - Ai[l + m« - (i)) (ohms) (2) 

where Ri is the resistance at fi deg. and at Is the coefficient from and at the 
temperature h deg. These formulas take no account of the change of dr- 

226 

Digitized by VjOOQIC 



PnOPBBTIBS OF MATBBIALS SeC. 4-8 

Bcnons with change of temperature and therefore apply to the caae of con- 
duetora of constant maas« usually met in engineering work. For a full 
ifitruHion of this subject see DeUinger, J. U. ** The Temperature Coefficient 
6t Copper," Bulletin of the Bureau of Standards, 1911, Vol. VII, No. 1, p. 
71: and "Copper Wire Tables," Circular No. 31, 3rd edition, 1914, Bureau of 
Standards. 

S. Kllaet of eheznical eompoiitlon. The resistivity of most metals 
is very sensitive to slight changes in chemical composition. Particularly is 
this true of copper; when alloyed, for example, with 1 per cent, of another 
netal, its inereaae in reaSstivity, measured in per cent., a many times 1 per 
«Bt. See Par. CI and M. Therefore it ia very essential when stating a value 
of resistivity for a given subetance to state also wliat the substance is com- 
posed of. or if it be so nearly pure that there are no more than limaU traces of 
Icreign substances, to state its percentage of purity. 

9. Blaet of mecbailleal taeatmant. When ductile metals are sub- 
iectcdto cold rolling, drawing, hammering, or to cold working of anyldnd, 
tiicy become harder, stronger and slightly more dense. At the same time 
the resistivity increases, sometimes markedly, and the initial properties can 
oaly be approached a^n by means of the kaneallng proeaii. While 
tUs proceaa will sometimes restore the initial properties, at least for most 
pnclieal purposes, it does not always do so. 

WnUE OAOX8 

U. TIm Bises of wlra have been for many years indicated in commercial 
praetioe almost entirely by gage numbers, especially in America and Eng- 
land. This practice is accompanied by some confusion because numerous 
gases are in common use. The most commonly used gage for electrical 
vires, in America, is the Americkn wire gags described fally in Par. It. 
The most commonly used gage for steel wires is the steal wire Ka(e briefly 
oentioned in Par. IB. 

There is no legal standard wire gage in this country, although a gage for 
•beets was adopted by Congress in 1893 (see Par. 114). In England there is a 
legal standara known as the standard wire gage, mentioned in Par. IT. 
In Germany, France. Austria, Italy and other continental countries prac- 
tically no wire gsge is used, but wire sises are specified directly in milli- 
meters. This system ia sometimes called the millimeter wire gace (see 
Pit. S3). The wire sixes used in France, however, are based to some extent 
sa the old Paris gage ("jauge de Paris de 1857"). For a history of wire 
gsgcs see Circular No. 31, "Copper Wire Tables," Bureau of Standards, 
3rd Edition, Oct. 1, 1914. 

There is a growing tendency to abandon gafe number! entirely and 
specify wire sises by^ the diftmetarin mill (thousandths of an inch). This 
practice holds particularly in writing specifications, and has the great ad- 
vantages of being both simple and explicit. A number of the wire manufac- 
toTffs also encourage this practice, and it was definitely adopted by the 
I'sited States Navy Dept. in 1911. 

XL. The mil is a term universally employed in this country in connection 
vith wire gagea and is a unit of length equal to one thousandth of an 



U. Tha dreular mil is another unirersal used term, being a unit of 
vca eqnal to the area of a circle 1 mil in diameter. Such a circle, however, 
has an area of 0.7854 (or t/4) aq mil. Thus a wire 10 mils in diameter has 
a emsi sectional area of ICX) circ. mils or 73.54 sq. mils. Hence, 1 circ. mil 
e^usb 0.7854 sq. mil. 



U. Tha Amarlesn wire gaga, also known as the Brown & Bharpo 
Ma, wss devised in 1857 by J. R. Brown. It is usually abbreviated A. W.Q, 
Tfai gsge has the property, in common with a number of other gages. 



that its sises repreeent approximately the successive steps in the process of 
vile drawing. Also, like many other gages, its numbers are retrogressive, 
s larpr number denoting a smaller wire, corresponding to the operations of 
dimwiBg, These gage numbers are not arbitrarily cho8eD,a9 in many gages, 
tiot (adow the mathematical law upon which the gage is founded. The gage 
ouaben ud aiies are given in Par. M. 



227 



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Sec i-14 PRdPBRTIBS OF MATBRIALS 

The tbeoretieally oxsct diameten in this gage, u giveD in th« aeeond eol- 
umn of Par. SO, contain more aignifioant figures than there ia any oommereial 
need for, and hence the large companies have atandardiied the sises given in 
the third column, using the nearest mil for large sises and the neareat 
tenth of a mil for the smaller sises. These commercial sises were adopted 
as standutl by the United States War Dept. in 1011. 

14. Tha baaii of the Amarloan wire gaga is a simple mathematical 
law. The gage is formed by the specification of two diameters and the law 
that a given number of intermediate diameters are formed by geometrical 
progression. Thus, the diameter of No. 0000 is defined as 0.4600 in. and of 
No. 36 as 0.0050 in. There are 38 sisea between theee two, hence the ratio 
of any diameter to the diameter of the next greater numb^ ia given by thia 
expression 

The square of this ratio — 1.2610. The sixth power of the ratio, <.«.^he 
ratio of any diameter to the diameter of the sixth greater number — 2.00SO. 
The fact that this ratio is so nearly 2 is the basis of numerous useful relatioua 
or short cuts in wire computations. 

II. Tha iteel wire gaga, also known originally as the Waahbum tt 
Moem gage and later as the American Bteel A Wire Co.'i gaga^ waa 
eatabliahed by Ichabod Washburn about 1830. This ga^e also, with a 
number of its sixes rounded off to thousandths of an inch, is known as the 
Boabling ^age. It, is used exclusively for steel wire. The numbers and 
aises are given in Par. SO. 

1(. The Birmlncham wire rage, also known as Stubs' wire page and 
Stubs' iron wire gage, is said to nave been eatabliahed early in the eighteenth 
century in England, where it was long in use. Thia gage waa uaed to desig- 
nate the Stubs* eoft wire aiaea and ahould not be confuaed with Stubs' steel 
wire gage mentioned in Par. 19. The numbera of the Birmingham gage were 
based upon the reductions of sixe msde in practice by dravring wire from rolled 
rod. Thus, a wire rod was called No. 0, nrat drawing No. 1, and so on. 'The 
lO'adations of siae in this gage are not regular, as will appear from ita graph. 
This gage haa been used to a considerable extent for designating iron and steel 
telegraph wires. Its numbers and sises are given in Par. SO. 

IT. Tha Standard wire gafe, which more properly should be designated 
(Brltiah) Standard wire gage, is the legal atandard of Great Britain for all 
wires, adopted in 1883. It ia also known as the New British Standard 
fare, the Bngllih lagal standard S*/f* and the Imperial wire gace. 
It was constructed by ao modifying the Birminghamgaee that the differences 
between consecutive aises became more regular. WniTe this gage is the one 
most largely uaed in England, there ia a tendency there, as here, to drop gage 
numbers and specify sises by the diameter in mils. This gage has never 
been extensively used in this country. Its numbers and sixes are given in 
Par. SO. 

M. Tha Old X2igUsh wire (race, also known as the London wire ga(e, 
differa very little from the Birmingham gage. It waa formerly used to some 
extent for brass and copper wires, out is now nearly obsolete. The numbera 
and sixes are given in Par. SO. 

It. Tha Stubi' Iteel wire mre has a somewhat limited use for tool 
steel wire and drill rods. It ahould not be confused with the Birmin^am or 
Stubs' iron wire gage mentioned in Par. 1(. TYm numbers and sixes are 
given in Par. SO. In addition there are twenty-rix larger sixes, Z to il, and 
thirty smaller aisca, No. 51 to No. 80, besides those given in Par. SO (see tool 
catalogue of Brown & Sharps Mfg. Co., or The L. S. Starrett Co.). 

10. The Trenton Iron Co.'a gac*, of which the numbers and sisea are- 

R'ven in Par. SO, ia used only to a ver^ limited extent. It differs but slightly 
om the steel wire gage mentioned in Par. li. 

11. The French wire gaga is an exception to the other gages given in 
Par. SO in the respect that ita sises are progreaaive, instead of retrogreesive, 
as the numbers advance. The sixes there given were taken from the Ameri- 
can Steel and Wire Co.'s handbook, "Electrical Wires and Cables," 1910. 

228 ^ 

DigilizedbyGoOgle 



PROPBRTIBS OP MATERIALS 



Sec. 4-22 



SS. Tht Ulion itamdard wlrs gr*g« was proposed >omo time befora 
1SS7 and was based upon the simple principle that the area of croeg-eeotion 
increased proportionately with the gace aumbera. Thus No. 5 » 5,000 circ. 
mils. No. 10 — 10,000 cir. mile, etc. Thia gage never came into general use. 

is 
1 



tS. The MiUlmeter wlrs garsi also known oa the Metric wire %»t*i i 
baaed on ^ving progressive numbers to the progreasive aiaes, calling 0. 
mm. diameter No. 1, 0.2 mm. No. 2, eto. 



St. The Oernuui rare, in which the diameters or thickness are az- 
preaaed in millimeterB, is retrogroaaive and contains 26 sixes. The gage 
ramben and aiaee ore given in Far. M. 

W . Lorga sUes of wire, above No. 0000 A.W.G., are S|>eoiSed by the 
total eroes-eeetion in circular mils. This applies in particular to large 



M. Tli« United States standard sheet race, for sheet and plate iron 
and steel, was adopted by Congress on March 3, 1893 (see 27 Stat. L., 746) 
sad established a uniform legal standard for the United States. The num- 
ben and thicknesaes in this gage are given in Par. 80, for comparison with 
wire ga^es. A full table of gage numb^, thickneeees and weights is given in 
Ptt. Sli. 

IT. The standard decimal gage (or sheet metals, designating the 
**"'*^»f^ in mils, was recommended in 1895 by the Association of American 
Steel Manufacturers, the American Railway Master Mechanica' Assooiation 
sad the American Society of Mechanical Kngineers. There are 38 sizes, 
nagiag from 2 mils to 250 mils. See Par. >!• for a full table of siiee and 



Hl Th* maasurementot wire diameters maybe accomplished in threet 
emys, vis., by means of a micrometer caliper, by meana of a wire gage such ' 
SS tlttt shown in Fig. 1. or by means of a V-gage. The most accurate 
■saas is a micrometer caliper, which reads directly to mils, and. by eatimat- 
isg tenths of the smallest scale division, to tenths of a mil. The most accu- 
rate type of micrometer is one equipped with a miniature friction clutch, which 
"^■~' — * 1 caused by gripping the wire too firmly between the jaws. 




Via. 1. — Gage for testing the sises of wires. 



n. Oermaii wire (•«• 

Diameters in millimeters 



No. 


Oiom. 


No. 


Diam. 


No. 


Diam. 


No. 


Diam. 


No. 


Diam. 


I s.so 1 


6 


3.75 


11 


2..W 


16 


1.375 


21 


0.750 


2 5.00 


7 


3.50 


12 


2.25 


17 


1.250 


22 


0.625 


3 4. SO 


8 


3.25 


13 


2.00 


IR 


1.125 


23 


0.562 


4 4.25 





3.00 


14 


1.76 


19 


1.000 


24 


0.500 


5 4.00 


10 


2.78 


15 


1.50 


20 


0.875 


25 


0.438 



220 



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Sec* 4-31 PROPBRTISS OP MATERIALS 

COPPKE 

31. 0«neral propertlei. Copper, which is by far the most important 
metal in the electrical industry, is a highly malleable and ductile metal, of a 
reddish color. The density varies slightly, depending on the physical state, 
an average value being 8.9. Copper melts at 1,083 deg. cent.* (1,981 deg. 
fahr.), and in the molten state has a sea-green color. When heated to a very 
high temperature it vaporiaes, and burns with a characteristic green flame. 
Copper bolls at 2,310 deg. cent. (4,190 deg. fahr.).t Molten copper reaidily 
absorbs oxygen, hydrogen, carbon monozide and sulphur dioxide; on cooling, 
the occluded gasee are Uberated, tending to give rise to blow holes and porous 
castings. The presence of lead in molten copper tenda to drive on both 
carbon dioxide and water vapor. 

Copper when exposed to ordinary air becomes oxidised, turning to a 
black color, but the coating is protective and the oxidising process is not 
progressive as with iron and steel. When exposed however to moist air 
containing carbon dioxide, it becomes coated with green basic carbonate. 
It is also affected by sulphur dioxide. It resists the action of hydrochloric, 
sulphuric and strong nitric acids, at ordinary temperatures, but is acted 
upon by dilute nitric acid. 

The electrical conductivity of copper depends most critically on its degree 
of chemical purity (see Par. CS) and alao, in much less degree, upon the 
physical state, being reduced slightly (from 2 per cent, to 4 per cent.) by 
cold rolling and drawing. The tensile properties depend greatly upon the 
physical state, being much improved by cold rolling and drawing. 

The alloys of copper are exceedingly numerous, both for electrical and 
mechanical purposes. Among the most important for electrical purpoees 
are German or nickel silver, bronse and brass. Cojjper solders readily with 
ordinary low- temperature solders; solder alloys witn copper at about 238 
deg. cent. (430 deg. fahr.). 

n. Cozmnerelal gradei of copper. In the copper trade there are 
three recognixed grades of copper known as electrolTtic, Lake, and cast- 
ing.t The first, electrolytic, is that refined bvthe electrolytic method and 
is highly pure (see Par. S4). The second. Lake, is also highly pure, in its 
natural or mineral state, and requires simpler to be melted down to bars, 
for convenient handling (see Par. S6). The third kind of copper, known as 
casting copper, contains more impurities and consequently runs lower ia 
conductivity. It is. as its name implies, more suitable for mechanic^ thaa 
electrical applications (Par. S8). 

81. Denaity of copper. The internationally accepted density of 
annealed copper, S expressed in grams per ou. cm. at 20 deg. cent., is 
8.89; this of course is also the specific gravity at 20 deg. cent., referred to 
water at 4 deg. cent. The American Society for Testing Materials has 
accepted this value, on account of its international endorsement, but con- 
siders that a value of 8.90 is probably nearer the exact truth. A density of 
8.89 at 20 deg. cent, corresponds to 8.90 at deg. cent. In English units 
the international standard equals 0.32117 lb. per cu. in. Also see "Copper 
Wire Tables," circular No. 31, Bureau of Standards, Washington, D. C; and 
"Smithsonian Physical Tables," Washington, D. C, 1910, 5th rev. ed., p. S5. 

84. Electrolytic' copper. The electrolytic refinement of copper ]| 
(see Sec. 19) not only produces metal of the highest purity, but it is eco> 

* "Tables Annuelles de Constantes Et Donn^ee. Num£riquee, de Chimie, 
de Physique et de Technologic;*' University of Chicago Press, 1912; V<^ 
I (1910), p. 48. 

t Fulton, C. H. " Principles of Metallurgy;" McGraw-Hill Book Co., 
New York. flni;p. 74. 

i See report of Committee B-2, on Non-ferroua Metals and Alloys; 
American Society for Testing Materials, 16th annual meeting, June 24-28, 
1913. 

§ Ratified at the meeting of the International ElectrotecfanicsJ Commission 
held in Berlin, Sept. 1 to 6, 1913; see Trans. A, I. E. E., Vol. XXXII, p. 
2148. 

11 Addicks. L. "Electrolytic Copper;" Journal of the Franklin Institute* 
Philadelphia, Fa., Dec.. 1905. 

232 

Digitized by VjOOQIC 



PROPBRTIBS OP iiATBRIALS 



Sec. 4-36 



Bomieally necoaary when precious metals are present in the ore. This 
iTxle o( copper should run higher than 99.88 {wr cent, of pure metal. An 
analysis of average electrolytic copper, representing neither the best nor the 
vorst, vas famished by Mr. Lawrence Addicks and appears in Par. Zi. 
The minute quantities of impurities there shown of course fluctuate from 
time to time in ai^ given refinery, and there are usually certain typical 
differences among the refineries, owing to individual characteristics of the 
bullion supply. Wire bars of electrolytic copper are made by melting down 
the cathode copper in a furnace and casting in the desirea form and siae. 

H. AT«rac« analTaia of oommarolal •leotrolytic copper 
(L. Addicks) 



Conductivity 100 per cent. 


Element 


Per cent. 


Element 


Per cent. 


Copper 


9P.93 
0.0010 
0.004 
0.0008 
0.0018 
0.0030 
0.0002 




O.oooe 

0.0003 
0.0030 
0.0020 
0.0004 


SwDDur 




Niekel 




Lead. 








Antimony 


Silver 


BHmath 


Gold 







(1) 0.4 OS. per ton. 

(2) 0.005 ox. per ton. 



M. L&ka etniper is the grade of material whioh oomea from the northern 
Mkbigan (U. S. A.) peninsular, being the only known variety wluch occutb 
in nature with the purity of electrolytically refined metal. The rock ore 
containing the metaJ is crushed in stamp mills, concentrated and melted, 
rei}nirinc no further treatment than "polins" (introducing sticks of green 
kardwood Into the metal) to reduce the oxides and bring it to tough pitch. 

Some ol the Lake copper coming from the deeper ore deposits nas been 
found to contain appreciable quantities of arsenic, which is very injurious 
to eleetrical conductivity.* Where the quantity of arsenic is high enough 
to injure the conductivity appreciably, the metal is either sold as araenieal 
copper or else refined electrolytically. 

tT. 8p«cific«tlozui for eleotrol^c and Lake Copper wire bars have 
been adopted by the American Society for Testing Materials, See the our- 
RBt " Year Book '* of the society, for full details. 

, tS. Casting copper ia more or lees impure copper, too low in conduo- 
Mty for electrical usee, but entirely suitable for most other applications. 
There are three sources of this grade of copper: (1) fire-refined copper from 
rinpo sources; (2) copper electrolytically produced by deposition from 
impure liquors; (3) and copper reclaimed from secondary sources. The 
copper contents of the better Known brands of casting copper run in general 
over 90 per cent., but some will run less. It is, as its name implies, exclusively 
a foundry copper. 

W. SUodards of reilstiTit^. The table in Par. M presents a 
^uunary of the standards of resistivity, temperature coefficient and resis- 
^rity which have been most in use. The particular standard temperature 
in each ocrfumn is indicated by enclosure in parentheses ( ), and the other 
Vvoes STP computed from the stondard temperature. A full discussion of these 
nJscB viU be found in "Copper Wire Tables," Circular No. 31, Bureau of 
Standards, pp. fi to 10. The latest accepted value of resistivity is the 
"blOTuaoiMl Annealed Copper Standard^" given in column 8; all 
lAlilescxTen in this section for annealed copper wire are based on this stand- 
ifd. wtueb is eorered more ^;>ecificaUy in Par. 41. 



*Addieks, L. "The Effect of Impurities on the Electrical Conductivity 
^Co^per-r Trana, A. I. M. £., lOpd. 



yGoogle 



Sec. 4-40 



PROPBRTIBS OF MATERIALS 



» £ s « 

■S.2 " 



■) a 






(do 



■ £»> 






■a a 
ft;: 3 9 ■) 









® s s 



coo 



so 



Si 






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8S 



So 



do 



no 
»*o 



do 






ctookoo 

8Si8 



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dded 



iSfeS 

pOOOw 

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too© 



sf.ss 



8^88 



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.a ■ 

Aid 

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P 

el 



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joogle 



PnOPBRTtBS OF MATERIALS 



See. 4-41 



at 20 dsg. cent. 



4t. Tba Intomationjtl Anneftlad Coppar Btandard is tbe inter- 

mtionally accepted value* for the reaiatiTity of annealed copper of 100 per 

eeat. eooduetivity. This Btandard ia expressed in terms of mass-resistivity 

ss 0.1IISS ohm (meter, gram), or the resistance of a uniform round wire 

1 in. lone weighing 1 gram, at the standard temperature of tO^ deff. eant. 

Equivalent expressions of the annealed copper standard, in various units of 

mass resistivity and volume resistivity, are as follows: 

0.15328 ohm (meter, gram) 

875.20 ohms (mile, lb.) 

1 . 7241 microhm-cm. 

0.67879 microhm-in. 

10.371 ohms (mil, ft.) 

0.017241 ohm (meter, mm.>) 

It may be convenient to note that a value of 0.017241 ohm (meter, mm.') 

ii exactly A ohm, so that the volume conductivity at 20 deg. cent, can be 

expreased 58 mho (meter, mm.*). 

It is important to observe that weight-measure rather than volume- 
neasure is commercially the more important in wire calculations, since 
wire is sold bpr the. pound. Therefore the most attention should be given to 
ma ss rys istivity and mass resistance. 

tt. Tamperaturs eoafflciant of nuis realatanoe. This coefficient , 
wbiefa applies to resistance calculations when a conductor is deSned in terms 
ef its mass, is the one commonly employed in engineering calculations; that 
ii to tay, in common practice, the mass of a conductor remains the same 
at all temperatures, ana changes of volume, length, or sag are disregarded. 
It is important to note that it does not apply to a conductor defined in terms 
<t its volume. 

The temperature coefficient (for constant mass) of the annealed copper 
•taadard, 100 per cent, conductivity, is 0.00393 per deg. cent., at 20 de^. 
eeat. The coefficient changes with the temperature of reference, as given in 
Par. 40, column 8. 

The ooaffldaati for copper of lass than itaadard (or 100 per cent.) 
eondnctiTity is proportional to the actual conductivity, expressed as a 
detima] percentage. Thus if n is the percentage conductivity (05 per 
cent. >" 0.05), the temperature coefficient will be o'l » nm, where oi is the 
eoeffident oi the annealed copper standard. 

The coefficients given in the table in Par. 4S were computed from the 
fonnola 

«' i ^ (3) 



r+((l-20) 



0(0.00393) 

The quantity — T given in the last column (Par. 43) is tbe inferred absolute 
MTO of temperature, assuming a linear relationship between resistance and 
temperature. At the absolute zero of temperature the reaistanoe would be sen). 
41. TiUa of temperatura ooeffleianto of eopper for different initial 
temperatorea (canttcrada) and different conductivities 



Ohms 










-T, 


(meter. 


Per cent. 








" Inferred 


gram) at 20 


conductivity 








absolute 


deg. cent. 










•ero " 


0.16134 


95 


0.00403 


0.00373 


0.00367 


-247.8 


0.1S966 


96 


0.00408 


0.00377 


0.00370 


-245.1 


0.15802 


97 


0.00413 


0.00381 


0.00374 


-242.3 


0.15763 


97.3 


0.00414 


0.00382 


0.00375 


-241.5 


0.1SS40 


98 


0.00417 


0.00385 


0.00378 


-239.6 


0.15482 


99 


0.00422 


0.00389 


0.00382 


-237.0 


(•.inss) 


100 


0.00427 


(O.OOSM) 


0.00385 


-234.4 


0.15176 


101 


0.00431 


0.00397 


0.00389 


-231.9 



F!trentheaea indicate the defined standard values. 

« 

* Batified at the meeting of the International Electrotechnical Com- 
tamoB held in BerHn. Sept. 1 to 6, 1913; See Trant. A. I. E. E., Vol. XXXII, 
^21S^ 

288 DigilizedbyV^iUUyHJ 



» 



SeC.i-44 PROPERTIES OF MATERIALS 

44. Boduetlon of obeervfttions to staudaird tamperaturo. A tabic 

of convenient corrections and factors for reducing resistiTity and resistance 
to standard temperature, 20 deg. cent., will bo found in *' Copper Wir« 
Tables," Circular No. 31* Bureau of Standards. 

45. Calculation of per cent. conductlTltT. The per cent, con- 
ductivity of a sample of copper is calculated by dividing the resistivity 
of the International Annealed Copper Standard at 20 deg. cent, by the 
resistivity of the sample at 20 deg. cent. Either the mass resistivity or 
volume resistivity may be used. Inasmuch as the temperature coefficient 
of copper varies vith the conductivity, it is to be noted that a different 
value will be found if the resistivity at some other temperature is usdd. 
This difference is of practical moment in some cases. In order that such 
differences shall not arise, it is best always to use the 20 deg. cent, value ol 
resistivity in computing the per cent, conductivity of copper. When th« 
resistivity of the sample is known at some other temperature, t, it is vera 
simply reduced to 20 deg. cent, by adding the quantity (20 -^O multiplied 
by the ''resistivity-temperature constant,'* given in Far. 46. 

46. KeslstiTity-temparature constant. The change of reHstivUy ptt 
degree may be reaidily calculated, taking account of the expansion of the meta] 
with rise of temperature. The proportional relation between temperature 
coefficient and conductivity may be put in the following convenient form foi 
reducing resistivity from one temperature to another: The change of reaiativUi 
of copper per degree cent, is a constant, independent of the temperature of refer' 
ence and of the sample of copper. This "resistivity-temperature constant" mai 
be taken, for general purposes, as 0.00060 ohm (meter, gravCi, or 0.006« 
microhm^cm. For further details, see ' * Copper Wire Tables," Circular No 31, 
Bureau of Standards, Washington, D. C. 

47. Complete copper-wire tables, based on the Internationa: 
Annealed Copper Stanciard, are given in Par. 00, and represent approxi- 
mately an average of the present commercial conductivity of copper. Foi 
annealed wires, the resistivity is independent of the sise. These tables an 
reproduced directly from Circular No. 31, 3rd Edition, issued by the Bureai 
of Standards. The quantities were computed to five significant figures am 
rounded off to the fourth place, bein^ therefore correct within 1 in the fourtl 
significant figure. The volume resistivity at 20 deg. cent., used in calculatinj 
these tables, was 0.67879 microhm-in. and the density, 8.89 at 20 deg. cent 
or 0.321,17 lb. per cu. in. The tables in Circular No. 31 contain additiona 
columns for deg., 15 deg., 25 deg. and 75 deg. cent. What the tables ^ow i 
the resistance at various temperatures, of a wire which at 20 deg. cent, ii 
1,000 ft. long and has the specified diameter, and which varies in length an( 
diameter at other temperatures. 

48. Explanatory notas on copper wire tables. 

Note 1. — The fundamental reststivity used in calculating the tables is th< 
International Annealed Copper Standard, vis., 0.15328 ohm (meter, gram 
at 20 deg. cent. The temperature coefficient for this particular resistivity 
is an « 0.00303, or ao •- 0.00427. However, the temperature coefiSoient t 

Sroportional to the conductivity* and henoe the change of resistivity pe 
eg. cent, is a constant, 0.000597 ohm fmeter, gram). The "oonst&n 
mass" temperature coefficient of any sample is 

0.0 00597+0.000005 

resistivity in ohms (meter, gram) at i deg* cent. 
The density is 8.89 g. per cu. cm. 

Note 2. — The values given in the tables are only for annealed ooppe 
of the standard resistivity. The user of the table must apply the prope 
correction for copper of any other resistivity. Hard-drawn copper may b 
taken as about 2.7 per cent, higher resistivity than annealed copper. 

Note 3. — This table is intended as an lutimate reference table, and i 
computed to a greater precision than is desired in practice. The praotioa 
user of a wire table is referred to the "Working Tables," Par. 61. 

46. Working copper-wire tables, based on the Tntemational An 
nealed Copper Standard, are given in Far. il. This table is carried onl; 
to three significant figures, and is more convenient for most practical work 
The table itself is adapted from Circular No. 31, 3d edition, issued by th 
Bureau of Standardst and amplified by the addition of values based on tb 
mile unit. 

236 ^- 

Digilized by VjOOQIC 



PBOPSBTIBS OF MATBRZALS 



Sec. 4-60 



Complate irlrt table, itandard anaaalad eopp«r 

American win gage (B. & S.)- English units 



Qav> 
no. 


Diame- 
ter in 
rniln at 
30 deg. 
eent. 


Croas-section at 20 deg. 
cent. 


Ohms per 1,000 ft.* 


Circnlar 
mils 


Square 
inches 


20 deg. cent. 

(-68 deg. 

fshr.) 


SO deg. eent. 

(-122 deg. 

fahr.) 


0000 

000 
00 


460.0 
409.6 
364.8 


211,600.0 
167,800.0 
133,100.0 


0.1662 
0.1318 
0.1045 


0.04901 
0.06180 
0.07783 


0.05479 
0.06908 
0.08712 




I 

2 


324.9 
289.3 
267.6 


105,500.0 
83,690.0 
43,370.0 


0.08289 
0.06573 
0.05213 


0.09827 

0.1238 

0.1663 


0.1099 
0.1385 
0.1747 


3 

4 
5 


220.4 
204.8 
181.9 


52,640.0 
41,740.0 
33,100.0 


0.04134 
0.03278 
0.02600 


0.1970 
0.2485 
0.3133 


0.2203 
0.2778 
0.3602 


• 

7 
8 


162.0 
144.3 
128.5 


26,350.0 
20,820.0 
16,510.0 


0.02062 
0.01635 
0.01297 


0.3951 
0.4982 
0.6282 


0.4416 
0.5569 
0.7023 


9 
10 

11 


114.4 
101.9 
90.74 


13,090.0 

10,380.0 

8,234.0 


0.01028 

0.0081SS 

0.006467 


0.7821 
0.9988 
1.260 


0.8855 

1.117 

1.408 


IS 
13 
M 


80.81 
71.96 
64.08 


6,530.0 
6,178.0 
4,107.ff 


0.00S129 
0.004067 
0.003225 


1.588 
2.003 
2.525 


1.775 
2.238 
2.823 


IS 
IS 
17 


57.07 
80.82 
45.26 


8,257.0 
2.583.0 
2,048.0 


0.902558 
0.002028 
0.001609 


3.184 
4.016 
5.064 


3.560 
4.488 
5.660 


18 
1» 
30 


40.30 
35.89 
31.96 


1,624.0 
1,288.0 
1,022.0 


0.001276 
0.001012 
0.0OU8O23 


6.385 
8.051 
10.15 


7.138 
9.001 
11.36 


21 
22 
23 


28.46 
25.36 
22.57 


810.1 
642.4 
S09.5 


0.0U06363 
0.0005046 
0.0004002 


12.80 
16.14 
20.36 


14.31 
18.05 
22.76 


25 
26 


20.10 
17.90 
16.94 


404.0 
320.4 
264.1 


0.0003173 
0.0002617 
0.0001996 


25.67 
32.37 
40.81 


28.70 
36.18 
45.63 


27 
28 
23 


14.20 
12.64 
11.26 


201.5 
159.8 
126.7 


0.0001683 
0.0001255 
0.00009953 


51.47 
64.90 
81.83 


57.63 
72.55 
91.48 


30 
31 

33 


10.03 
8.928 
7.950 


100.5 
79.70 
63.21 


0.00007894 
0.00006260 
0.00004964 


103.2 
130.1 
164.1 


116.4 
146.5 
183.4 


33 
34 
33 


7.080 
6.305 
5.615 


50.13 
38.75 
31.62 


0.00003937 
0.00003122 
0.00002476 


206.8 
260.8 
328.0 


231.3 
291.7 
367.8 


3S 
37 
38 


6.000 
4.453 
3.965 


25.00 
19.83 
15.72 


0.00001964 
0.00001667 
0.00001285 


414.8 
523.1 
668.6 


463.7 
584.8 
737.4 


33 

40 


3.531 
3.146 


12.47 

9.888 


0.000009793 
0.000007766 


831.8 
1,048.0 


929.8 
1,173.0 



• Rreiitanoe at the stated temperatures of a wire whose Isngth is 1,000 ft. 



•tJOdsceant. 



237 



Sec. 4-50 



PROPERTIES OF MATERIALS 



80. 


□omplata wire table, lUnderd uinealed copper. — Continued 


Case 

No. 


Diameter 

in mils at 

20deg. 

cent. 


Founde 
l,(^ft. 


Feet 
pound 


Feet per ohm* 


20 deg. cent. 

(-68deg. 

fehr.) 


60 deg cent. 

(-122 deg. 

fahr.) 


0000 

000 

00 


460.0 
409.6 
384.8 


640.5 
507.9 
402.8 


1.561 
1.968 
2.482 


20,400.0 
16,180.0 
12,830.0 


18,250.0 
14,470.0 
11,480.0 




1 

2 


324.9 
289.3 
257.6 


319.6 
253.3 
200.9 


3.1.30 
3.947 
4.977 


10,180.0 
8.070.0 
6,400.0 


9,103.0 
7,219.0 
5.725.0 


3 
4 
5 


229.4 
204.3 
181.9 


169.3 
126.4 
100.2 


6.276 
7.914 
9.980 


5,0/5.0 
4,025.0 
3,192.0 


4,640.0 
3,600.0 
2,866.0 


6 
7 
8 


162.0 
144.3 
128.5 


79.46 
63.02 
49.98 


12.58 
16.87 
20.01 


2,631.0 
2,007.0 
1,592.0 


2,264.0 
1,796.0 
1,424.0 


9 
10 
11 


114.4 
101.9 
90.74 


39.83 
31.43 
24.92 


25.23 
31.82 
40.12 


1,262.0 

1,001.0 

794.0 


1,129.0 
895.6 
710.2 


12 
13 
14 


80.81 
71.96 
64.08 


19.77 
15.68 
12.43 


50.59 
63.80 
80.44 


629.6 
499.3 
396.0 


503.2 
446.7 
364.2 


16 
16 
17 


57.07 
50.82 
45.26 


9.858 
7.818 
6.200 


101.4 
127.9 
161.3 


314.0 
249.0 
197.5 


280.9 
222.8 
176.7 


18 
19 
20 


40.30 
35.89 
31.96 


4.917 
3.899 
3.092 


203.4 
256.8 
323.4 


156.6 
124.2 
98.50 


140.1 
111.1 
88.11 


21 
22 
23 


28.40 
25.35 
22.57 


2.452 
1.945 
1.542 


407.8 
514.2 
648.4 


78.11 
61.96 
49.13 


69.87 
65.41 
43.94 


24 
25 
26 


20.10 
17.90 
15.94 


1.223 

0.9699 

0.7692 


817.7 
1,031.0 
1,300.0 


38.96 
30.90 
24.50 


34.85 
27.64 
21.92 


27 
28 
29 


14.20 
12.64 
11.26 


0.6100 
0.4837 
0.3836 


1,639.0 
2,067.0 
2,607.0 


19.43 
16.41 
12.22 


17.38 
13.78 
10.93 


30 
31 
32 


10.03 
8.928 
7.950 


0.3042 
0.2413 
0.1913 


3,287.0 
4,145.0 
5,227.0 


9.691 
7.685 
6.095 


8.669 
6.875 
5.462 


33 
34 
3S 


7.080 
6.305 
6.615 


0.1517 
0.1203 
0.09542 


6,691.0 

8.310.0 

10.480.0 


4.833 
3.833 
3.040 


4.323 
3.429 
2.719 


36 
37 
38 


6.000 
4.453 
3.965 


0.07568 
0.06001 
0.04769 


13,210.0 
16.660.0 
21,010.0 


2.411 
1.912 
1.516 


2.168 
1.710 
1.366 


39 
40 


3.531 
3.145 


0.03774 
0.02993 


26,500.0 
33,410.0 


1.202 
0.9534 


1.076 
0.8529 



* I.«ngth at 20 deg cent, of a wire whose resistance is 1 ohm at the atatec 
temperatures. 

238 

DigiiizMbjV^iUUyiC 



PROPERTIES OP MATERIALS 



Sec. 4-50 



lit 

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jii^edbyv^iuuyie 



PROPKRTIES OF MATERIALS SeC. 4-52 

U. Befaranca to eopp«r-wlra table* in other >a(ee. For copper- 
vira tables in the British Standard Wire Gage and in the Millimeter Gage, 
bawd on the International Annealed Copper Standard, aee Bulletin No. 31, 
Sd edition (Oct. 1, 1814), issued by the Bureau of Standards. 

a. CondnetlTitT of hard-drawn eoppar. The conductivity of hard- 
dnvn copper, exiireesed as a percentage of the conductivity of the annealed 
copper standard, varies with the aiie of wire, becoming smaller as the wire 
becomea smaller. It is impracticable, however, to state any general rule, 
bccatiee of differences in manufacturing practice, as to the number of draw* 
■DCS between annealings, amount of reduction to each drawing, etc. The 
Bureau of Standards found that the conductivity of No. 12. A-W.G. hard- 
drawn copper was 97.3 per cent. The copper-wire specifications of the 
American Society for Testing Materials, call for resistivities which correspond 
lo the following percentage conductivities, baaed on the annealed copper 
standard. 

Per cent., 
conductivity 

Annealed ooppar 08.2 

Uecfium-hard drawn, above 0.325 in 97.7 

Medium-hard drawn, below 0.325 in 96. 7 

Hard-drawn, above 0.325 in 97.2 

BardHlrawn, below 0.326 in 96.2 

Tte density of all these grades of wire is taken as the same, or 8.89 at 20 
deg. cent. 

H. Tampantora eoaffietant of expansion. The temperature 
coefident of linear expansion of copper is approximately 0.000017 per 
dsg. cent. The values given in the Tables Annuelles de Constantes et 
Donn^ Num^riques," for 1910, are as follows (p. 44 and p. 45); Between 
- 190 deg. and 17 deg. cent., 0.00001418; between 17 deg. and 100 deg. cent., 
0.00001636; and by St^phan's determinations (1910). 

2(-2.fl-|-0.000016O7l-|-O.OO0OOO0O4O3(>) (6) 

Matthiessen's mean coefficient* between deg. and 100 deg. cent., was 
amOOiaee and nzeau found the value* at 40 deg. cent, to be 0.00001678. 
By compntation from St^phan's results the mean coefficient between 
d^ and 100 deg. cent, is 0.0000165. The mean of these four results is 
(UX)00166 per deg. cent. The corresponding value in the fahrenheit scale 
is 0.00000922 per deg. 

H. Coneantric strand, or cable, is a conductor made up of a straight 
•entral wire (or group of wires) surrounded b^ helical layers of bare wires 
(or groups of wires), the alternate layers havmg a twist m opposite direc- 
^mm. The term "concentric-lay" applies when the strands are composed 
of BOEle bare wires; the term "rope-lay" applies when the strands are made 
op of groups of wires, each group in concentric lay. All the individual 
brands are of the same sise. If there are n layers over the core of a con- 
cent rie-lay cable, not counting the core as n layer, the total nnmbar of 
it ra nds or wires will be 

>r-3n(n-f-l)-(-l (6) 

Tha (Hamatar of snch a cable is the diameter of the ofamunseriUng 
ordc, or 

D-d(2n-H) (7) 
wWrc d is the diameter of any strand or individuai wire. In a rope-lay 
^ble, aoeb as some forms of extra flexible cable, where instead of individual 
na^ wires there are groups of wires, each group consisting of a concentrio-Iay 
tMt, the total number of wires N in the entire cable will be that given 
by Eg. 6 for ooncentric-lay cable multiplied by the number of wires 
•a each component group. Thus a rope-Isy cable comprising 1 layer, 
with 7 wires m each group,. would have 7X7^49 wires, and is sometimes 
failed s 7X7 rope. Such an expression as a 19X7 rope strand means 19 
Mraodi, each compoeed of 7 wires. A 7X7 rope strand is not economical 
'« large conductors and is usually confined to sises like No. 4 A.W.G. or 
•nilltr. For large sises a 19X7 or 37X7 rope strand ia more compact and 
ge»^ts s smoother exterior. 

'"SmHbWPiaoPhjnieal Tables;" Washington, D. C, 1910; 6th rev. ed., 
»122. 



243 



y Google 



S«c.i-56 



PROPERTIES OP MATERIALS 



» 



TIm niunlxr of dreuUr mUi in a cable comi>oa«d of N vine is 

CM.- Nit (a 

where d is the diameter of each wire in mils (thousandths of an inoh). 

The equivalent solid eondaetor is one having the same number c 

oiroular mils, or its diameter is 

ly-Vlfd' (0 

It Is n^ equal to the normal croas-eeotion of the oablo; because in the las 
ease the stoands are cut at a slight angle (due to their pitch) and suoh . 
section is therefore larger than the true section, equal to the sum of the norma 
sections of all the strands, each taken normal to its own axis. 

The ratio of the diameter of concentric strand to the diameter a 
equivalent solid conductor is given by 

*> VN ^ 3»«+3»+l 
Substitution in this formula from n-0 to »-8, gives the following value 
of the ratio. 



n 


JV 


D 
D' 


n 


N 


D 
D' 


n 


N 


D 




• 1 

2 


1 
7 
19 


1.000 
1.134 
1.147 


3 

4 
5 


37 
61 
91 


1.161 
1.152 
1.153 




7 
8 


127 
169 
217 


1.154 
1.154 
1.154 



Thia shows that the larger the number of strands, for a given cross-section 
the larger will bo tlie outside diameter, approachinc, however, a limiting rati< 
of 1.154. Therefore the sise and the cost of a conductor of given croes-sectioi 
increase as the number of strands increases. 

The Individual wires of a cable can sddom be drawn to anv of thi 
standard ^age numbers, because the diameter of the wire is fizca by th< 
rmuired stse of the cable, and the number of wires composing it. Also aet 
"Wire In Electrical Construction," John A. Roebling's Sons Co., 1906; anc 
**£leotrical Wires and Cables," Amer. Steel A Wire Co., 1010. 

H. Composition of standmrd oonoentiio strands* 



Bange of sise 


Number of wires 


Standard 

concentric 

strands 


Flexible 

concentric 

strands 


2,000,000 to 1,600,000 cir. mils 


127 
91 
61 
37 
19 
7 


160 


1,500,000 to 1,100,000 dr. mils 


127 


1,000,000 to 550,000 cir. mils 


91 


600,000 to 260,000 cir. mils 


61 


No. 0000 to No. 1 A.W.G 

No. 2 to No. 8 A.W.Q 


37 

19 1 



IT. Pitch or laj of coneontric strand. The axial length of one com- 
plete turn of any individual strand in a coo- 
centric-lay cable, divided by the diametw oi 
the cable, is called the pitch or lay. The 
pitch angle of the cable is shown in Fig. 2, 
where ae represents the axis of the cable and 
I is the axiallength of one complete twist; ab 
is the length of any indi\'idual strand, 2 + Al, 
in one complete twist* and the angle bac, or 0, 
is the pitch angle. Tne side be is equal to the 
circumference of the circle circumscribing the 
In thia case the pitch p is given by p >■ l/d. There is no fixed 




Fio. 2. — Pitch angle in con- 
centric lay cable. 

cable, 



* See Circular "So. 37, "Eloctric Wire and Cable TerminoloEv;" Bureau of 
Standards; 2nd ed„ Jan. 1, 1015, page 13: A. I. £. K. Standarduatioa I^i4^ 
1014; also see latest edition of Standardisation Rules, Sec. 24. 



2M 



ijiizidbyv^iuugle 



PROPERTIES or MATERIALS 



Sec. 4-^ 



■Uadard pitch used by all cable manuf acturen. Alao aee " Kleotrica] Wins 
aad Cables." Amer. Steel t Wire Co., 1910, pp. 27 to 35. 

R. Inereaaa in man and reilstuioe due to itrandinf . The Bureau 
of Standards has shown in Circular 31 (3rd Edition, 1914, p. 71) that the 



equal to the per cent, decrease oi resistance ot a cable in wnicn each wire 
nakss perfeet oontact with a neighboring wire at all points of its surface. 
That is, if J?« is the resistance of the equivalent solid roa or wire, Ri is the re- 
Bvtanee of the cable with perfectly insulated wires and 22s is the resistanoe of 
the cable in which all the wires make perfect contact with their neighbors, 
theaS. — i(£i + Ki). In general, fii>A.>fis. The resistance of a cable is 
generally somewhat less than Rt, which is shown by the fact that the actual 
rewtance of a cable increases slightly with age, probably due to the formation 
o< oxide on the contact surfaces. 

n. Conwr eabl* tablet. The table in Par. U gives the properties of 
bare eoDeentri»4ay copper cables, based on the International annealed 
es|)per ■tandard (see Far. 41). The column headed "Diameter of Wiree" 
was calculated in each case from the total cross-section. The values given 
for "ohms per 1,000 ift." and "lb. per 1,000 ft." are 2 per cmL grtattr 
diaD for a solid rod of eroes-section equal to the total cross^ection of the 
aires of the caUe. This increment of 2 per cent, means that the values are 
eotrert for cables having a pitch of 15.7. If the pitch is different, the resb^ 
saee and the mass may be calculated by multiplying the values in the table 
by the factor 

/ 493 
f 



l^m-2)tO-> 



(U) 



Far exami>le, if the pitch is 12, the resistanoe and the mass ^ven in the table 
•hoold be increased 1.4 per cent. ; if the pitch is 30, the valuee should be de- 
cnssed 1.5 per cent. 

tt. Bemp-eantr* eabl«i. If the core of a concentric strand is replaced 
W hemp, the characteiistios of the cable are altered in several respects. Ths 
mmttrr of the cable, for a^ven croes nc ction, is greater than the diameter 
tt tu all-metal cable; the flexibility is slightly greater, for the same sise, 
httog more marked in the case of 7 wires than a greater number; and the skin 
eleet, for equal sises, is slightly diminished. The tensile strength of a 
•emp.e«itre cable would be computed on the basis of the eroas^eetion of 
a<*al, disregarding the hemp. Such cables are not in general manufactured 
is standard sises, but made up to order. See article by D. B. Rushmore in 
StatnlSUclric Rfiew, June, 1912, discussiag objections to cables of this 

vn*. 

a. Waicht ot hamp-centre, coneantrie-laj, eoppar eabto * . 

Made of six wires around a hemp centre 
(The American Brass Co.) 



8beof 

Kxh. 


Made of 


Sise of 

each wire 

(in.) 


Outside 

diameter 

(in.) 


Approximate weight (lb).] 


Per 1,000 ft. 


Per mile 


No. 0000 
.No. 000 
No. 00 
No. 

3;: \ 


Swires 
A '* 


0.1879 
0.1872 
0.1489 
0.1328 
0.1181 
0.10S2 
0.0937 
0.0836 


0.664 
0.502 
0.447 
0.398 
0.354 
0.316 
0.281 
0.260 


673 
551 
418 
332 
266 
212 
167 
133 


3,553 
2,909 
2,207 
1,753 
1,404 
1,119 
882 
702 



.'The wetghta for heffip.centre cable were not calculated, but. were ob- 
■aiaed by weighing lots of finiidiied cable. 



246 



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S«c.4-62 



PROPERTIES OP MATERIALS 



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Sec 4-63 



PROPERTIES OF MATERIALS 



» 



•a. Bttect of ImpuzitioB on the conductivltr of eoppar. It ia w« 

known that the conductivity of copper la highly senaitive to aught impurities. 
A swies of progressive testa on the eCFect of the preeenoe <A very small quanti 
ties of foreign elements, with respect to eleotn<»l conductivity, was made b 
Mr. Lawrence Addicka. In order to obtain a comparative figure, Af i 
Addicka divided the percentage decrease of conductivity by the percent&j^ c 
impurity added, and obtained the results given in Par. 64( which are stnctl; 
true only for an infinitely small lowering of conductivity. The factor la see! 
to bear a general relation to the i>eriodic arrangement, becoming smaller -nri tl 
inoreasing atomic weight within any one ^oup, though there is no eviden 
relation between one group and another. This factor is of use when exaTnin 
ing the analysis of a copper which shows low conductivity, as a means o 
indicating the probable cause of the trouble. Commercial copper w^hei 
ezaminea under a microscope reveals a structure made up of grains of purt 
oopper enclosed in matrices of impurities, thus forming a complicated chain o] 
two substances. By adding certain impurities the conductivity of th< 
impure portion of the chain may be increased without changing that of the 
oopper itself, thus showing an increase in the total conductivity of the ch&in. 

64. BeUtion between percentage Impurity and percentage chaac'* 
In oonducuTity 

(Uwrence Addicks, Proc. A. I. M. E., Vol. XXXVI, p. 18, 1900) 



Peri- 
odio 
group 


Element 


Fac- 
tor* 


Atomic 
weight 


Peri- 
odic 
group 


Element 


Fac- 
tor* 


Atomic 
weight 


I 
I 
II 
II 
III 
IV 
IV 
IV 


saver 

Gold 

SSno 

Cadmium.. 
Aluminium 

Silicon 

Tin 

Lead 


e 

10 
30 

9 

fiOO 

70 

67 

3 


108 

197 

65 

112 

27 

28 

119 

207 


V 
V 
V 
V 
V 
V 
V 
VII 


Phospborua** 

Araenic 

Antimony 

Biamuth 

Ozygen 

Sulpnur 

Tellurium 


3000 
720 
190 

4 

2S 

8 

4 

140 


31 

76 

120 

208 

16 

32 

128 

56 





'Factor' 



Percentage decrease of conductivity 



Percentage of impurity added 
** This value is probably too high and later results indicate an average 
value of about 600. 

W. TansUa atrongth. The mechanical properties of copper extend 
over a considerable range, depending on its state of hardness. The tensile 
strength of annealed copper wire ranges from about 32,000 lb. or 34,000 
lb. per s^. in., in the larger siies, to as nigh as 40,000 lb. per sq. in. in the 
smaller sues; a very fair aasumption is 34,000 lb. as a representative value. 

The process of cold drawing increases the strength quite rapidly. So- 
called medium hard, or half hard, copper wire has a tensile strength in the 
larger sises ranging from 40,000 lb. to 60,000 lb. per sq. in., and in the smaller 
aisee from 50,000 lb. to 60,000 lb. per sq. in. 

Rard-drawn wire has a tensile strength ranging from 50,000 lb. per sq. 
in. in the large sises to about 65,000 lb. per sq. in. in the small sises, or 68,000 
lb. in the very small sises. 

Fig. 3 shows the results obtained by Addicksf in making a determination 



* Ferrine, F. A. C. "Conductors for Electrical Distribution;" D. Van 
Nostrand Co., New York, 1903, pp. 8 to 10. 

Addicks, L. "The Electrical Conductivity of Commercial Copper:" Tran9, 
A. I. E. B., Vol. XXIIj>. 695 (1903). 

Addicks, L. "The Effect of Impurities on the Electrical Conductivity of 
Cooper;" TVons. A. I. M. E., Vol. XXXVI, 1906, p. 18. 

Hoffman, H. O. "Metallurgy of Copper;" McGraw-Hill Book Co., New 
York, 1914. 

I Addicks, L. "The Electrical Conductivity of Commercial Copper;" 
Trans. A. I. E. E., Vol. XXII (1903), p. 695. 



248 



y Google 



PROPERTIES OP MATERIALS 



Sec. 4-66 



f tbe rdationship between tensile atrenflrth and conductivity of copper 
This shows, among other things, that the properties of copper, after 
been through a cycle of hard drawing and annealing, are not com- 

hcdy restored, but nearly 

Concantric strand or 

should have a total 
_ equal at least to 90 
cent, of the strength of 
_ eomponent strands. The 
Mmate strength, however, 
theoretically a function of 
t pitch, and in addition 
c internal streeees in a 
under load are \'ery 
x, BO that a factor of 
Iper cent, is approximate. 
Cast copper ranges in 
strength from 20,000 
to 30,000 lb. per sq. in. 
has a crushing strength 
about 40,000 lb. per sq. in. 
The tinning proceu, 
to copper wir^ 
are intended to re- 
any kind of insulation 
ng rubber as an in- 
jnt, removes some of 
temoer of hard-drawn 
aoa hence impairs its 
strength. Also see 
of tensile strength in 
.T.M. apwcifications for 
jwr wire, current issue of 
'ear Book." 

K. Klongation and fracture. Annealed copper is very ductile and has 
I oltimate elongation of 35 per cent, to 40 per cent, in the large sizes of wire; 
the smaller liiies the elongation decreases to a value of 20 per cent, to 25 
bv cent. The elongation of medium hard and of hard-drawn wire ranges 
■MD 4 per cent, in the largest size to about 1 per cent, in the smallest. The 
r fracture of cast copper is gran- 

I n ular and irregular, while that 

■ l—~*»vl I I t I I I I I I I I ! i I I I of forged, rolled, or drawn 

copper is fibrous, with a silky 
luster. At fracture there is 
considerable reduction of area, 
with drawn copper, in the plane 
of rupture. 







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au 


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out 


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PcrcvDt ConducUTltj 

Fig. 3. — Relationship between conduc- 
tivity and tensile strength in copper wire 
(Addick.s). 



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Is 


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67. The effect of anneal- 
ing temperature on tensile 
properties of copper is illus- 
trated in Fig. 4. 8pc Hoffman, 
H. O. "Metallurgy of Cop- 
'• loo an joo 400 500 000 700 &00 »*j 1000 per;" New York. McGraw-Hill 
f ,iiir f — "-i"-! — "— f--'- Book Co., Inc., 1014, page 5. 

Tio. 4.— Mwrhanira! properties of electro- 68- Meet of Impurities 
bi* copper as affected by temperature 01 tensile strength. One 
tHoffmanJ. of the most common impuri- 

' ' ties in copper is oxygen, in 

the form of auboxid of copper 
^^>. While minute quantities are not harmful, an excess is the cause of 
fMmeta. The preeence of lead makes the metal "red short," or "hot 
' The presenre of bismuth or tellurium makes the metal both "red 
a<ul"oQld short," 



249 



V Google 



Sec. 4-6fi 



PROPERTIES OF MATERIALS 



t9. Table of brMkUnc loads of copper win 

(Baaed on tensile requirements of the American Society for Testing Material! 



i 



Ga«No. 
jCV.O. 


1 

Diam. 
in mils 


Breaking load (lb.) 


Annealed 


Medium hard 


Hard drawi 


0000 


460 


5,980 


6,980 -8.140 


8.140 


000 


410 


4,750 


5,680 -6,600 


6.730 


00 


365 


3,780 


4,620 -5,360 


5,540 





325 


2,980 


3,730 -4,310 


4.520 


1 


289 


2.370 


3,020 -3,480 


3.680 


2 


268 


1,030 


2,450 -2,810 


3,000 


3 


229 


1,530 


1,980 -2.270 


2,440 


4 


204 


1,210 


1,590 -1,820 


1.970 


5 


182 


963 


1.260 -1.450 


1.590 


8 


162 


763 


I.OIO -1.160 


1,280 


7 


144 


607 


810 - 925 


1,030 


8 


128 


481 


646 - 737 


828 


9 


114 


381 


615 - 587 


663 


10 


102 


314 


410 - 467 


52S 


11 


01 


249 


328 - 373 


423 


12 


81 


198 


262 - 298 


337 


13 


72 


157 


209 - 237 


268 


14 


64 


124 


167 - 189 


214 


IS 


67 


98.6 


131 - 151 


170 


16 


61 


78.2 


106 - 120 


13S 


17 


4S 


62.0 


84.8- 96.1 


108 


18 


40 


49.3 


87.9- 76.8 


85.8 


(English gages) 


8 B.W.G. 


165 


792 


1.050 -1.200 


1,330 


10 B.W.G. 


134 


522 


698 - 797 


894 


12 S.W.G. 


104 


314 


427 - 487 


551 


13 8.W.G. 


92 


256 


337 - 383 


436 


14 SW.O. 


80 


194 


256 - 292 


330 


18 B.W.G. 


65 


128 


171 - 195 


320 




0.001 0.003 0.003 0.00< 
SloncatlOB 

Fio. 5. — Stree»«traio curves of No. 9 
A.W.Q. hard-drawn copper wire (Water- 
town Arsenal teat). 



70. 8tr«H-itz»ln d& 
granu. A typical streea-atra 
diagram of hard-drawn eopB 
wire is shown in Fig. 5. wan 
represents No. 9 A.w.G. T1 
curve a« is the actual strai 
strain curve; a6 represents t! 
portion which oorreaponda 
true elasticity, or for wU 
Hooke*s law nolds rigoroual 
ed is the tangent to ae. Wu 
fixes the Johnson elastic liml 
and the curve qT repreaea 
the set, or permanent oloiM 
tion due to flow of the naa[ 

* The Johnson elastic linoit 
that point on the str ess atn 
curve at which the natural ta 
gent is equal to 1.5 timett ^ 
tanifent of the angle of f 
straight or linear portion of t 
curve, with rei«>ect to the ■: 
of ordinates, or Y axis. E 
Johnson, J. B.. "Material* 
Construction." John WIlav 
Sons, New York, 1912. 



250 



Digili 



i.jv^iuuyie 



PROPERTISS OP MATBRIALS 



S«c. 4-71 



uder strefls, beins the difference between ab ftnd tu. The teet length wae 
id in. *nd the eloncktion *t rupture wu 1.3 per cent. The true elwtio 
linit was 27,000 lb. per sq. in. or 44 per cent, (rather low, below averase) 
If the ultimate tensile atrencth; Johnson elastic limit, 44,0001b. per sqTin. 
«72 per cent, of the ultimate; ultimate tensile streii(tb, 61,400 Tb. per aq. 
ia.: modulus (Younc'a) o( elasticity, 17,500,000. 

A seriea of atrase-strain curve* on annealed, half-bard, and hard copper 
tirta was published in 1904 by Mr. F, O. Blackwell in a paper entitled " Con- 
hrtors for Long Spans," Trans. International Elec. Cons., St. Louia, 1004. 
W. n, p. 331. 

Tig. 6 shows a stress-strain diagram, from Mr. Blaekwell'i paper, for 
i*mp-centre. hard-drawn, concentrio-lay, copper cable composea of six 
9.16^in. strands. The curve A is for the cable, and B for one of the strands. 
Tlie elastic behavior is notably dilTerent from that of solid wire, since the 
irtnal elongation of a new or previously unstressed cable appears to comprise 
two components, one due to tightening or readjustment of the outer strands 
around the core, sod the other to actual stretching of the material. 



nm 










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C J J Jl 4 .» .« .t .S .1 t.0 U Li U LI M 



tta. 6. — Stress-strain curve for hemp-centre, ooncentrio-lay, six-strand, 
hard-drawn copper cable. 

n. Zlaitie limit and ylsld point. The stress-strain eurve* for an- 
nealed copper show that it has no very definite elastic limit and in fact com- 
menees to set (flow under stress) at comparatively low stresses; it also has no 
yidd point, i.e., a point at which a marked increase in elongation suddenly 
takes place with little or no increase in load. Copper of medium or of full 
hardness behaves differently and exhibits a fairly definite elastic limit, but 
no yield point. 

The rate of application of the load also playa an important part in the re- 

sulta. When given sufficient time, hard copper takes a set before it reaches 

the dastic limit. In the strictest meaning oithe term, copper probably has 

f/ no sbaoluteljr definite elastic limit whatever. What is oroinariiy meant by 

' elastic limit is the value obtained in tests made in a specified manner and 

I at a definite rate of loading, such as outlined bv the American Society for 

'• Testing Materials. The stress-strain curves also show very plainly that 

' the oltimate elastic limit ia raised by stressing the material' Deyond the 

initial elastic limit, or giving it a set. 

Since annealed copper wire receives some hardening by handling, and also 
,' by stressing under ordinary safe loads, it is customary to assume that it has 
a f juriy hign elastic limit, one of the accepted values being as high as 85 per 
eent. of the ultimate strength.* Accepted values for half-hard and full-hard 
I copper range from 50 per cent, to 65 per cent, of the ultimate, being higher for 
g e iiea which have had the most drawing. A conservative value for copper of 
mil degrees of hardness is 50 per cent, to 55 per cent., never excesoing 60 
per cent, as a maximum for small wires which have had many reductiooa in 
ar»«ing. 

* Report of Committee on Overhead Line Construction, N. E. L. A.. 181 1 ; 
p. 173 (Appendix A). 



261 



yGoogle 



Sec. 4-72 



PROPERTIES OP MATERIALS 



n. VatUrus undor load. Under long^ustained loads approaching the 
normal tensile strength* copper has somewhat less strength tnan the values 
obtained by ordinary test. Mr. F. O. Blackwell, in the paper referred to in 
Par. TO, found that a 0.168-io. hard-drawn wire stressed to 54,000 lb. per 
sq. in., stretched continuously, and broke in 7 days, 8 hours; pieces of the 
same wire afterward broke at 61,000 lb. in the testing machine. He concluded 
that a hard-drawn wire would stand continuously a stress of about 80 per 
cent, of its normid tensile strength. 

n. Toun^'a modulus of elasticity for annealed and hard copper is 
not a very definitely known quantity and the values given for it fluctuate 
over a considerable range. This may be accounted for, in the case of annealed 
copper, by the lack of any very definite elastic limit, and the fact that the 
imtial stress-strain diagram departs at a very early stage from Hooke's law; 
and as soon as a slight load has been applied the properties commence to 
change. The same difficulties are present, in less degree, in the caae of 
hard-drawn copper. In all cases, the final value of the raodiilus, after slxesa- 
ins, is almost invariably greater than the initial modulus. The following 
vuues represent the extreme range, and a probable average, drawn from sev- 
eral authorities,* expressed in in-Ib. measure. 



Steta 


Range 


Probable 
average 




7X10«tol7X10« 

sxio«to lexio* 

13X10«tol9X10« 
lOXlWto UXIO" 


12X10« 
9X10« 
16X10« 
12X10> 


Annealed coDcentrio strand 

Hard-drawn wire 


Hard-drawn oonoentrio strand 



It. Speeiflo heat of copper is not independent of temperature. The f ol - 
lowing values were taken from "Tables Annuelles de Constantes et Don- 
n£es Num£riques de Chemie, de Physique et de Technologie" (For 1010; 
University of Chicago Prees, 1912), p. 60. 

Speoifio heat, at -SO deg. cent 0.0S62 

Specific heat, at deg. cent 0.0910 

Speoifio heat, at +50 deg. cent 0.0928 

Specifio heat, from 2.4 to 21.6 deg. cent 0.09165 

Specific heat, from 17 to 100 deg. cent 0,0925 

The Bureau of Standards gives, for the range from 15 to 50 deg. cent., the 
ezpreaaion 0.0917-1-0.000048 ((-25); this is in terms of water at 20 deg. 
cent. For values at high temperatures see Hoffman, H. O. "Metallurgy of 
Copper;" p. 7. 

TS. Thermal eenduetlTlty of copper is a function of temperature, as 
expressed in the formula Xi ■■ X« (1 + of). The fallowing values of thermal 
conductivity, in g-cal. (cm-cube) per sec. per deg. cent, were determined by 
Lorens.t 

Thermal conductivity, at deg. cent 0.7180 

Thermal conductivity, at 100 deg. cent 0.7226 

Temperature coefficient, from and at deg. cent 0.000051 

Hoffman states the thermal conductivity aa 0.72 g-oal. Ccm-cube) per deg. 
cent.; Langmuir gives 0.84 g-oal. for commercial copper and 0.92 g-cal. for 
pure copper. 

TC. Properttai et copper at very high temperaturea. See a paper by 
Carl Hering, "The Proportioning of Electrodes for Furnaces, Trans. 
A. I. E. E.. Vol. XXIX (1910), pp. 485 to 545. Also covers carbon, 
graphite and iron. 

TT. Bpeelfleatloiu for copper wire, annealed, medium hard and hard 
drawn, have been adopted by the American Society For Testing Materials 

' Blackwell, F. O. "Conductors for Long Spans;" Tram. International 
Elec. Congress, St. Louis, 1904; Vol. II, p. 341. 

Blackwell, F. O. "Long Spans for Transmission Lines;" 7fan«. A. I. E. 
E.,Vol. XXIH, 1904, p. 511. 

"Smithsonian Physical Tables," 5th rev. ed., 1910, p. 75. 

American Steel & Wire Co. ; "Handbook of Electrical Wires and Cables." 
1910, p. 14. 

t "Smitbaonian Physical Tables," 1910; p. 199. 

252 Digilized by VjOOQIC 



PROPERTIES OP MATERIALS 



Sec. 4-78 



ud will b« foand in the ciUTect iwue of the "Year Book." They are too 
Btended for reproduction. 

It. Steadard laotioiu for eoppar tooUey wire are prescribed in the 
■DKifieationa of the A. 8. T. M. (see " Year Book ") and are abown in 
nn. 7 and 8. Theee sections are known reepeetively as "grooved" and 
"Qnre eiKht." Copper trolley wires are always hard drawn, in order to 
j-dnesi 



■cure marimnm hard 



t and Btrensth. 




sciijuis. laajoooiijuis. lu.aoeoibMiu. 

Fis. 7. — "American Standard" grooved trolley-wire sections. 





f-^ 




CItJUJs. UMNClrJiai. 



-.-0.100 ^ 

lW,lM01lJUlI, 




FiQ. 8. — Croes se ctions of figure-eight trolley wires. 
ALUMUUH 

n. GMisral p r ope r tl sa. Aluminum ranks second to copper in its 
importanoe as an electrical conductor, and in some respects is superior to 
ss upu . It is one of the softest and moet malleable of metals, and is nearly 
wfatc, or silver-white, in color. The density depends to some extent upon the 
Vhysieal state, an average value being 2.7. Aluminum melts at 658 deg. 
cent.* (1,216 deg. fahr.}. Molten aluminum is very fluid and care should be 
takes not to overheat it. In the molten state it readily absorbs gsses, but 
spon cooling these occluded gases are partially liberated, giving rise to blow 
hclea in '•«»t;»ip Aluminum boils at 1,800 dec. cent. (3,272 deg. fahr.).t 

like co pp er, aluminum can be cast, forged, rolled or drawn, and also be- 
eoeacs haraened by working, although it requires less annealing than copper 
er brass. By cold rolling and drawing it can be given considerable rigidity 
■ad temper, with accompanying increase in tensUe strength. The general 
aSset of eold or hard drawing upon aluminum is quite similar to the effect 
vpoD copper. 

Alominnm when exposed to dry air is not affected, but in the presence of 
Mosst sir it tarnishes rapidly, the coating consisting of oxide of aluminum 
CAiiOi) or alumina. This coating is protective, so that the corrosion is not 
proposive; the oxide is also very refractory, which accounts for the diffi- 
eol^ of aoldering aluminum. Hydrochlono acid and alkaline solutions 
rcsiuly attack aluminum; concentrated sulphuric acid, hot dilute sulphuric 
acid, and hot nitric acid affect it to a less extent. Sulphur and sulphur 

• Circular No. 7, "Pyrometer Testing and Heat Measurements;" Bureau 
c< Standards. 1«10; p. 4. , „ 

t Pahon, C. H. ''Principles of Metallurgy;" McGraw-Hill Book Co- 
las., New York, 1910; p. 74. 



2S3 



DiyihiOi 



yV^iDUVLC 



Sec. 4-80 



PROPBRTISS OP MATSRIAIS 



dioxide do not affect it at ordinary temperatures; it is not attacked by sul- 
phuretted hydrogen, or carbonic acid. It reaiata the action of sea water 
better than copper, provided there is no electrolyais, but it is a highly elec 
tropositive metal. The presence of impurities in considerable quantities 
lowers the resistance to corrosion in marked degree. There is also dan^ser 
ifrom electrolytic corrosion if aluminum is alloyed with an electronegative 
metal. 

The electrical conductivity of aluminuraj like that of copper, depends onits 
degree of chemical purity. The conductivity of hard-arawn aluminum is 
about 2 per cent, less than that of soft or annealed aluminum. The tensile 
properties, in like manner, depend greatly upon the physical state, being 
much improved by cold rolling and drawing. 

The alloys of aluminum are very numerous. The so-called light alloys, 
containing but small percentages of other metals, are light, bard and strong, 
but do not resist corrosion from galvanic action. The heav^ alloys, or alunni- 
num-bronxea, with but 2 per cent, to 10 per cent, of aluminum, and respec- 
tively 98 per cent, to 90 per cent, of copper, have high tensile strength and 
strongly resist corrosion in air or sea water. A very small proportion of 
aluminum, about 0.01 per cent., added to iron, steel or braaa in casting re- 
moves the oxide and prevents blow holes. 

The tinning process, which is applied to copi>er wires intended to receive 
an insulation of rubber compound (sulphur being present),. is unnecessary 
in the case of aluminum. 

Aluminum poBsesses an insulating film which ordinarily has a dielectric 
strength of about 0.5 volt, and by electrolytic action this value can be 
somewhat increased. 

80. Commercial grades of aluminum. The impurities most com- 
monly found in aluminum are silicon and iron. Silicon in aluminum exists in 
two formSj one seeminsly combined with aluminum as combined carbon 
exists in pig iron, and tne other as an allotropic grapbitoidal modification. 
Small quantities of copper, sodium, carbon and occluded gases are also 
found in aluminum. The Aluminum Company of America classifies alumi- 
num commercially in three grades,* as follows: 

Extra-pure aluminum, No. 1 grade or so-called pure aluminum, and No. 2 
frade for castings, or structural shapCs. The average composition is as 
ollows: 



Aluminum. 

Silicon 

Iron. 



No. 1 



No. 2 



(per cent.) (per cent.) 



09.55 
0.30 
0.15 



90 
2 
2 



Pure aluminum (No.l grade or better) is necessary to secure high electrical 
conductivity, extreme malleability, ductility and maximum resistance to 
corrosion. For other purposes small amounts of copper, nickel, tunesten, 
manganese, chromium, titanium, sine or tin may be aavantageously added to 
aluminum to produce hardness, ri^dity and strength. These metals when 
alloyed with aJuminum do not diminish its resistance to corrosion so much as 
silicon or iron, 

81. Typical analysis. The following analyses nf aluminum are t}i>ical. 



Aluminum j 
Co. of Richards 
A mer. t ' (per cent.) 

(per cent.) I 



Aluminum . 

Silicon 

Iron 



99.57 
0.29 
0.14 



99. 2S 
0.61 
0.04 
0.02 
0.01 



pertips of Aluminum;" Aluminum Co. of America, Pittsburgh, Pa., 
-f^iveaii of Standard,, Circular No. 31, Third Ed., Oct. I, 1914; p. 14. 



* "Propertica of Aluminum 
1909: p 



2S4 



DigilizedbyV^iOOyi' 



PROPBRT1B8 OF MATERIALS See. 4-82 

at. Motfaiodi of worUnc alwmtnwtn are described &t some lenstb in a 
pdblirarton issued by the Aluminum Company of America.* Sections or 
■bapea similar to thoaein which steel is rolled can do made of aluminum and its 
allaya; sheets can be rolled commercially as thin as No. 40A.W.G. Aluminum 
esa ako be stamped, drawn, beaten, spun, forged^ extruded and machined, 
vith suitable methods, tools, dies aiul lubricants. Aluminum can be drawn 
into a ^eat variety of f(tf ms; except for slight differences, the methods used 
in drawing copper wire are applicable. Like most other metals it is hardened 
sadstreogthened by working, and softened again by annealing. The anneal- 
iag temperatures depend on the composition of the metal, but probably Ue 
between the limits of S43 deg. cent. (060 deg. fahr.) and 482 deg. cent. (000 
dcflLcent.}- 

Cleaning or pickling is done by dipping first in bensene and then in hot 
eaaatic alkali (such as caustic soda or caustic potash), in nearly saturated 
sotatioa. UfKin removal the metal should be washed in cold running water 
and next imm rsed in a hot solution of strong nitrio acid, to neutruise the 
caudc. Finally it should be washed in hot running water and then quickly 
dried in hot air; small articles should be placed in sawdust. 

The ordinarv low- temperature solders, containing lead, are not suitable 
icr sfrfderiiu; ajuminum, since the surface oxide will not disaolve under the 
setion of a flux or salt as in the case of copper, tin, or sine. The temperature 
at which solder alloys with aluminum is approximately 340 deg. cent. (660 
dag. fahr.)- It is first necessary to tin the surface of aluminiim bv heating it 
ia s hot flame (blow-torch) and pour over it melted tin or half-and-balf solder, 
bat Richards solder is the best; meanwhile the solder should be rubbed into 
the surface with a fine metal brush. In this way the oxide is melted and the 
•older ia alloyed with the aluminum. After this tinning operation is com- 
idcted, the usual scrfdered joint may be made. Joints in bare line conductors 
are luually made with sleeves or with clamps (see Sec. 11). Clamps are 
abo used for joining aluminum conductors to copper or steel conductors; 
sweated bushing t <u'c employed, of swtable metal to prevent electrolytic 
corroaion in the joint. 

Alaminam rod can be readilv butt-welded by merely pressing the ends 
tc^^ber in the flame of a blowuimp. No flux is necessary for this process. 
It is also possible to weld aluminum by the autogenous process and this 
nethod is generall^jr adopted for jointing plate or sheet. 

It is easy to obtain qmte as good a machined surface with aluminum as any 
other metal. Lubricants should be used only for drilling and screwing and 
then only paraffin. Filing should be done with a single cut file as croasHJut 
fis are readily clogged. Aluminum will take and retain a very high polish, 
Iidly equal to that of silver. 

IS. Denxitr. The value for the density of commercial hard-drawn 
irfaBuaom, accepted by the Bureau of Standards, t is 2.70. The Aluminum 
Comimny of America gives 2.56 for pure east aluminum, 2,66 for annealed 
vbe and sheets, and 2.68 for unannealed wire and sheets. The British 
Alominum Company, Ltd.. ^ves 2.56 to 2.60 for castings, and 2.71 for rolled 
or drawn aluminum. The Smithsonian Physical Tables (5th rev. ed., p. 
9S\ Bve 2.56 to 2.58 for castings and 2.65 to 2.80 for wrought aluminum. 
ThcEneyclopedia Britannica (ed. of 1010, Vol. I, p. 771) ipves 2.583 for cast- 
iB0 and 2.68S for rolled aluminum at 4 deg. cent. Mr. H. W. Buekf gives 
2.68 for sluminnm wire. 

The best average value from the foregcang authorities seems to be 2.57 for 
eastings and 2.60 for sheets or wire. The utter value is in close agreement, 
f or ^igineering purpoeee, with the value 2.70 uaed by the Bureau of Stan- 
*~ ' '■ ■ ■ * ' bles " 



■ and tsJken as the basis of the aluminum wire tables in this section (Par. 

n.)- A density of 2.70 g. per cu. cm. corresponds to 0.00755 lb. per ou. in. 

14. XeaiftlTlty. Much less has been published about the effect of im- 

pwitiea on the conductivity of aluminum than in the case of copper, and such 

. '"Methods of Working Aluminum;" Aluminum Co. of America, Pitts- 
bw^ Pa.. 1000. 

t "ittitnietions for Installation and Maintenance of Aluminum Electrical 
Coadanors;** Aluminum Company of America. 

iCireiilar No. 31; '^Copper Wire Tables'*; 1014; Third Edition, p. 14. 
^ I Bock, H. W. "The Use of Aluminum as an Electrical Conductor; 
Traaa. lat Elee. Congrev, St. Louis. 1004; VoL II, p. 313. 

250 

DglzedbyGoOgle 



Sec. 4-86 PR0PXBTIK3 OF MATERIALS 

information at the present time ia lori^y redded as among the secreta of the 
trade. The ordinary peroentage of impunties in oommerciaUy pure ^umi- 
num. No. 1 grade (see Par. SO), is 0.4S per sent. In terms of the British 
standard for hard-dravn copper at 60 deg. fahr. (IS. 6 deg. cent.) Mr. 
Burkewood Welbourn stated* that a (volume) conductivity of 60 per cent. 
corresponds to 0.71 per cent, of impurities, and a oonductivity of 01.7 per 
cent, corresirands to 0.5 per cent, of impurities. 

The Aluminum Company of America stateef that the electrical (volume) 
conductivity of pure (No. 1 grsde) aluminum is about 62 per cent, in the Mat- 
thiessen standard scale. The British Aluminum Company, Ltd., gives 
(June, 1914) the following values of resistivity, expressed in microhm-cm. 



^ 





Annealed 


Hard- 
drawn 


Volume resistivity, microhm-cm. at 60 deg. fahr. . . 
Volume resistivity, miorohm-cm. at 32 deg. fahr. . . 


2.770 
2.610 


2.870 
2.70 



The Bureau of Standards} gives the following average values of resistivity 
for conunerdal hard-drswn aluminum. 

Mass resist! vity,*ohnis (meter, gram), at 20 deg. cent 0.0704 

Mass resistivity, ohms (mile, pound) , at 20 deg. cent 436 . 

Mass per cent, conductivity 200.7 

Volume resistivity, microhm-cm., at 20 deg. cent 2 . 828 

Volume resistivity, microhm— in., at 20 deg. cent 1.113 

Volume per cent, conductivity 61.0 

Density, g. per cu. cm 2.70 

Density, lb. per cu. in. 0.0078 

Theee values given by the Bureau of Standards are the basis of the alumi- 
num wire tables in Par, 87. Since aluminum is very rarely used as an 
electrical conductor in the softstate, theforegoing values given by the Bureau 
of Standards, for hard-drawn wire, have the moet commercial significance. 
Annealed aluminum, however, is used abroad for the conductors of under> 
ground cables. 

M. TemperatiiTa eoaflloiant of reiiitenM. On the authority of the 
British Aluminum Company, Ltd., the temperature coefficient of resistance 
of aluminom, for constant mass, varies from 0.0032 to 0.<X)40 per des. 
cent, and from 0.0018 to 0.0022 per deg. fahr. 

A determination made in the laboratory of the Westinghouae Electric and 
Manufacturing Company, under the direction of Prof. Charles F. Scott, gave 
as the average coefficient between deg. and 50 deg. coot., the value 0.00388 
per deg. cent. ; in the fahrenheit scale the equivalent of this value is 0.002 16 
per deg. Prof Scott's determination is quoted by the Aluminum Company 
of America. 

The Bureau of Standards gives 0.0089 per deg. cent, at 20 deg. cent, 
(circular No. 31, Third Edition, 1914, p. 14.) 

M. Alnminnm wire tablaa. The complete tables for aluminum wire 

S'ven in Par. BT wore taken from circular No. 31, Third EcUtion, issued by 
le Bureau of Standards, and are based on a volume conductivity, in terms of 
the annealed copper standard, equal to 61.0 per cent. 

Aluminum wire is practically never used in single strands for overhead 
oonstniotion, but the tables are very useful in computing the resistance of 
concentric strand. In commercial practice the aluminum delivered under 
contract varies in conductivity from 60 per cent, to 62 per cent, of the former 
Matthiessen standard, many contracts being placed at 61 per cent. 

* Welbourn, B. "Insulated and Bare Copper and Aluminum Cables for 
the Transmission of Electrical Energy, with Special Reference to Mining 
Work;" TVan*. (British) Institution of Mining Engineers; 1013. Gives 
bibliography on aluminum wire. 

t "Fropertiea of Aluminum;" Aluminum Company of America, Pittsbursh, 

Pa., IOCWTp- 27- 

X Ciroalar No. 31, "Copper Wire Tables;" 1914; Third Edition, p, 14. 

256 

Digili^edbyV^iOUyie 



PSOPKRTIBa OF MATERIALS S«e. i-87 

TaMa of kard-drmm «lnmlinim wit* at M d«c- o«ot. 

Engliah Units: Amerioan Win Qage (B. AS.) 





d 
z 

■ 

3 


E& 
Q- 


Craw-Mction 


Ohma 

p«r 1000 

feet 


Ponndi 
per 1000 
^eet 


Pounds per 
ohm 


Feet per 
ohm 




Circular 


Sqnare 




3 


mib 


incbe* 












000 401. 


212000. 


0.166 


0.0804 


195. 


2420. 


12400. 




000410. 


168000. 


0.132 


101 


154. 


1520. 


9860. 




00 365. 


133000. 


0.109 


0.128 


122. 


957. 


7820. 




3». 


106000. 


0.0629 


0.161 


97.0 


602. 


6200. 




1289. 


83700. 


0.06S7 


0.203 


76.9 


379. 


4920. 




Z2S8. 


66400. 


0.0521 


0.256 


61.0 


238. 


3900. 




3229. 


52600. 


0.0413 


0.323 


48.4 


150. 


3090. 




*;f>4. 


41700. 


0.0328 


0.408 


38.4 


91.2 


2450. 




5 IS2. 


33100. 


0.0260 


0.514 


30.4 


59.2 


1960. 




e 162. 


26300. 


0.0206 


0.648 


24.1 


37.2 


1540. 




7 144. 


20800. 


0.0164 


0.817 


19.1 


23.4 


1210. 




8 128. 


16600. 


0.0130 


1.03 


16.2 


14.7 


970. 




9 114. 


I3I00. 


0.0103 


1.30 


12.0 


9.26 


770. 




loioe. 


lOMO. 


0.00815 


1.64 


9.55 


5.83 


610. 




11 91. 


8230. 


0.00647 


2.07 


7.57 


3.66 


484. 




12 81. 


6530. 


O.0OM3 


3.61 


6.00 


3.30 


384. 




13 72. 


5180. 


0.004O7 


3.29 


4.76 


1.45 


304. 




U M. 


4110. 


0.00323 


4.14 


3.78 


0.911 


241. 




15 S7. 


3260. 


0.00256 


6.22 


2.99 


0.573 


191. 




Ifr 51. 


2580. 


0.00203 


6.59 


2.37 


0.360 


152. 




17 45. 


2060. 


0.00161 


8.31 


1.88 


0.227 


120. 




Ig 40. 


1620. 


0.00128 


10.5 


1.49 


0.143 


95.5 




19 3«. 


1290. 


O.OOIOI 


13.2 


1.18 


0.0897 


75.7 




10 32. 


1020. 


0.000802 


16.7 


0.939 


0.0564 


60.0 




21 28.5 


810. 


0.000636 


21.0 


0.745 


0.0358 


47.6 




H 25.3 


642. 


0.000505 


26.5 


0.991 


0.0223 


37.8 




23 22.« 


609. 


0.000400 


33.4 


0.468 


0.0140 


29.9 




24 20.1 


401. 


0.000317 


42.1 


0.371 


0.00882 


23.7 




25 17.9 


320. 


0.000252 


53.1 


0.295 


0.00555 


18.8 




2« 15.9 


254. 


0.000200 


67.0 


0.134 


0.00349 


14.9 




27i 14.2 


202. 


0.000168 


84.4 


0.185 


0.00219 


11.8 




28l I2.t 


100. 


0.000126 


106. 


0.147 


0.00138 


9.39 




29 11.3 


127. 


0.0000996 


134. 


0.117 


0.000868 


7.45 




30 19.0 


101. 


0.0000789 


16. 


0.0934 


0.000646 


5.91 




31 (.9 


79.7 


0.0000636 


213. 


0.0733 


0.000343 


4.68 




32 8.0 


63.2 


0.0000496 


269. 


0.0681 


0.000216 


3.72 




33 r.i 


50.1 


0.0000394 


339. 


0.0461 


0.000136 


2.95 




S4 4.3 


39.8 


0.0000312 


428. 


0.0365 


0.0000854 


2.34 




10 S.» 


31.5 


0.0000248 


540. 


0.0290 


0.0000537 


1.85 




v\ .s.o 


25.0 


O.OO0O196 


881. 


0.0230 


0.0000338 


1.47 


37l 4.5 


19.8 


0.0000156 


858. 


0.0182 


0.0000212 


1.17 


as *.o 


15.7 


0.0000123 


1080. 


0.0145 


0.0000134 


0.9* 


.w J.s 


12.5 


0.00000777 


1360. 


0.0115 


0.(l<XKXI84fl 


0.73! 




1 (fl J.I 


9.9 


1720. 


0.0091 


0.00000528 


0.581 



U. Alomlnnm eabi* tables are vven Id the foUowiog pai-ssraph. The 
Taluee of reaistance and weight per 1,000 ft. are 2 per cent, greater than for a 
•olid rod equal to the combinea croae-sections of the wiree of the cable;* this 
increment correeponds to a pitch of 15.7. The component wiree are asfrtimed 
U> have the aame valne of realativity a« the hard-drawn aluminum in Par. 
or, temperature differences being lUlowed for. .'■lee Par. SB to 09 on the 
general properties of concentric sUands. 



IT 



257 



yGoogle 



See.4-gg 



PKOPBSriBS OP MATBRIALS 



m. 



Tabto of bara ooneantrlo-Uy eftblei of hard-drawn alumlaun 

(EncUih Unita) 



» 



Circular 


A.w.a. 


Obm* per 1,000 ft. 


Pounda 


Conoentrie 
•tranding 






I 


O.S 


a 


mils 


No. 


26 deg. pent. 


65 dec. cent. 


uSxtt. 


•s 


.SJ! 

"Si 






(77 dec. fahr.) 


(149deg.falir.) 




6 


1= 












S 




8 


1,000,000 




0.0177 


0.0204 


938. 


37 


164.4 


IISI 


900,000 




0.0197 


0.0227 


844. 


37 


156.0 


looa 


800,000 




0.0221 


0.0255 


760. 


37 


147.0 


102S 


700,000 




0.0253 


0.0291 


667. 


87 


137.6 


003 


600,000 




0.0295 


0.0340 


663. 


19 


177.7 


800 


500,000 




0.03S4 


0.0408 


469. 


19 


162.2 


810 


400,000 




0.0442 


0.0510 


375. 


19 


145.1 


72S 


300,000 




O.OS90 


0.0680 


281. 


19 


126.7 


630 


300,000 




0.0590 


0.0680 


281. 


7 


207.0 


021 


250,000 




0.0707 


0.0816 


235. 


7 


188.0 


667 


312,000 


0000 


0.0834 


0.0962 


199. 


7 


174.0 


623 


168,000 


000 


0.1063 


0.1214 


168. 


7 


154.9 


465 


133,000 


00 


0.1330 


0.1533 


126. 


7 


187.8 


414 


106,000 





0.1668 


0.1924 


99.4 


7 


123.1 


369 


83,700 


1 


0.2113 


0.2436 


78.5 


7 


100.8 


327 


66,400 


2 


0.2663 


0.3071 


62.3 


7 


97.4 


292 


62,600 


3 


0.3362 


0.3876 


49.3 


7 


86.7 


260 


41,700 


4 


0.4241 


0.4890 


39.1 


7 


77.2 


232 


33,100 


5 


0.5343 


0.6160 


31.0 


7 


68.8 


206 


26,300 


6 


0.6724 


0.7753 


24.7 


7 


61.3 


184, 



N. Balnforead (iteel oantra) aluminam eoneantrte itraad. A 

eoncentrio atrand conaiating of aix hard-drawn aluminum wires laid. over a 
centre or core conaiating of a calvsnixed ateel wire lias been manufactured 
to a very limited extent, for experimental uae. The ateel employed had a 
tensile atrength of about 125,000 lb. per aa. in. On account of the different 
coefficients of expansion, with these metaia, the diatribution of atreases in a 
suniended cable under changing temperature conditions ia quite complicated. 
in another instance the core was composed of 7 strands of ateel laid into a 
eoDoentrio cable; about this were laid atranda of hard-drawn aluminum. 
The tenaile atrength of the ateel was about 220|000 lb. per aq. in. and the 
atrength of the aluminum waa 28.000 lb. per aq. m. This type of 'conductor 
waa uaed in a ! .000-f t. ravine epan. See BUetrieal ATeuw, Vol. XXII, p. 34; 
alao The Canadian Bnoineer, Dec. 11, 1913, " Trans m ission Line Work;" by 
E. V. PanneU. 

tl. Coafflelant of Unatz axpaailon. The value given by Sir Roberts- 
Austen for the linear ooefficient of expansion is 0.0000231 per deg. cent, from 
to 100 deg. cent.; the correaponding value per deg. lahr. ia 0.0000128. 
The value per deg. cent, given by the British Aluminum Company ia 
0.0000234. The 5th revised edition (1910) of the "Smithsonian Physical 
Tablea" (Fowle, F. E.) gives the coefficient as 0.(X)002313 at 40 deg. cent.; 
the mean value between and 100 deg. cent, is 0.0000222 per dec cent. 

t>. Taniile itrsnsth. The tensile strength of aluminum depends upon 
its state, previous working and beat treatment. The strength of aluminum 
ia increased by cold working, as in the case of copper. The approximate 
range of tenaile atrength of aluminum in varioua forms is given next below, 
in lb. par sq. in. (Aluminum Co. of America). 



258 



yGoogle 



PBOPBRTIES OF MATERIALS 



Sec. 4-93 



12,000 to 14,000 

24,000 to 40,000 

tm 28,000 to 40,000 

Wire 25,000 to 65.000 

The tenule >treiictli of aluminum wire, in the siiee used commercially, 
nat« from 14.000 to 33,000 lb. per aq. in., depending upon the size of the 
wire and upon its meehanical and neat treatments. Raro-drawn aluminum 
vn, in the sises nsaally employed in the construetion of concentric cables, 
laiM from about 23,000 to 27,000 lb. per sq. in. It is poaaible to produce 
ksrd-drawn wire of greater strength than this, but it is likely to be short" 
■r brittle and is not satisfactory commercially. 

Tbe British Aluminum Company. Ltd.. civee the following table showing 
the strength of progreeaire sises of hard-drawn wire, which is practically 
the same as the range stated by the Aluminum Company of America. 



8.W.G. 
No. 


Diam. 
(in.) 


Tensile 

strength 

(lb. per sq. in.) 


8.w.a. 

No. 


Diam. 
(in.) 


Tensile 

strength 

(lb. per aq. in.) 


2 

4 
« 
8 


0.500 
0.400 
0.324 
0.276 
0.232 
0.192 
0.160 


22.000 
23,000 
23,000 
23,000 
24,000 
24,000 
26,000 


10 
13 

14 
16 
18 
20 


0.128 
0.104 
0.080 
0.064 
0.048 
0.036 


25,000 
26.000 
27.000 
28.000 
29.000 
32,000 









Soft or annealed aluminum is never used in overhead spans, but is used to 
WBe extent for underground cables. 

Coneentrie cables have a breaking strength somewhat less the sum of the 
Ireakjng strengths of the strands, not usually exceeding 85 to 90 per cent. 
If the latter. Theoretically the strength of conoentric-lay cable is a fu nction 
«( the pitch. 

n. Waitir limit. Undo' the definition of Hooke's law, aluminum 
has no definite elaatio limit, because it stretches under load, if the load is held 
eeastant for any appreciable length of time. See streea-strain diagrams in 
Fiia- 9and 10. Taking as the definition of elastic limit, the maximum load 
sader which the material win not continue to stretch, it can be stated that 

the elaatic limit of hard-drawn 
wire will range from about 
13,000 to 17,000 lb. per sq. in., 
or from 50 to 60 per cent, of 
the ultimate tensile strength. 











' 




' " 1 


__ 












~ ^1 


^«I 


/'' 












\mm 


' f 












'iw 


\r 












iZ 


'7 












l» 


/ 












iz 


/ 












iZ 


/ 












iH 


/ 


























f 














§111 

3 rf d < 


39i 

t 3 4 < 


M 


l\ 




3 3 s i 

d d €> d 




tl ISM lTlllll>»l»* 

Ra. 8. Btrtss strain diagram of hard- 
drawn alomiaum wire. 



0.4 o.e 

EluiCMloD Ptr cmt 



Fio. 10. — Str es s s t rain diagram of 
bard-drawn aluminum wire. 



H, 111 Ml iliilii dlagraTni of hard-drawn wire are given in Figs. 9 
ud 10. The wire represented in Ti%. '9 was 0.162 in. in diameter, eold- 
*a«n from a 0.376-in. annealed rod. Fig. 10 shows a wire of 0.2037 in. 
, the test length being 60 in. The figures associated with the arrows 



3S9 



cdby^iuuynj 



> 



Sec. 4-05 PROPXRTixs of materials 

indioAte the number of minutes the load wee held at each of several points. 
This apeoimen broke at 23,900 lb. per sq. in., with an elongation of 1.25 per ' 
oent, 

tS. Xlony atlon at rupture. The total elongation at rupture, for bard- 
drawn wire in commercial sisce, ranges from about 2 to 4 per cent. 

M. Tonav't modulus of •lutlettj in tension ranges from 8,000,000 
to 12,000,000, with an average of S.000,000 to 10,000,000. F. O. Black well 

Sives the modulus for concentric cables as 7,600,000 (Trans. Int. Elee, Cone., 
t. Louis, 1004, Vol. II, pp. 331-347). 

•T. Bpaeille haat of aluminum at deg. cent, is 0.2080 and at 100 deg. 
oent. is 0.3228; the mean specific heat between 16 and 100 deg. cent, is 0.2122 
(5th rev. ed., "Smithsonian Phys. Tables," p. 228). 

M. Thormal conduotMtr of aluminum at deg. cent, is 0.344 gnun- 
calorie (em-oube) per deg. cent, per see., with a temperature ooeffioient of 
0.00054 per deg. oent ("Smithsoman Phys. Tables," 1910). 

M. Altimlmim ban ore used in power-plant switchboard eonaeetiona 
for bus bars, and for carrying very large currents in electrolytic work. 8inc« 
bus bars are generally designed to have a stated carrying capacity limited 
by a stated temperature rise, the comparative cross-sections of aluminum 
and oopper are not required in praoticeto be in inverse ratio to the respective 
oondttcnvities, because of the difference in radiating surface. 

COPPKB-CLAD STUL 

100. Compound or bi-metalllc wires composed of copper-oovered 
iron or steel have been manufactured by a number of different methods, and 
were first attempted many years ago. Aluminum-covered steel has alao 
been tried, on an experimental scale. The general object sought in the 
manufacture of such wires is the combination of the high conductivity of 
copper or aluminum with the hi^h strength and toughnees of iron or steel. 
The resulting conductor is obviously a compromise between copper (or 
aluminum) and iron, being inferior as a whole to the former and superior to 
the latter. 

101. Union batwaon the metals. In the early attempts to produce 
bi-metallio wires, the two metals were not welded, but merely in close 
physieal contact. Clonsequently there was a marked tendency toward 
electrdysis wherever moisture and air had access to the junction between 
the disvmilar metals. No great sucoess attended the use of such wires until 
modern processes were developed for effecting a weld or molecular union 
between the metals. 

IM. Copper-dad steel wire is manufactured by two processes, known 
as the Monnot proeeaa (Duplex Metals Co.) and the OrllBth process 
(Colonial Steel Co.). The Monnot process consists briefly of dipping a mild 
steel billet in bath of molten copper maintained at high temperature, thus 
forming on the surface of the billet an iron-copper alloy; the billet is then 
withdrawn and placed in a mold, and a copper jacket is cast around it. 
The billet is then re-heated and hot-rolled to wire rods, and finally cold- 
drawn to wire. 

The Griffith process consists briefly of coating a mild steel billet with 
copper by electrolytic deposition (Sec. 19), then inserting the copper-coated 
biuet in a copper tube, closing the ends, and heating the compound billet 
preparatory to rolling; it is then hot-rolled to rods, and cold-drawn to wire. 

IM. Commercial grades of copper-clad steel wire. It has become 
customary commercial practice to rate coppei^clod steel wire in terms of the 
ratio of its volume conductivity to copper. Thus one manufacturer mokes 
three grades of wire, having respectively 30 per cent., 40 per cent, and 47 
per cent, conductivity ratio to copper; another manufacturer has stand- 
ardised a 30-per cent. wire. These ratios are usually average ratios, and in 
practice certain tolerance limits must be recognised, above and below the 
average; or else the rated conductivity can be specified as the absolute 
acceptable minimum. 

280 

Digitized by VjOOQIC 



PROPERTIES OP MATERIALS 



Sec. 4-104 






1 I t^ 

o g 



a 

;s 



ntk 



••b 



E 
.a 
O 



E 
O 



Sb 



ib 



a.tS 



B 
O 






I 



C •-' * 



ooo 1-tM^ oio«co ^u)t^ o>i-<^ ooeoa 



8 Oh 



ootoe4 oot*t« oocoio to 

oeoh> (Hto^ cguSo b-*-to «o^o> i^ioc) 

•^*4,^ C40K0 ^tO«D 00<-«-««< t^Mt« *0 ^ CO 

odo odd odd d^^^ ^<n« eoVw 



r»o« iai4t<- lOQb- _ _ 

C4«0 I0C4O — fli«-i eS-H>0 wot* MCflO 

'Hi-m NCO^ >0000 0090 OOC4 •-)C90 

odd odd GCi^ fH-HfH cicieo ^>od 



Ocoo onn t«h> 





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sss 


s;?s 




S^S 


ooo 


ooo 


oo-< 


rt-l« 


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iSS S§i §88 SS8 K8S 22S 

" t-OOO «OM OO^Cl CiXO lO'^eO 

UJ'I*^ CONN »-*»-i.-i 



|Sn $o1 



sSS ONO Son SSoo 



^.^ 



(^ Z: 









Q 



S 






0> t*)0^ OONi-^ eo<ou3 



w3.-i^ K>Q«o aor*N eowo oora oo^*- 
or*t^ a>«oo ^^0* b-«OTi" ccnn ^^-i 
«oveo N«»H ^^ 



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<-<<0P0 



oaiSs 
M3;OM 

ooo 



■*«« -^NN t*t!0 

N«00 'CN-' gOOON 

Or«0 NOOtC OCON 

N^M tooo nooo 

•o-veo NN^ »H^ 



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ftooo onto '^no oeo 

o^ ^o>r* o^<-> N'V 

OO N00*O NO" " 

^^eO CONN NN 



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,. . — ■^^O ON-t 
«,,« -0§ MgJ 



OOO ooo ooo ooo ooo ooo 



go o»-»ff* ^^^•o «eh-» oO"-! 222 



261 



,Gopgle 



Sec. 4-105 



PROPERTIES OP MATERIALS 



\ 



1^ 
ia 

8 o 

II 

I 



-5 
o, , 

a' 

i 

.9 



all 






ni 
m 



Is 



2§ 



a 
8-5 

li 



a 
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'I 



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s 




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ooo 


ooo 


o 








onN 


sss 




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ooo 


ooo 


o 


sss 


sll 


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ooo 


ooo 


o 


%ll 


ogo 


S 




















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oiaio 




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M-^»H 




r>c>4c^ 


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lli!£S 


■*«« 




ooo 


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cooot^ 












ssS 






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3S!3 


K.^^ 


QO 








ooo 


ooo 


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Men 


Hi 


H 


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o 


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geo^ ^(or^ 9^v C40O 
oo ooo 0^*4 cte^a 

odo odd odd do 



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> oo .-t«^ 



ooo ooo ooo 



do 



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^(Ot* nc^u) tctD-4 



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ooftoo t*tco lOio^ con 
^do do'd ddd oo 



—B 



262 



yGoogle 



PROPBRTIBS OF MATKRIAL8 SeC. 4-106 

UN. PropertiM of coppar-cUd tt«al wira depend upon the raUttire 
•nportinuie of copper and steel, the constituents of the latter, the mechanical 
hrtment and the heat treatment. The cold-drawins process hardens the 
rtsel core to an unpermisaible degree and it becomes necessary at intervals 
1l anneal it before proceeding further with the drawing process. The com- 
Mrcaal grades are obtainable either dead soft (annealed) or hard drawn, as 
iHcred. The properties of the commercial grades of wire are given in 
Pkr.lM and IM, taken from the manufacturerir tables. In drawing speci6- 
CitiooB it is customary to fix tolerance limits, or else minimum (or maximum) 
faha. For technics articles dealing with the properties of copper-clad 
Mad wire, see the following: BUdrical World, Vol. LII. pp. 701 and 818; 
tciatific AmfTiatn, Vol. XCVIII, p. 347; Iron Age, Vol. LXXVIL p. 62; 
imtnud o/ InduMtriai and Bngintering Chemittry, Sept.. 1909; Electrical 
ftrld. Dec. 22, 1910, Dec. 29, 1910 and Jan. 12, 1911; Teitphme Bmiinter, 
Act, 1910 to July, 1911, inclusive. Proceedings A. S. T. M., Vol. X, pp. 
nO-2»t: Tdeiilumt Snginetr, Dec., 1911 to Mar., 1912, inclusive. 

ItT. T«inp w»tui e eoe£ftoi*nt of raditknoe of the 40 per cent, grade of 
tner-dad steel is approximately 0.0045 per deg. cent., from and at xero. 
Toe coeffident ranges from about 0.004 to 0.005, aepending apparently upon 
Oe eonstitaeDts of the wire and its physical condition. 

IM^ PaniMablUtr of steal core is about 70, for small magnetising foroea 
IM SOO cycles per sec; at power frequencies it is from 100 to 125. Tha 
]r--'-ni-T permeability will be from 600 to 800 at roughly 5,000 gausses. 
fAe measured hysteresis loss in the core of No. 1 A.W.O. wire^ at 10.000 
■PBBSS (max.), was 15,000 ergs per cu. cm. per cycle. The resistivity of the 
«d will range from 12 to 13 nucrohm-cm. at 20 deg. cent., approximately. 
iSv method of calculating internal inductance see Blectrical Warn, 1910, V<u. 
XVI. p. 1521. 

IM. CoafBdant of Unaar ezpaaiion of the 40 per cent, grade of eopper- 
dtalatael is 0.0000129 per deg. cent. 

UiL Tba daosttj or specific gravity of copper-dad steel depends on the 
jtdbtrrc proportions of copper and sted. The 40 i>er cent, grade has a den- 
■ty of 8.2. 

i UL Taaalla itransth of oopper-dad steel denends in great measure 
iwon the kind and conmtion of steel in the core. The strength of the whole 
•Be wiB range as high, as 80,000 to 1(X),0(X) lb. per sq, in., hard-drawn. The 
tjpiesl ■tiaaa-straln diacram is similar to the curve for hard-drawn copper 
IS Kg. 6. The breaking loads are given in the tables. Par. 104 and l0(. 

Ul. Toonc'i modulus ranges from 19X10' to 21 X 10* lb. per sq. in. 
lor ksrd-drawn wire and ISXIO* to 20X10* for conoentric cable. 

lU. SpocUcatiani for copper-dad steel wire will be found in tha 
"HanoaT" of the Railway Sisuial Association. Also see "Handbook of 
Orcrfacad Line Construction," N. K. L. A. 

IBON AHD STUL 

UC Oanaral proparUei of iron and steel are covered in detail in another 
potion of this section, under "Structural Materials." The so-called iron 
win is usually steel, containing carbon^ manganese and silicon. The effect 
of these constituents on the resistivity is discussed in Par. 116. In general, 
&ose elements which increase the tensile strength of steel also increase its 
reastivity; similarly, the mechanical and heat treatments which increase 
theatrmgth. again increase the resistivity. 

lU. Baa UU fl ty of iron. The researches of Barrett, Brown and Bad- 
faM (Scieot. Trans. Royal Dublin Soc, VII, Ser. 2, part 4, 1900; Jour. 
list Elee. Kag., 31, p. 674, 1902) on the dectrical and magnetic properties 
<< inn and iron alloys are especially important. They found that Swedish 
cksrcoal iron containing 99.85 per cent, iron bad a resistivity of 10.2 



These investigators also found that 1 per cent, of any element added to 
pwe iron increased its specific resistance by an amount approximately 
fropertJonai to the specinc heat or inverady proportional to the atomio 
"^^ of the alloying dement. . 

TeascB gives the following values for different grades of annealed iron 
(ne BaUetm Na 72, Ens- Exp. Sta., Univ. of 111.), in miorobm-om. at 20 deg. 



908 



DigilizedbyCOOgIC 



Sec. 4-116 



PROPBRTISS OP MATBRIALS 



Eleotrolytio iron melted in tsnto 9,S 

Swedish charooal iron remelted in taeuo lO, 8 

CommeroiKl grades: 

Swedish charooal iron out from plate 10. fl 

Standard transformer steel 11.0 

Silioon (4 per cent.) steel 51 . 1 

Hopkinson tested and analysed 35 different samples of iron (PhU. Train 

?. 403, Part If, 188S) and found resistivities (mierohm-em.) ranging froi 
3.78 for wrought iron to 100 for oast iron. 

Also see Bouaouard, O. "Electric Resistivity of Special Steels," IX, 6, N< 
10, Sixth Congress Int. Assoc, for Testing Materials, New York Citj 
1912. 

lU. Preeea't tetU on reiUttvitr of annaalcd iron wlro 
(Munroe and Jameson) 




IIT. KSecta of dIBaront aUoylng alementa upon the ralitiTlty o< 
pur* iron were found by Barrett to be as follows: the values pven in the 
table represent the increase in resistivity (microhm-cm.) resulting from the 
addition of 1 per cent, of different alloying elements. 





2.0 
3.0 
3.5 
6.0 




5.0 ^ 


Cobalt 




8.0 
13.0 
14.0 


Nickel 


Silicon , 









US. T6inpar*tur« eo«fflol«nt of raiittanoc. The average coefficient 
per deg. oent., between and 100 deg. cent., based on the measurementa by 
Dewar and Fleming, is 0.00622. Tbie value compares with 0.00635 based on 
recent measurements publishsd by the Bureau of Standards (Scientifio 
Paper No. 236). The mean value between and 20 deg. cent., det^mined 
by Dewar and Fleming, is 0.00527 per deg. cent. 

Itf. ZnfOt-iron, described more fully in Par. S79, has been found on 
teet to have a volume conductivity of 16.76 per cent, and a mass conductivity 
of 18.06 per oent., in terms of the International annealed copper standarcx. 
See BUe. Railway Journal, June 6. 1914. "Pure Ingot Iron for Third Rails." 
Carbon steel rails containing 0.73 per cent, carbon and 0.34 per cent, man- 
ganese, have a volume conductivity equal to 13 per cent, of that of copper. 
(Also see Sec. 16.) Ingot iron wire weighs about 4,600 lb. per mile-ohm at 20 
deg. cent, and has a tensile strength of about 52,000 lb. per sq. in. 
. ItO, BesUtlTitj and temperature coefficient of carbon steel. Barue 
and Strouhnl found that the temper of carbon steel affected its electrical 
properties as shown below. 



Temper 



Soft 

Light blue. . . 

Blue 

Yellow 

Light yellow. 
Glass bard. . . 



Rniistivity. 


Temperature 
coefficient. 


miorohm-cm. 


at deg. cent. 


per deg. cent. 


15.9 


0.00423 


18.4 


0.00360 


20.5 


0.00330 


28.3 


00280 


28.9 


0.00244 


45.7 


0.00161 



See "Smithsonian Physical Tables," Sth rg^,j;^.,<^9|9^«)i|^. 

264 ^' 



PKOPSBTIS8 OF ilATSBIALS 



Sec. 4-121 



Ul. BerirtlTl^ of east iron and eait rtMl. The reaiativHy of cut 
oa ia about ten tunes that of pure iron, owing to both the combineid carbon 
the sraphite; a value of 74.4 microhm-cm. for aoft gradea and 97.8 
rohin-«m. for hard gradea ie given in the "Smithfionian Physical Tables." 
fth r«v. «<1., 1910, p. 263. Tbia authority also gives 19.1 microhm-cm. for 
■■t ateel. The chemical composition, mechanical treatment and heat 
fetatmeat affect the resistivity in a pronounced manner. 

Ut. Ohnu p«r mlto-pound of galvanlaad iron wlro 
(Telephone and telegraph) 



Extra Best Best 
(E. B. B.) 



Beat Best 
(B. B.) 



Steel 



Roeblins 

Steel A Wire Co.. 
Amer. Elec. Works 






4.700 to 5.000 

4,700 to 5.000 

4.700 



S.600 to 6.000 6.S00 to 7,000 

5,600 to 6.000 6.500 to 7.000 

5,500 6,500 



Roebling gives the ultimate strength aa equal to the ivoduet of the weight 
ialb. per mile b^ the following factors: 3.0 for E. B. B.; 3.3 for B. B.; 3.7 for 
Stsel. The ratios used by the Amer. Steal and Wire Co. are respectively 
i.5, 2.8 and 3.0. 

IM. Tabl* of calvanlied iron wire 
(American Steel and Wire Co.) 



B.W.G. 


Diam- 
eter in 
mils 


Approxi- 
mate 
weight in 
pounds 
per mile 


Approximate break- 
ingload in poonda 


Resiatanre per mile 

(ohms) at 68 deg.fahr. 

or 20 deg. cent. 




Ex. 
B. B. 


B. B. 


Steel 


Ex. 
B. B. 


B. B. 
3.38 


Steel 
3.93 





340 


1,655 


4,138 


4,634 


4.965 


2.84 


1 


300 


1.289 


3.223 


3.609 


3.867 


3.65 ! 4.34 


6.04 


2 


284 


1,155 


2.888 


3.234 


3.465 


4.07 ; 4.85 


5.63 


3 


259 


960 


2.400 


2.688 


2,880 


4.00 


5.83 


6.77 


4 


238 


811 


2,028 


2.271 


2.433 ! 5.80 


6.01 


8.01 


S 


220 


693 


1,732 


1,940 


2,079 


6.78 


8.08 


9.38 


6 


203 


590 


1,475 


1.652 


1.770 


7.97 


9.49 


11.02 


7 


180 


463 


1,168 


1,296 


1.380 ■ 


10.15 


12.10 


14.04 


8 


165 


390 


975 


1,092 


1,170 


12.05 


14.36 


16.71 





148 


314 


785 


879 


942 


14.87 


17.84 


20.70 


10 


134 


258 


645 


722 


774 


18.22 


21.71 


25.29 


11 


120 


206 


515 


577 


618 


22.82 


27.19 


31.55 


12 


109 


170 


426 


476 


510 


27.65 32.94 


38.23 


13 


95 


129 


310 


347 


372 


37.90 45.16 


52.41 


14 


83 


99 


247 


277 


2S7 


47.48 56.56 


65.66 


16 


72 


74 


185 


207 


222 


63.52 175.68 


87.84 


16 


65 


61 


163 


171 


183 


77.05 91.80 


106.55 



IM. Table of nropertiai of iteel troUer vlre 
(A. A J. M. Anderson Mfg. Co.) 



Sise 
A.W.G. 


Weight (lb.) 


Ultimate 

breaking load 

(lb.) 


Reaistance; ohms 
at 60 deg. fshr. 


ijSoatx. 


mile 


1,000 ft. 


per 
mile 




00 

000 

0000 


281 
354 
446 
562 


1481 
1870 
2357 
2066 


6600 
8300 
9900 
12600 


0.7161 
0.5678 

0.4500 
0.3574 


3.781 
2.998 

2.376 
1.888 



Made in standard round and grooved sections, bare or galvanised. 



265 



joogle 



^ 



Sec. 4-125 



PROPBHTIBS OF MATSRIAL8 



Its. ?«rm«ftbUity of Iron wlr«. The permeability of iron or eofi i 
wire, in the ordinary oommerdal bihs, at frequencies <h 60 oyeles or lei 
from 100 to 125; at 800 cydea, it is about 70. This applies to small mr' 
isingforces. sueh as exist within the wire due to the current flowing th 
it.^rheee values hold for the steel core of copper-clad steel. 

119. St*«l ratll. The resistivity of common rail steel varies in con 
degree, depending upon the chemical composition. Special soft steels < 
for third rails have resistivities ranging from 7-0 to 9 times that of cop, 
track rails, from 11 to 13 timee that of copper. In manganese steels 
ratio sometimes exceeds 30. The effeotive resistanoe of rails conveying al 
natlng currents will be increased somewhat on aooount of skin effect \ 
eddy-currents. See *' Report of the Electric Railway Test Comir*-~' 
McCh»W^H||lBookOau.In0., New York, 1906. Also see Par. 119. 

ItT. ]>eiUllty of pure Iron is 7.86, whioh is fairly precise for wrought iit 
and steel. The National Tube Co. computes the wdght of steel at 0.2833 H 
per cu. in. (489.5 lb. per cu. ft.) and iron at 2 per cent less. 

US. Tenaila proparties of Iron and steel wirea. The tensile propcf 

ties are dependent upon the oomposition of the metal from which the wire: 

drawn, upon the amount of worldng the wire has received in the procenc 

manufacture and upon the heat treatment. For information upon the effei 

of the constituents of iron and steel on tli 

tensile properties, see "Structural HaK 

riak," in another portion of this section. 

The tensile strength ranges from abov 
45,000 lb. per sq. in., for the purest anneals 
wrought iron, up to extremely high value 
for hard steel, in the neighborhood < 
500,000 lb. per sq. in. Carbon, mangami 
and silicon are the chief constituents whki 
impart Btreogth and hardness; they also ii 
crease the electrical resistivity. Both carbo 
and manganese decrease the magneti 
permeability. 

The elastic limit and the yield poia 
occur at about the same relative values a 
in structural iron and steel; in other wordi 
the elastic ratio does not change. 

Fig. 1 1 shows a typical stress-strain dii 

gram; the wire was 0.164 in. in diamet* 

and broke at 55,100 lb. per sq. in., while th 

elastic limit was 25,000 lb. per sq. in. an 

in 60 in. Time was allowed for thewir 

' Trans. Int. Elei 




0.2 0.4 0.6 

UaafkUoQ Per cent 



Fio. 11. — Stress-strain diagram 
of galvanised iron wire. 



the elongation was 11 per cent. 

to set (see Blackwell, F. O. "Conductors for Long Span 



Cong.. St. Louis, 1904, Vol. II. pp. 331-347). 

Blackwell gives Young's mooulus as 24 X 10' lb. per sq. in. for iron win 
27X 10* for steel wire, and 22X 10* for iron and steel concentric cable.' 

It9. GoeflOclent of azpftnaion. Blackwell gives 0.0000064 per deg. fafai 
for iron and steel wire. 

150. Spedflc heat of wrought iron, from 15 to 100 deg. cent., is 0.112 
hard-drawn iron, from to 18 deg., 0.0086 and from 20 to 100 de«., ail 
("Smithsonian Phys. Tables," 1910). 

151. Thermal eondaettvi^ of iron in gram-calories (cm-cube) pi 
deg. cent, is from 0.167 to 0.207 at deg. cent., with a negative temperator 
coefficient of 0.00023 "(Smithsonian Phys. Tables," 1010). 

BSONZK 
ISS. Bronie is an alloy of copper and tin, with the addition in soma esse 
of sine and other metals. There are numerous varieties of bronse, som 
designated by a prefix indicating the special or distinguishing constituent, an 
others known by trade names. 

ISS. Phosphor bronaa is an alloy of copper, fin and phosphorua, contain 
ing from 2 to per cent, of tin and 005 to 013 per cent, of pnosphorus. It 
volume conductivity is not over 35 per cent, of that of copper. Industrii 
bronses carry sine and lead, and a larger proportion of phosphOTua. 

1S4, Silieon bronse is an alloy of copper, ailiooa and sodium; tinandiiD 



266 



hy'^TUuyie 



PBOPKBTISS OF MATERIALS 



Sec. 4-135 



ac abo added, in aome caaea. J. Bucknall Smith (" Wire, Its Manufacture 
aad Uaea," London. 1801) save the following values of oonduotivity and 
tlBailc BtrenKtIi. 



CoEidaetivity Tenaile strength 
(per oernt.) (lb. per sq. in.) 


Conductivity 
(per cent.) 


Tensile strength 
(lb. per sq. in.) 


95 56,000 
80 70,000 


46 
34 


100,000 
100,000 



The pade of silicon bronse used for trolley and span wires has from 2.2 to 2.6 
times the resistivity of copper and is from 35 to 70 per cant, stronger. 



isa. 



Phono-alaetria wire tftblaa 

(Bridgeport Brass Co.) 



8ise 
A.W.G. 

0000 


Oiam., 
mils 


Weight per 
mile, lb. 


Weight, 
lbs. per 
l.OOO ft. 


Breaking 
load, 
lb. 


Tensile 

strength, 

lb. per 

sq. in. 


Resistance 
per 1.000 ft. 
n ohms, 75 
deg. fahr. 


460.0 


3,382.0 


640.6 


11,460 


68.780 


0.12 


000 


409.6 


2,082.0 


507.9 


9.140 


69.180 


0.1518 


00 


364.8 


2.127.0 


402.9 


7,400 


70,620 


0.1929 





324.9 


1,687.0 


319.5 


6,300 


75,830 


0.2423 


1 


289.3 


1,338.0 


253.4 


5,250 


70,670 


0.3077 


3 


257.6 


1,061.0 


200.9 


4,180 


80.000 


0.3868 


4 


204.3 


668.0 


126.5 


2.700 


81,150 


0.6150 


« 


162.0 


420.0 


79.5 


1,680 


81,280 


0.9771 


8 


128.5 


264.0 


50.0 


1,075 


82,700 


1.555 


10 


101.9 


166.0 


31.5 


685 


83,810 


2.472 


12 


80.81 


105.0 


19.9 


420 


83,700 


3.932 



IM. Proixrtlea of bronaa wlret 

(Perrine) 



Wire 


Per cent. 

oonduotivity 

ratio to 

annealed 

oopper 


TenaUe 

strength, 

lb. per 

sq. in. 


Per cent, 
elongation 




97.0 
95.2 
85.0 
81.6 
80.0 
60.2 
38.8 
35.0 
30 .0 
26.0 
15.8 


64,000 

73.000 

71,000 

87,000 

79.700 

109.000 

79.000 

80,000 

105,000 

102,000 

100,000 


1 























Abo see Parahall and Hobart, "EHeetrio Machine Design." London. 1006; 
pp. 566 to 567. 

UT. Ybono-alaetrie wira is a oopper alloy of greater tensile strength and 
snaller conductivity liian hard-drawn copper. The manufacturers claim 
that it is noa-coTToaive and perfectly homogeneous in structure, the tensile 
strngth being uniformly dismbuted over the croes-section normal to the axia 
al tbe wire. Teata on No. and No. 00 A.W.G. hard-drawn copper and 
phoao-eleetrie to determine the fusing currents showed that the latter mate- 
ni fued at about 75 per oent. of the current required to fuse the former. 



267 



V^iUUVlL' 



Sec. 4-138 



PROPSRTIES OF MATEBTALS 



Phoiii>.deatrio wire, on account of it* high tensile propertiea, hu been used foi 
trolley wire and for long spane in tranflmisaion linee and in telephone a-nc 
telwraph lines. 

The tensile strength of hard-drawn wire ranges from 68,000 to 84,000 lb 
per sq. in. The total elongation at rupture is about 1 per cent, and Young'i 
modulua is about 18,100,000. The temperature ooemeient of resistance ii 
0.00088 per deg. fohr. and the coefficient of linear expansion is 0.000O14( 
per deg. fahr. 

MI8CILLAKKOI78 HKTALS 
in. BeiistiTity of Tarioui meteU 

(Compiled from "amithsonlan Phys. Tables," 1910) 



> 



Resistivity 



Temp. coef. 

x.f . : I .'X"^""'"'^. [per deg. cent., 

MeUI !at p deg. cent P ^ Ig deg. 

(mierohm-cm.) *"• ^nj 



Antimony 

Arsenic 

Bismuth 

Boron 

Cadmium 

Caldum 

Cobalt 

Gold 

Indium 

Lead 



35.4 to 4S. 8 

33.3 

108.0 

8 X 10>» 

8.2to7.0 

7.6 

8 

2.04 to 2.09 

8.38 
18.4 to 19.6 



Lithium 8.8 

Magnesium ' 4.1 to S.O 

Mercury 94 . 07 

Niolcel 10. 7 to 12.4 

Palladium 1 10 . 6 to 13 . 6 



Platinum 

Potassium 

Silver 

Thallium 

Tin 

Zinc 



9.0 to IS. .5 

25.1 
1.5 to 1.7 
17.8 to 106 
9.53 to 11.4 
5.66 to 6.04 



0.00389 



0.00354 

oiooiii' 



0.00325* 
0.00366 



Density 



0.00387 



0.00381* 
0.00072 
0.00622* 
0.00364* 

0.00367* 



0.00377 
0.00398 
0.00366 
0.00366 



6.62 to 6.69 

8.73 
9.79 to 9.90 
2.6 to 2.6 
8.54 to 8.67 

1.56 

8.71 

19.3 

7.12 to 7.42 

11.36 

0.534 
1.69 to 1.75 

13.56 
8.00 to 8.90 

11.4 

21 2 to 21.7 
O.seto 0.88 
10.4 to 10.0 
11.8 to 11.9 

7.30 
7.04 to 7.19 



Therm, coad. 

(g-cal.per era 

cube per deg. 

per sec.) 



0.044 

oioio' 

'6.'22"" 



0.70 
6!684' 



0.37 
0.016 
0.14 
0.17 

0.16 



1.10 



0.15 
0.26 



* Average values, for range from to 100 deg. cent. 

139. Tungttan.* The tungsten metal of commerce, prior to the dis- 
covery of ductile tungsten, was a very hard, dark gray powder; in some 
cases the metal was heated with low-carbon ateel in a crucible furnace, 
producing the alloy known as ferro-tungatcn, containing 80 to 86 per cent, 
of tungsten. The higher-grade alloys are produced in the electric furnace. 
Cast tungsten is an extremely hard brittle metal, having a specific gravity 
of about 18.7. In 1910 a process was announced for the production of 
ductile tungsten, by rolling, swaging or hammering a heated body of 
coherent tungsten until it becomes ductile at ordinary temperatures 
ISUctrical World, Jan. 10, 1914, pp. 77, 78). The melting point is 3,100 
± 60 deg. cent. 

140. Ductile tungsten is a bright, tough, steel-oolored metal, which 
can be drawn into the finest wire. The operation of wire-drawing increases 
the Htrength; Fink stated that tungsten wire of 0.0012 in. diam. had a tensile 
strength from 580,000 to 610,000 lb. per sq. in., and the density inorecued 
from 1881 before drawing, to 19 30 after drawing to 0.15 in. It retains 
its luster almost indefinitely. Wrought tungsten lias been used as a sub- 
stitute for platinum contarts in electrical apparatus, for targets or snti- 

* Baskerville, C. " The Chemistry of Tungsten and the Evolution of the 
Tungsten Lamp;" Trans, of the New York Electrical Society; New Series, 
No. li Oct. 29, 1912. 



.268 



yGoogle 



PROPERTIES OF MATERIALS 



Sec. 4-141 



athodes for Rfintgen tubes and for the reeistor in electric heater elementa; 
of course its most extensive application is in the form of drawn-wire fila* 
Dents for incandescent lamps (Sec. 14). The processes of making ductile 
tBi«itea are described in British patent No. 2759, issued in 1910; U. S. 
patent No. 1,062,033 issued Dec. 30, 1913 to W. D. Coolidge. The resis- 
Imty at 25 d«r. cent, is 5 microhm-cm., annealed, and 6.2 microhm-cm., 
hard-drawn. The mean temperature coeffi- 
cietit of resistance between and 170 deg. 
wot. is O.OOSI per deg. cent. The resist- 
uoe-temperature corre is given in Fig. 12. 
Coefficient of linear expansion, 20 to 100 
d<c. cent., 336X10-*. 

111. Tkntalnm is a white lustrous 
BKtal having a specific gravity of 10.6. It 
is duetila'and workable, and can be drawn 
iato fine wire, in which form it has a tensile 
strength as high as 130,000 lb. per sq. in. 
The resistivity at deg. cent, is 14.6 ,mi- 
CTDhm-«m., and the temperature coefficient 
is 0.0033 per deg. cent. 

141. Wood'* fiuiblo allor contains 4 parts of bismuth, 2 parts of lead, 
1 part of tan and 1 part of caamium. The melting point is 60.5 deg. cent. 

14S. Bom'i fiulbla alloy contains 2 parts of bismuth, 1 part of lead, and 
1 part of tin. The melting point is 03.8 deg. cent. 

144. Compoaition and meltliiff point of fnilbl* aUoyt 
(Perrfne) 























/ 


/ 




<L00 




































' 


















1 


X 






















^ 


' 




















^ 




















L.fiii 


^ 




















^ 





'O fiOO 40U 000 SOO 1000 lax) 
IraipM«tur< 0«iiUcT»d« 

Hg. 12. — Remstanoe-temper- 
ature earv« for tung8t«D. 



Tin . 

"4"' 
1 
8 




Composition 




Melting point, 
deg. cent. 


Bismuth 


1 
Lead | Cadmium 


Mercury 


20 
15 

2 
8 


20 t 


60 


20 

65 

08 

132 


8 1 3 

1 




12 









67 
SO 


90 

8 

33 

20 


1 • 


160 
164 
166 
200 


22 1 




' 




, 





141. riulnc currant* of diifarant Had* of wDtm were investigated by 
W. H. Preeee, who developed the formula 

/ - <Kf' (12) 

vfaere I a the fusing current in amperes, d is the diameter of the wire in 
ia. and a is a constant depending upon the material. He found the 
foUowiag values for a. 



Copper 10,244 

Afanmimm 7,585 

Platinum 6,172 

German silver 5,230 


Iron 

Tin 


3.148 
1,642 
1,318 
1 X7a 


Alloy (2Pb-ian) 


Fbtinoid ^ 4,750 


' 





Also see Perrine. F. A. C. " Conductors for Elpctriral Distribution," New 
Vock. 1903; Chap. II. 

UC l«j»litmn is a non-metallio element chemically resembling sulphur 
ssd teOunum - and occurs in several allotropic forms varying in specific 
irtvity from 4.3 to 4.8. itelenium melts at 217 deg. and boils at 600 deg. 



^ 



260 



jv^iueivie 



,y, 



Sec. 4-147 



PROPERTIES OP MATSRIALS 



■gx 






I? 
Kg 
%3 
•1 

" o 

a 
o. 
6 
e 

U 



>u!)|3(a xojcidv 
Ctuao °Sap) 'dai3) 



-jaaa 'Sap 
jad notmifidxa jva 
-ail /o ^aaioigaoQ 



(*ui 'b* jad -qi) 
q)liaaj%g ananax 



Aiauaa 



')aao Sap ojaf 
%v ffiioA-ojaitu 'jad 
-doo t^TA ' jaMod 

oij^jap-ouijaqj. 



')aaa 
'9ap jad '-^aao 
'Sap 02 9? aoav^BTB 
-aa JO •jeo 'duiaj^ 







s is 



00 00 1-4 



--^^^« 









:i : 






SSSS3 



OMOCOOt 



C4*^ ^<0-« 



§ I 



00 00 



ood 







O -f 00 (D to t« M 



00 



OOOOOBOk • 



WtOOOiOOO 



000000 

QOO>0>OQ 



•8 

•a 






^15 

Zn« 
i5S 



8 



•3s25 



^^ r- W 3 

b9 



d g S £.£ 



zz _ 
00 



5! 



It, 



=.S : a 
Sz^o 



tt 4) aj fl) o 
J<^J4JI,M 
O U U 61 

'S's'S'S'S 

IB fe si b 

acbba 
oeoeo 
UOUOU 






270 



Digili^edbyV^iUUyiL' 



PROPBBTIBS OF UATKRIALS 



S«C. 4-147 



,8 

l\ 

I* 

If 



l« ayiOA-oiaiui 'j»d 

-dOO qilA JOMOd 



»jn)a«}mnK «eo»o^eo o» — -•(o c4v<-4<-4r* 



(-^oaa Sap) )tnod 
Saitjaoi "xojddY 



(*)a90 *99p) *dtaa^ 



foao 'Sap 
j»d aowovdxa j«9 



{in bs j»d *qO 



iC|imi8Q 



'S»p jod **ina9 
*S9p OS |« 9oa«)iin 
-oj jO -J903 'dmaj. 



I' 



ca 



SI 



■sa 



S« 



C4-4^C4e« 



1111 

TTTT 

O O O O 

zzzz 



• & 



lain 

171 



Si :S 



oooS 



xoooooo 



II 

XI 
22 



M m'^ O 

d g « 
« B ■ o 

B.UZH 






sSg 



•oS 



ississ 



>OOCW3U3 



6<5a(5(S 



zzzzz 



It-Si s 

OHZZO 



Or^ 



t^ 



g Of 



CI Q 

^1 



GO 



Pig 

QEhHS 



h, V^3' 



oogle 



Sec. 4-148 



P&OPSnTIBS Of UATBBtALS 



cent. At lero deg. cent, it has a reaiativity of approximately 60,000 ohm-om. 
The dieleotrio oonatant rangee from 6.1 to 7.4. It haa the peouliar property 
that ita resistivity decreases upon exposure to light; the resistivity in darkoeas 
may be anywhere from A to 200 times the resistivity under exposure to IiKht 
Bee paper by W. J. Hammer, Trans. A. I. E. E., 1903, Vol. XXI, pp. 372 to 
393. 

EI8I8TOB HATKKIALB 

MS. Qamuui •Ovar is an aUoy of copper, nickel and sine. It is usually 
listed commercially in terms of its nickel content; thus 18 per cent, wire 
contains 18 per cent, of nickel. The properties vary considerably with the 
composition. Perrine gave the following composition of three grades of 
German silver: 57 Cu, 12.fi Ni, 30.5 Zn; 56 Cu, 20 Ni, 24 Zn; SO Cu, 30 Ni. 
20 Zn. The resistivities were respectively in the ratio 1 : 1.25 : 2.S1. 
Eighteen per cent, alloy has about 18 times the resistivity of copper, and 30 
per cent, alloy has about 28 times the resistivity of copper. See Par. 14T. 

149. Ooppar-nuuigansM alloy containing either nickel or aluminuna is 
used for resistors, and has a very low temperature coefficient. The alloy 
composed of copper, ferro-manganese and nickel, or copper, manganese ana 
nickel, is known as mangMiln. The com- 
position of manganin varies somewhat, one 
formula being 65 Cu, 30 Fe-Mn, 5 Ni. 

! uol I I \ j ( '\ - \\ I I I I I *••• Copper-nickel alloy is used exten- 

i c. aively for resistor wires. The alloy of ro|>- 

1 LOS — /- per and nickel found in nature is known aa 

" I 1 /1 I I I 1 1 M M I Monel metal (Par. 899). See Par. 1*T. 

m. Hlekal-steel alloy has a very high 

electrical resistivity but is not as resistant to 

corrosion, for resistor servioD, as some other 

alloys. The nickel-chromium alloys are 

superior in the respect of having somewhat 

larger resistivity. See Par. 147, 

15S. Mlekal-ehromittin alloy is used for resistor wires where very high 

resistivity is desired. One alloy of this kind has a reaistivity of more than 

700 ohms per mil-ft. The nickel-chromium alloy known as " Nichrome '* has 

a oharacteristio resistance-temperature curve of the form shown in Fig. 13. 

CARBON AND QRAPHITI 
111. Torms of carbon. Carbon occurs in two forms, amorphous and 
crystalline. The crystalline forms include diamond and graphite, the 
latter also being known as plumbago. The amorphous forms include char- 
coal, coke, lamp black, bone black; coal is an impure variety of amorphous 
carbon. The densitv of carbon in the diamond state is 3.47 to 3.56; gra- 

{ihite, 2.10 to 2.32; charcoal, 0.28 to 0.67; coke, 1.0 to 1.7; gas carbon, 1.88; 
ampblack, 1.7 to 1.8. 

IM. BesUtlTlty. The resistivity of amorphous carbon (petroleum coke) 
at ordinary temjperature (25 deg. cent.) may be taken as varying between 
3,800 and 4,100 microhm-cm. An average value for retort carbon, such 
as used for electrodes in electric furnaces, at about 3,000 deg. cent., may 
be taken as 720 microhm-cm. Graphite at 3,000 deg. cent, has a resis-^ 





1— 


~ 




~ 






~ 


■■ 


■ 






, 
























/ 














^ 




■ 




















/ 


















1 Aa 






/ 
























i 






















LUO 


6 






_ 






_ 


_ 


_ 




_ 


_ 



soo 400 eoo 8Q0 1000 laio 

Fia. 13. — Resistance- tern {Xir- 
ature curve for nichrome. 



tivity of apDrozimately 812 miorohm-cm. Experiments by Mr. C. A. 
Hanson* made in the research laboratory of the General Electno Company 
show that the resistivity of carbon depends upon the tem^rature at which 



it is fired. Aa the temperature of firing increases, the resistivity decri 
approachinff a constant value which is approximately the same as that of 
praphite. If carbon be heated above the temperature at which it was fired. 
Its resistivity is permanently decreased, and upon cooling it will not return 
to its origincu value, but to a value corresponding to that which it would have 
if fired at the temperature to which it nas been heated. Also see table of 
brush characteristics. Par. IBS, and electrode carbon. Far. 1B9. 

Experiments made by Morris Owen show that graphite possesses mai^netic 
susceptibility, and under certain conditions . the electrical resistivity is in- 
creased in very marked degree by magnetisation. 

* mfttrockem. and Mt. Ind„ Vol. VII. p. 614 (1909). 



272 



),g,l,.edbyC00gle 



PSOPERTIMS OF UATSRIALS 



Sec. 4- 



S c *• J 

£S£7 
eg" 



TTTTT 



mil 



iiiii 









1^ 






ISSS! 



NC4C«M^ 



MVeoco»o 






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ll 



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ddodd 



SS3SS 

a d a d 



il 1 

o C o 

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is o.ao.a 
la flS SI 4 « 

a b b h h 

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a 2 

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■§ 3 

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20000 



O V 






0.0 



.§ .If 



I 111 
7 8°«t 

O HS50. 



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el 9 c 



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o.ti.5 — 
o.a.a-a.a 
^ aaaa 

ad c3 IS « 
k hi b hi 
oooo 



■2-a 

4cS 



373 



i.jv^iuuyic 



Sec. 4-166 



PROPERTISS OF MATSRIAtS 



IN. BMUtanM of are lunp oarboni. The r«utance of \ in. X 12 
in. enoloaed aro oarboiu ywi« irom 0.012 to 0.015 ohma per linear inch. 
Other aiies down to } in. diameter vary according to their croae-BectionAl 
areaa. Tli« resistance of a f-in. diameter projector cartwn varies from 
0.009 to 0.011 ohma per linear inch. The i-in. and fern, earbona vary 
according to their cross-sectional areaa. 

All high-grade forms of carbon, such as that used in the manufacture of 
search-light carbons and also enclosed aro carbons, may be given the value of 
about 0.002 ohms per cu. in. Flame-aro carbon matoial sueh as is used in 
the homogeneous electrodes varies from 0.004 to 0.006 ohms per ou. in. All 
the above values are for ordinary room temperatures. 

KT. Temperature eosffioient of retlatanee. Carbon exhibits a 
decreasing electrical reaiativity and a decreasing thermal reaietivity with 
riaing temperature. Graphite exhibits but little change in electrical re- 
aiativity, tending downward with rising temperature, but its thermal resi*- 
tivity increases slightly with risins temperature. The coefficients vary over 
a conaiderable range; see Landolt and Bornstein, " Phyaik^ish-Cherolache 
Tabellen," 1012. 

1S8. Beilatanee* of oarbon oontacta vary with pressure, current and 
time. See results of investigation published by A. L. Clark in the PkysiooZ 
RmitvB, Jan., 1913. 

IM. Electrode properties of carbon and ipraphlte were given by 
Hering in his i>aper, "The Proportioning of Electrodes for Furnaces ' 
(Trans. A. I. E. ET, Vol. XXIX, 1910, pp. 485-545), from experimental de- 
terminations. The table below is abstracted from Table I in Bering's 
paper above mentioned; the paper itaelf gives elaborate details and many 
curves. Other papers by Hering on this general subject are noted below. ' 



Material 


Furnace 

temp. (deg. 

cent.) 


Temp, drop 
cent.) 


Electrical 

resistivity, 

ohm (in-cube) 


Thermal con- 
ductivity, twatts 
(in-cube) 


Carbon 


20.0 
360.0 
751.0 
042.0 


0.0 
260.0 » 
651.0 
842.0 


0.00181 
166 
150 
148 




0.95 
1.32 
1.88 


Graphite 


20.0 
389.6 
546.1 
720.2 
913.9 


0.0 
289.6 
446.1 
620.2 
813.9 


0.000337 
330 
324 
316 
323 




3.60 
3.45 
3.26 
3.10 



1 1 watt •• 0.2380 g-caL per sec.; I g-cal. per sec. - 4.186 watts. 
SKIH imCT 

IM. SUn effect is briefly defined in See. 2. Also see Sec. 12, Par. 41. 

m. ronnuUi and tablet (or lUm effect. If A' is the effective re- 
sistance of a linear cylindrical conductor to sinusoidal alternating current 
of given frequency and R is the true resistance with continuous current, 
then 

W'KR (ohms) (13) 

where K is determined from the table in Par. l(t, in terms of x. The 
value of X is given by 

«-2wo\/^ (14) 

P 

* "Laws of Electrode Losses in Electric Furnaces;" Trant. A. E. S., Vol. 
XVI, 1909. 

"Empirical Laws of Furnace Electrodes;" Trant. A. E. B., Vol. XVII, 
1910. 

"The Design of Furnace Electrodes;" Eltetrieal World, June 16, 1910. 



274 



JbyV^iUUyiL' 



PROPBBTIBS OP UATBRIALS 



S«C. 4-162 



is ihm radius of the conduetor in om., / is tKe frequenoy in cycles per 
•ee-, f is the macnetic permeability of the conductor (here assumed to 
be eonstAnt) and p is the resistivity in absohms (10~* ohm) per cmnsube. 

If L' ■■ the effective induetance of a linear conductor to sinusoidal alter- 
nating current of a given frequency and L is the true inductance with con- 
tinaooa eurrent, then 

L'-Li+K'Lt (15) 

wfam La b the external portion of the inductance, Li is the internal portion 
(doe to th« macnetic field within the conductor) and K' is determined from 
the table in Par. IM in terms of z. Thus the total efleotiva inductance per 
amt IcDCth of conductor is 

L-21og.(|) + JC'(J) (18) 

See See. 2 tor further discussion of inductance of linear conductors; also see 
See. 11. For details underlyinz the above formulas see Bulletin of the 
Bureau of Standards, Vol. VIIITno. 1, op. 172 to 181; 1012. Fig. 14 shows 
TshMB of X in terms of av/ for cylindrical copper conductors of 100 
per cent, conductivity. 

w 

u 
u 

M 

u 

u 

u 



Pia. 14. — Cnrre showing the proportional change in effective resistance of 
eyUndrical copper conductors with alternating currents. 





■ — 












" 




^ 


~ 






- 




~ 


■ 






7 


R^XBt 








/ 












/ 












/ 








- 


K'v a \/r 




/ 


' 










a - SmIIui of «ln InMnOoMlut 


/ 






































^ 




































^ 






































/' 






































^ 




































/ 






































^ 






















































































, 


























I 





] 


* 


1 


« 


1 


i 


1 





% 


\ 


4 


g 


J 


t 


M 



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• MMStMWMIOnWlM 





n" 
















IIS 
















JL._ _k 


::dx i ii 


lb[i^ " 




-t-, = s3 




KA 


Tt-5 


•i ^ 1 






t-t . i 


- - 1* < 






U-l-~ 




2 


it/--- 




10 


/;/=- 


- iX±::-==: 



Fra. 15. — SUn effect in copper-clad 
sted wires at 60 cycles. 



Fio. 



18. — Skin effect In iron wires 
at 50 cycles. 



W. Ub sSaet in oopfMr-oUd Itaol wir* is illustrated in Fig. 15, 
bised oB tests of the effective resistance of solid round wires at 60 cycles 

Cr see. The effects at 25 cycles are somewhat less. The effects in 
n coneeotrio-lay cables are somewhat greater, and the increase at 60 
tjatm reaches valuea as high as from 80 to 1(M) per cent. ; when the core is 
composed of solid copper, the skin effect is less severe. In the smaller 
*ir« (No. 10 to No. 12 A.W.G.) the skin effect at 800 cycles per sec., 
^k enrreata of telephonic strength, range from 3 to 6 per cent, (increase 
cfroistasee). 

ta. SUn sAaet in iron win at SO cycles ia illustrated in Fig. 16. based 
OS dau suppHed by the Felten * OuiUeaume CarUwerke (Elek. Zeit., Deo. 



276 



DigilizedbyV^iUOyi' 



Sec. 4-164 



PKOPBBTIES OF MATERIALS 



10, 1914). In No. 12 B.W.G. iron wire (B. B. grtde), at 800 oyclM per 
sec, and with currents of telephonic magnitude, the increase in resistance 
was found by measurement to be 47 per cent. See Par. lOt. 

IM. BSeet of TW7 hlcb tr«qa«nct*« on Iron has been investigated by 
E F. W. Alexanderson: see "Magnetic Properties of Iron at Frequencies 
up to 200,000 Cycles," Tram. A. LE. E., Vol. XXX, 1911, pp. 2433-2454. 
He concluded that the permeability is unaffected by the frequency. In' 
applying Bteinmeti's formula for skin effect (see "Transient Eleotrio 
Phenomena apd OaeiUations," New York, 1000), he reoommended usinft 
average constants as follows: permeability, 2,2S0 and conductivity, 
0.9 X 10», for soft bon. 

IW. Table of eonitenti for skin-effect fonnolat 



X 

0.0 


K 


K' 


X 


K 


K' 


X 


K 


K' 


1.00000 


l.OOOOO 


1 1 ! 

4.0 1.67787 0.68632 


12.6 


4.67993 


0.22667 


0.1 


1.00000 


1.00000 


4.1ll.71516;0.67135 


13.0 


4.86631 


0.2170.3 


0.2 


i.mnm 


1.00000 


4.21.75233 0.65677 


13.6 


5.03272 


0.2090.1 


0.3 


1.00004 


0.99908 


4.3 1.78933.0.64262 


14.0 


6.20915 


0. 20160 


0.4 


1.00013 


0.90993 


4.4 1.82614 0.62890 


14.6 


5.38660 


0. 19468 


0.5 


1.00032 


0.90984 


4. 611.862760. 61563 


16.0 


6.66208 


0.18822 


0.6 


1.00067 


0.90966 


.4.6 


1.89014 0.60281 


16.0 


6.91509 


0. 17649 


0.7 


1.00124 


0.99937 


4.7 


1.93533 0.690441 


17.0 


6.268170.166141 


0.8 


1.00212 


0.99894 


4.8 


1.97131 


0.67862 


18.0 


6.62129,0,156941 


0.9 


1.00340 


0.99830; 


4.9 


2.00710 


0.66703 


10.0 


6.97446 


0.14870 


1.0 


1.0051S 


0.90741 


6.0 2.04272 


0.66697 


20.0 


7.32767 


0.14128 


1.1 


1.00768 


0.99621 


6.2 2. 11363!0. 535061 


21.0 


7.68091 


0.13456 


1.2 


1.01071 0.99465 


6.4 2.18389 


0.51566 


22.0 


8.03418 


0.12846 


1.3 


1.01470,0.99266 


5.6 2.26303 


0.49764 


23.0 


8.38748,0.12288 


1.4 


1.01969 0.09017 


5.8 2.32380 


0.48086 


24.0 


8.74079 0.11777 


l.S 


1.02S82|0. 98711; 


6.0 2.39359 0.46621 


26.0 


9.09412 0.11307 


1.6 


1.03323 0.983421 


6.2|2.46338|0.46066 


26.0 


9.44748 0.10872 


1.7 


1.04206 


0.97904 


6.4 2.533210.43682 


28.0 


10.15422 0.10096 


1.8 


1.05240 


0.97390 


6.6 2.60313!0.42389 


30.0 


10.86101 0.00424 


1.9 


1.06440 


0.96796 


0.8 


2.67312 


0.41171 


32.0 


11.56785 0.08835 


2.0 


1.07816 


0.96113 


7.0 


2.74319 


0,40021 


34.0 


12.274710.08316 


2.1 


1.09376 


0.95343; 


7.2 


2.81334 


0.38933 


36.0 


12. 98160|0, 07854 


2.2 


1.11126 


0.94482! 


7.4 


2.88365 


0.37902 


38.0 


13.68852 0.07441 


2.3 


1.13069 


0.93527 


7.6 


2.96380 


0.36923 


40.0 


14.39545,0.07069 


2.4 


1 . 15207 


0.92482 


7.8 


3.02411 


0.36992 


42.0 


16.10240 0.06733 


2. '6 


1.17538 


0.91347 


8.0 


3.09445 


0.35107 


44.0 


15.80036,0.06427 


2.6 


1.20056 


0.90126 


8.213.16480 
8.43.23518 


0.34263 


46.0 


16.51634 0.06148 


2.7 


1.22753 


0.88825 


0.33460 


48.0 


17.223330.06892 


2.8 


1.25620 


0.87461 


8.6:3.30557 


0.32692 


50.0 


17.93032,0.05656 


2.9 


1.28644 


0.86012! 


8.83.37507 


0.31958i| 60.0 

1 


21. 4664l|0. 04713 


3.0 


1.31809 


0,845171 


B.o'3.44638 


0.31257 70,0 


25.00063 


0.04040 


3.1 


1.35102 


0.82975 


9. 2X. 61680 


0.30685 1 80.0 
0.299411 90.0 


28.53593 


0.0S636 


3.2 


1.38504 


0.81397> 


9.4I3.68723 


32.07127 


0.03142 


3.3 


1.41999 


0.79794, 


9.6:3.66766 


0.29324 100.0 


36.60666 


0.02828 


3.4 


1.46670 


0.78175 


9.8 3.72S12 


0.28731 » 


a> 





3.5 


1.49202 


0.76560 


10.o'.1.798.57!o. 28162 | 






3.8 


1.62879 


0.74929 


10.3 3.9747710.26832 






3.7 


1.66587 


0.73320 


11.0,4. l.'ilOO 0.26622, 






3.8 


1.60314 


0.71729 


11. 54.32727 0,24516 






3.9 


1.64051 


0.70165 


12. 4.. 50358 0.23501.1 







276 



DigilizedbyCOOgle 



PROPERTIES OF UATSRIALS 



Sec. 4-166 



IM. BUn aSmt in itMl 
c«hl«i Bt SO cydes per sec. is 
abova in Fig. 17, baaed on teat 
data from tbe Allgemeine Elek- 
tricitataGeaeUacliaft(£Ict. Zeil., 
Dee. 10, 1914). 

BIBLIOOKAPBT 

1(T. Bafarance litarMura 
on eondueton. 

PKKWNa, F. A. C. — "Conduc- 
tora for Electrical Diatribution." 
D. Van Noatrand Co , New York, 
1903. 

CoHB?r, L. — "Calculation of 
Aliematinx-eurrent Problems." 
McGraw-Hill Book Co.. Inc., 
1013. 

DsL Mae, W. A.— "Electric 
Power Condnctors." D. Van 
Noatrand Co., New York, 2nd 
edition, 1914. 

Bureau of Standards, Circular 
No. 31.— "Copper Wire Tables," 
3fti edition, Oct. 1, 1914, Wash., 
DC. 

Troa*. A. I. E E.,.^our. I. E. 
K.; Bulletins of the Bureau of 
Suodards; rraiu. A. E. H. 



360 








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2'°° 






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5 




/] 


' 


1,1 


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y 




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<^ 


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J 180 


- 


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/ 


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, 


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£ 120 




/ 


,// 


h 


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/■ 


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M 










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250 300 



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100 i^ 200 
Ampereg 

17. — Skin effect in ateel cables 
at 50 cycles. 



MAGNETIC MATERIALS 

CLABBinCATZON 

IM. Parunaffn«tic mataiiaU include all those materials in which the 
intcDsity of ma«netiiation ^Sec. 2^ is a positive quantity. The principal 
pTamacnetic naaterials aic iron, nickpl, cobalt, and certain of their ailoys; 
also certain non-ferroua aJlo3^, known as the Heusler alloys. The only mate- 
rials of great industrial importance are iron and its alloys. 

ICf . lMafnayii«tlc matarlala are those which are less magaetio than 
ether or air, or in which the intensity of magnctiiation is negative. There is 
fto known material in which this effect has more than a very feeble intensity. 
Bismuth is tbe leading example of materials of this class. 

ITO. Commercial nuffnetlc materials can be classified as follows: cast 
iron, semi-steel, wrought or puddled iron, soft or low-carbon steel, hi^ h-car- 
bon steel, and alloy steel. These arc the materials whose properties are 
important in practical engineering work. 

ITl. Retentive and non-re tentive materials. The commercial mate- 
rials are divisible as a whole into two classes, one suitable for all applications in 
vfaieh the retentivity, coercive force and h>'Btereai9 should be as small as 
pDseiUe, tbe other suitable for applications in which maximum retentivity is 
the moet-desired characteristic. The former class is useful in. all types oT 
dertromagnetic mechanisms, such as generators, motors, transformers, 
electromagnets, etc.; the second class is useful only in permanent mag- 
nets, measuring instruments, magnetos, relays, etc. 

COKFOaXTION AND PBOPS&TZIB 

m. Dependence of propertiei upon composition and treatment. 

The magnetic properties of all materials depend upon the chemical compos!- 
tioo. heat treatment and mechanical treatment. These factors are con- 
udcred in some detail in the succeeding paragraphs. 

171. Effect of Impurities on magnetic properties of iron. The general 
effect of impurities is to decrea.se the permeability and increase the iron loss. 
Mn«t impurities are as a whole injurious in their efTect, but there are certain 
spparent exceptions. The effect of silicon appears to be to decrease the iron 
MS and increeee the permeability up to iQUuctions from. 12,000 to 14,000 



277 



hy^^iDUyiC 



Sec. 4-174 



PROPSRTIBS or UATBRIALS 



\ 



Ksuases, after which the permeability decreases below that of soft iron, while 
the iron loss begins to increase rapidly. See also Ruder, W. £.. " The Effect 
of Chemical Composition upon the Magnetic Properties of Steels;" General 
BUetrie Rmiew^ March. 1015, pp. 197 to 203. 

174* BBteot of earbon. Carbon increases the resistivity, decreases the 
permeability, lowers the saturation point and increases the coercive force 
and the retcntivity. Concurrently the hysteresis loop is broadened and its 
area increased. _ These eflfects are greater in hardened steel than in soft or 
annealed material. In slowly cooled iron-carbon alloys the carbon exists as 
pearlite up to the eutectoid point (about 0.85 carbon) ; above this point the 
carbon exists as cementite (^eaC). The cementlte carbon dimimshes the 
conductivity less than does the pearlite carbon. At a Quenching tempera- 
ture of 860 deg. cent, the limit of dissolved carbon is about 1 .4 per cent. ; 
no excess of carbon above 1.4 is soluble at this temperature. 

ITS. Iffeet of m&niT&neM. Very small proportions of manganese are not 
injurious In any substantial degree, out it is customary to limit the propor- 
tion of manganese as much as practicable. The true effect of small pro- 
portions of manganese is difficult to determine because of its association in 
most oases with carbon. See Jew. I. E. E.. April, 1911, Vol. XLVI, No. 
306, pp. 263 to 266. When the manganese content reaches 12 per cent, the 
steel oecomes practically non-magnetic. 

176. Bflaota of tlUoon And aluminum. The researches of Barrett, 
Brown and Hadfield (1000 and 1902} established the fact that the only mag- 
netic allosrs superior to the purest commercial iron are the allovs of iron with 
silicon, and with aluminum. The best silicon alloy contained 2.5 per cent, 
of silicon, and the best aluminum alloy contained 2 . 25 per cent, of aluminum. 





Maximum 
permeabil- 


(Bfor 
maximum 
permea- 
bility 

4.000 
4.000 
5.000 


Hysteresis 
losa, ergs 

per cu. cm. 
per cycle 

forACmaz) 
-9.000 

2.334 
1.549 
1.443 


Coercive 
force for (B 


Swedish charcoal iron 

2.5 per cent, silicon 

2 . 25 per cent, aluminum . . 


2,100 
5.000 
5.400 


1.10 
0.80 
0.80 



Guggenheim has shown (Elek. Kraft U. Bahnen, Sept. 24. 1910). for iron 
oontaining 0.2 per oent. of carbon, that silicon in quantities up to 1.8 per 
cent, decreases the permeability, but from 1.8 to Sj^cr cent, it improves the 
permeability and decreases the hysteresis loss; for (S(max) — 10.000 in sheets 
0.5 mm. thick the hysteresis loss was 2,910 ergs per cu. cm. per cycle, for best 
silicon steel, compared with 6,000 ergs for ordinary sheet iron. 

For electrical and mechanical effects of silicon and aluminum, see ^pro- 
priate portions of this section. 

117. KSeot of nickel. The addition of nickel, up to 2 per cent., causes 
little change in magnetic quality (Burgees and Aston). A higher nickel 
content rapidly decreases the permeability. At 25 to 30 per cent, nickel, 
the mapietio properties are greatly impaired, but improve again upon a 
further increase in nickel. 

178. Heots of tunntan, chromium aoA molybdenum. These 
dements have the general property of increasing the magnetic hardness and 
particularly the coercive force, making a very desirable steel for permanent 
magnets. See " Magnet Steel," Par. ISS to tSO. 

179. ISeeta of •nenio and Un. Thcae elements are similar in their 
effects to silicon and aluminum, increasing the resistivity and reducing the 
hysteresis loss. Tin increases the permeability at higher inductions and 
decreases the hysteresis loss even more than silicon. 

180. Sulphur, phoaphoru* and ozygan are iasenwal injurious in tlMir 
effeota, erea in amall pareentages. 



278 



, Google 



PROPKRTIBS OP MATERIALS 



Sec. 4-181 



Ul. Ifteet at hauX traatiiMnt. Suitable hakt titatmant during manu- 
facture reduces the iron lo«, inoreaaes the permeability and gires better 
phyeical properties. The beet physical properties and the permeability are 
to some extent opposed, and the most suitable heat treatment as regards 
macnetio properties is not generally the one which gives the highest physical 
properties. The general method of annealing is in Doxes, under oorer, with 
slow cooling. 

US. KBeet at tempenture. Both iron and steel lose their magnetia 
properties at about 750 to 800 deg. cent., and are non-magnetic above that 
temperature. The exact temperature at which this transformation occurs is 
somewhat variable, and depeiids upon the chemical compoaition of thametai. 

m. Hbet of tempar»tur« on panneabllitr. Hopkinson's experi- 
ments (Phil. Mag. and Proa. Roy. Soc.; showed that with weak magnetising 
forces the i>ermeabiUty increases with rises of temperature up to the critical 
point, or about 785 deg. cent., above which iron becomes non-magnetic. 



Under moderate magnetising forces the permeability first increases sirghtlvt 
with rise of temperature, and then decreases rapidly as the critical pomt Is 
approached. Under strong magnetising forces the permeability suffers no 
change at first, and then decreases gradually as the critical point is ap- 
proached. See Cliap. VIII of Ewings "Magnetic Induction in Iron and 
Other Metals." 



aii,ooo 




00 ao 30 1 ) w (jo jo a) « loo no lao no no ipo ii» ITO i»P 'i* a o *io 

io M 30 . ^0 so 80 70 80 5i 100 

K ita 0,G*8, Aactromsfsatic UalU 

Via. 18. — Normal saturation curves (General Electric Co.). 

. IM. normal gatoration eurraa for castriron, cast-steel and annealed- 
steel (low-carbon) sheets, of the qualities ordinarily used in electrical con- 
structioii, are given in Fig. 18. Also see Fig. 37 (Par. Tl) in 8cc. 8; Fig. 
33 (Par. ■•)in Bee. 7; and Commercial Sheets" in this section. For pre- 
cautions and rules in extrapolating magnetisation curves see Ball, J. D., 
<7en<raf EUctric Rtvitv, Jan. IBIS, pages 31 to 33. 

1U._ Indnotlon-pennaability cuirea for csstiron and malleable iron are 
given in Fig. 19. These curves are typical of the shape of induction-per- 
meability curvee in generaL 

IM. AfUDg. Aside from the immediate change in the magnetic quality of 
iron whien results from heating, it produces a slow deterioration which results 
in reduced permeability and increased hysteresis. Even so low a tempera- 
ture as SO deg. cent., if continued for some weeks, will produce an appreciable 
effect. The tests bv S. R. Roget (Ptoc. Roy. Soc, Msy 12, 1898 and Deo. 8, 
1898) showed that tne hysteresis loss increased 9 per cent, when the iron was 



279 



h,*^]i.)uyie 



Sec. 4-187 



PROPBRTISa Of MATERIALS 



^ 



1 

S9OO 



heated for 27 days at 60 deg. cent. ; 5Z per oe&t. when heated for 25 days at 
05 deg. cent.; 89 percent, when heatedfor 25dayBat87dec. cent.; 140 per 
cent, when heated for 25 days at 135 de^. cent. Alao see Mordey, W. M., 
Proc. Roy. Soc, June, 1SQ6; also see aging tests in "Eleotrio Machine De* 
ugn," by Parshall and Hobart; Allen, T. 8., "The Comparative Aging of 
Electric Sheet Steels;" Electrical World, 1908. Vol. LII, p. 579. 

18T. Kon-&^liig steal. Silicon-steel, aside from having low hystereais 
and high resistivity, also posseases the valuable property of being non-acing. 
That is to say, its magnetic properties are not impaired by prolonged heatins 
at moderate temperatures, but on the contrary may be ui^tly improved. 
While as much as 3 to 4 per cent, of silicon is present in aiUoon-ateel, it is also 
useful, in much smaller quantities, in improving the aging quidities of low- 
carbon steel. Parshall and Hobart recommend "'Eleotrio Machine Design," 
p. 36) the following compoBition for sheet steel having good aging qualities: 
carbon, 006; manganese, 0-50; silicon, 0-01; sulphur, 0*03; phosphorus, COS. 
188. Effects of meohaziical stress on ni«ffn«tilgfttton. Ewing 8tmt«s 
(Chap. IX, ** Magnetic Induction in Iron and Other Met^**) that the i>re»- 
ence of any moderate amount of longitudinal pull increases the 8usoeptibilit;y 
when the magnetism is weak, but rraucea it 
when the magnetism is strong. With hard- 
ened metal the effects of stress are in general 
much greater than with annealed metal. 

189. Paffs sffeot is the faint metallic sound 
resembling a light blow which is heard when a 
piece of iron is suddenly magnetised ordemag^ 
netised. 

IM. Cast iron is magnetically inferior to 
wrought iron or low steel, but is used to a 
limited extent on account of the facility with 
which it can be molded into complex lorms. 
The permeability is decreased by the presence 
of carbon, the eflfect being in the ratio of com- 
bined to graphitic carbon. Cast iron of good 
magnetic quality oontains from 8 to 4-5 per 
cent, carbon, of which from 0-2 to 0.8 per oent. 
is in the combined form, A normal induction 
curve for castiron is given In Fig. 18. Curve 
1 in Fig. 19 applies to cast iron^oontaininx 
0.105 combined carbon, 3-29 graphitic carbon, 
3.01 silicon, 0.320 manganese. 0.988 phoe- 
phoruB and O-OS sulphur. Curve 5 is for cast 
iron containing 0-72 combined carbon, 2.07 
silicon, 0-38 manganese, 0-85 phosphorus and 
0.035 sulphur. 

Silicon and aluminum in small pr(^>ortiona 
make the casting more homogeneous and tend to reduce the combined 
carbon. Silicon tends also to counteract sulphur. 

191. Halle&bls cast iron is magDetically superior to east iron, beinc 
lower in combined carbon and improved by the heat treatment which, it • 
receives. Curve 7 in Fi^. 19 is for malleable cast iron (see Parshall and 
Hobart, "Electric Machine Design") containing 0.83 combined carbon, 
2.201 graphitic carbon, 0-93 silicon, 0.116 manganese, 0-039 phosphorus and 
0.080 sulphur. 

198. Wroufht iron is among the beet of magnetic materials from the 
standpoint of permeability, but has higher core losses than silicon steeL See 
Par. iOO comparing Sweoish iron with other materials. 

198. Boiled steel of the low-carbon variety is used very extensively in 
the form of electrical sheets and rods. A normal induction curve is shown in 
Fig. 18. ' Commercial sheets are described in Far. 817 to 994. 

194. Cast steel is extensively used for those portions of magnetic circuits 
which carry uniform or continuous flux ana need superior mechanical 
strength. Parshall and Hobart state ("Electric Machine Design," p. 22) 
that oast steel of ^ood magnetic qualities should be limited in its composition 
as follows: combined carbon, 0.25; silicon, 0.20; manganese, 0.50; phos- 



100 



:h: 




Kilonuni 
Fio. 19. — Induotion-per- 
meabilitv curves oCoastuoQ 
and malleable iron. 



MlbyV^iUUyiC 



?l 



PKOPKRTIES OP MATERIALS SeC. 4-195 

ikaniB, 0.08; sulphur, 0.05. A normal induction curve it thowii in Fis< 
8. 

IM. AUoy itaal. The principal alloy steel in eztensire use is silioon steel. 
Its prcniwrtiee are covered under "Commercial Sheets,'* Par. SIT to M4, and 
FlcS'^^ud26. It is low incoreloss, non-acins, and high in permeability ex- 
cept at the hisher densities. Tungsten steel and tungiten-chrome steel are 
used extensively for permanent magnets; see " Msgnet Steel," Par. IM to 
no. Mltig Iron is steel to which has been added a small proportion of 
aluminum, ranging from 0.06 to 0.27 per cent. Magnetically it is a little 
better than ordinary steel up to densities of about 100 IcUolines per sq. in., 
and inferior at higher densities. See Parshall and Hobart, "Electrio 
Machine Design;" published by Enginetrint, London, 1906; p. 26. 

IM. BMt eompoiltton of dynamo ghooU; Do VoUr «nd ▼•yro*. 
Bish carbon and cold working are both injurious to electrical sheets. The 
reeommended composition and treatment is as follows: (1) The steel should 
have lea* than 0.1 per cent. carlx>n, from 3 to 4 per cent, ailicon, lesathanO.3 
per eeot. manganese, less than 0.03 per cent, sulphur and phomhorus; (2) 
the sheets after rolling should be annealed at 750 to 800 deg. cent, with slow 
eooUng; (3) the rolling should be finished at low temperature; (4) after final 
anneaUng, no cold working slionld be allowed (IX 6, No. 9, Sixth Congress of 
Int. Assoc, for Testing Materials, New York City, 1012). 

197. Xlaetroljtle Iron moltod in raeno. "Magnetic and Other 
Properties of Electrolytic Iron Melted in Vacuo " is the subject of a valuable 
monogrl^>h by T. D. Vensen, and is published as Bulletin No. 72, Engineer- 
ing Experiment Station, Univ. of 111., 1914; this monograph is the source 
of the following data. 

The electrolytio iron was doubly refined from Swedish charcoal iron 
anodes, and contained from 99.97 to 99.98 per cent, of chemically pure 
iron, 0006 carbon and 0.01 silicon. The iron as deposited was crushed, 
cleaned and placed in a magnesia crucible; then it was melted in a vacuum 
fnmaee and allowed to cool. Hnally it was hot forged to rods about 0.5 in. 
diameter and 20 in. long. The average results from rods annealed st WX) 
deg. cent, were as follows: 

Carbon content, per cent 0.0125 

Maximum permeability 12,050 

Flux density at maximum permeability 6,550 

Hysteresis loss, ergs per cu. cm. per cycle: 

At « (maximum) - 10,000 1,060 

At (B (maximum) = 15,000 1,990 

Coercive force, <B (maximum) " 1.5,000 0. 34 

Betentivity, (B (maximum) - 16,000 9,940 

Resistivity (mierobm-cm.) at 20 deg. cent 9. 96 

Critical temp., deg. cent 894 

The magnetic quality of electrolytic iron melted ta Mcue is decidedly 
superior to any grade of iron thus far produced; the maximum permeability 
obtained was 19,000 at a density of 9,500 gausses, and the average hysteresis 
loss obtained is less than one-naif that found in the beet grades of cora- 
mereia] transformer iron. Swedish charcoal iron melted in taeuo ap- 
proachee electrolytic iron in magnetic quality, due chiefly to reduction of 
carbon content. Low-carbon iron melted >n mcuo will lose 50 to 90 per cent, 
of its orijsinal carbon. Electrolytic iron is at present purely a laboratory 
or experunental product, and therefore too expensive for commercial appli- 
cations. See the bibliography appended io Mr. Yensen's monograph. 
Also see Proc. A. I. E. E., Feb., 1916, pp. 237-261. 

IM. Approzlmate saturation valuei of different magnetic materials 
nre given by Steinmcts as follows, in gausses. 





20,000 
12,000 
6,000 


1 Magnetite 


s.ooo 

4,000 


Cobalt. 


1 Manganese allosrs up to 

1 


Nickel 





IM. Xazimuni laturatlon Intonglty. HadAeld and Hopkinson have 
shown that a great number of magnetic materials, including commercially 
pure iron ana many iron alloys, have a definite saturation intensity of 



281 



dbyv^iuuynj 



Sec. 4-200 



PROPERTIES OF MATERIALS 



^ 



macnetism (Hadfield^ Sir R. A. and Hopkinson, B.. "The Macneti 
Properties of Iron and Its AUoys in Intenae Fields. " Jour. I.E. E., Apri 
igiO, Vol. XLVI, pp. 235-306). Theintensity of macnetisationiB defined a 
the quantity / in the formula <Bm3C+4«J, or the magnetio moment pc 
unit of volume. 

Every alloy which they examined was found to have a definite aaturatio 
intensity of magnetism, which they termed the ipeeiflo magnetlam 
This iotenaity was reached in most cases in a field of 5,000 units. Xh 
specific magnetism of comraercially pure iron of density 7.80 was found, t 
be 1,680 within 1 per cent. The presence of carbon in annealed iron-carbo 
steel reduces the specific magnetism by a percentage equal tosixtimea th 

Ssrcentage of carbon, if other elements are present only in small propoi 
ons. No allo^ was noted having a higher specific magnetism than pure iroi 
Quenching an iron-carbon alloy from a high temperature reduoea its specifi 
magnetism by a large but uncertain amount.^ The addition of silicon c 
aluminum to iron reduces the specific magnetism roughly io proportion t 
the amount added; but if carbon is present, silicon seems to neutralise i 
to some extent. 

too. Comparlsoiui of inafn*tio mat«riftb 
(T. D. Yensen. BuUetin No. 72. Eng. Exp. Sta., Univ. of 111., 1914) 



Material 



Swedish charcoal iron 
out from plate. 



Standard transformer 
steel. 



Four per cent, silicon 
steel. 



Swedish charnoal iron 
ronielted in vacuo. 



Electrolytic iron 
mcltea in vacuo. 



t 

Jib M 



4,870 



0.163 



0.008 



0.0125 



3,8S0 



3,400 



10,350 



12,950 



'I 



6.600 



7,000 



4,300 



7,000 



6.650 



Hyatereaifl 

lofle in ergs 

per cu. cm. 

per cycle 



n 



2,490 



3,320 



2,260 



1.290 



1.060 



e 

ii 



J5 



4,53o!o.95 8,000 



5,910 1.33 



3,030 



2,640 



1,990 



0.« 



0.48 



0.34 



9,900 



5,400 



11,200 



9,940 



•si 
•a 



i 



10.57 



11. OS 



51.15 



10.30 



».96 



Ml. Formula for induotton-pannoabllltr curra. A. 8. McAlliste: 

haa shown that the induction-permeability curve can be expressed with i 
fair degree of accuracy by an equation of the form 

.-2.800-3.2 [<^?^,^-''] (17 

The constants in this equation hold for the ordinary grades of sheet iron 
between the limits (B — and (B = 15,000, where CB is the maximum instan- 
taneous value. The numerical constants take different values for cast iron 
cast steel, silicon steel, etc. See McAllister, "Alternating-current Motors,* 
New York, 1909, p. 137. 

101. PenneabUltr in woak Held*. Ewing give* the permettbilit] 
in very weak fields, with values of 3C less than unity, according to the fof 
lowing formula based on investigations by Baur. 

i<-183 + l,3823C (18; 

This applies to soft iron. Lord Rayleigh found for harder grades of iron 

M-81+643C (lOJ 



282 



ilizedbyV^iUUyiC 



PROPBSTIBS OF MATMRIALS 



Sec. 4-203 



The Utter applies to hard-drsira iron wire; in another ease the initial 
pmneability was 87. The foref^oing relatioosliips are accounted for by the 
fact that the saturation eurre is sensibly a parabola in its earliest stages, 
•taitiiis, however, with a finite inclination to the axis of 3C. For •<- 
tresDcly feeble forces it is virtually an inclined straight line. See Ewiog, J. 
A., "Magnetie Induction in Iron and Other Metals,' London, 1900, 3rd rer. 
d.. CSiap. VI. 

M>. Pannaabllltr of iron at high treqneaclM has been investigated 
by E. F. W. Alexanderson and H. Pender (see " Magnetic Properties of Iron 
St PrMMDcica up to 200,000 Cycles," Trans. A. I. E. E., 1911, Vol. XXX, 
pf. 34SB-2454). Mr. Alexanderson concluded that iron has practically the 
same permeability at 200,000 cycles as at 60 cycles, but the magnetic pene- 
tration is greatly reduced at high freouencies, on account of the excessive skin 
effect, which must be taken into full account. See Par. IM. 

SOi. Haualer's mlloys are compoeed of copper, manganese and aluminum, 
and possess marked magnetic properties. The permeability increases with 
the addition of manganese until the proportions of manganese and aluminum 
are the same relatively as their atomic weights (Par. *Bt). The maximum 
magnetisation obtained is about one-third of that of the best iron. * Copper 



apparently no other purpose than to make the alloy soft enougo to 
be east and handled, MoTaggart* performed experiments on these alloys, 
noying the composition in many ways. The particular eompceition which 
(ilubited the best magnetic properties contained 14.3 per cent, aluminum, 
28.6 manganese and 57.1 per cent, copper. 

Dr. Heiisler, who discovered these alloys in 1901, stated that the most 
msgnetie alloy contained 25 per cent, of manganeee, 12.S per cent, of alo- 
Binasa, and 63.6 per cent, of copper, or in the respective proportions of their 
atomic weights. Also see tests made by Guthe and Austin, Bulletin of the 
Bureau of Standards, 1906, Vol. II, No. 2, and tests by 8tepbenson,Bu]letin 
No. 47, Eng. Exp. Sta., Univ. of 111., 1910. 

Mt. naetnm thaorr of mafmstlim. Mr. E. H. Williams has written 
sa extended monoaapn on this subject, which is published as Bulletin 
!(a. 62, tJnir. of III., Bug. Exp. Sta., 1912, and contains a bibliography 
of the important works up to that date. Also see Chap. XI of Ewing^l 
"Magnetie Induction in lion and Other Metals." 
COBK L088I8 

IM. Total mro Iom is composed of two elements, hysteresis and eddy- 
earrents. These two losaesfollow differentlaws, briefly setforth in Sec. 2. 
The loss may be stated in terms of total energy per unit volume per cycle; 
or it may be stated in terms of power loss per unit weight of material at 
some st^ed frequency. The effect of wave-form is discussed in Par. tlO 
and 111. 

tat. Talaaa of hraterasis ooefiEUiiant for different mAtariala 
(M. G. Uoyd) 



Material 


» 


Authority 


Material 


» 


Autho- 
rity 


lard tnagsten 
iteeL 

flaidniekei 

SardcMtstwd... 
Msgnetie iron ore. 

Gorged steel 

Fwo-mil steel wire 

SMtinm 

Mtniekd 

::aMstcd 

:Uibait 


0.058 

0.039 
0.025 
0.020 
0.020 
0.016 
0.013 
0.013 
0.012 
0.012 
0.012 
0.009 


Steinmets 

Steinmets 

Steinmets 

Steinmets 

Steinmets 

Lloyd 

Steinmets 

Steinmets 

Steinmets 

Steinmets 

Qumlioh 

Schild 


Soft machine steel. 
Annealed cast steel 
No. 36 iron wire. . . 
Ordinary sheet iron 


0.009 

0.008 

0.006 

0.004 

0.003 

0.0021 

0.002 

0.002 

0.0016 

0.0010 

0.0010 

0.0009 

0.0006 


Foster 

Foster 

Lloyd 

Lloyd 

Qumlich 

Qumlich 

Foster 

Lloyd 

Lloyd 

Lloyd 

Lloyd 

Qumlich 

Lloyd 


Heualer alloy II... 

Soft iron wire 

Annealed iron sheet 

Ingot iron 

Best annealed sheet 
Silicon steel sheet. . 

Silicon steel 

Best silicon steel... 


SeosUr aOo^ I. . . 
Seetrolytie iron. . 



Bee Loyd. M. Q., "Magnetic Hjrsterasis," Journal o/ th* Franklin IntiluU, 
hAi, 1910. pp. 1-aS. 

• MeTaggart. H. A. Univ. Toronto Studies, Papers from Phys. Lab., 1908, 
So. 23. 

AfiO DigihzGd by V^iOO^lC 



Sec. 4-208 PROPERTIES OF MATERIALS 

108. HyitoTMiB eoeflleitnts in Sieimneti*s formula fTk^-f/Bi* ar« 

flven in Par. SOT (Lloyd. M. Q., ** Macnetio Hyatercais," Journal of the 
'ranklin Inatitute. July, 1910, pp. 1-25). In this formula W% is the loes in 
ergs per cu. cm. per sec, /ia the frequency in cyclea per sec.. (Bis the maxi- 
mum induction and ia here 10.000 gauasea, and ^ ia the hyatereais coefficient. 
The exponent of <A, which ia 1.6, departa widely from this value at very low 
and very high denaitiea. 

t09. Total oor« lotaei for ihoots ore given in Fig. 20. Uoyd and Fisher 
give the following total core lossea, in watts per lb. at 00 cycles and 1U,0(MI 
gauasea, for No. 20 gage (3.57 mm.): unannealed(3.18to4.76: annealed, 1.25 
to 2.36: aUicon ateel, 0.605 to 1.06. See Trana. A. I. E. £., 1009, Vol. "XXVIII. 
p. 465. Alao aee Sec. 7. Par. S14. 

SIO. Kflect of wava form upon hTSterails lou. Dr. M. G. Lloyd, in 
his paper entitled "Dependence of Magnetic Hyatereais upon Wave Form" 
(Bulletin of the Bureau of Standards, Vol. V. No. 3, Feb. 1900, pp. 3S1-4 1 1) . 
reached the following Gonclusions. 

" For a definite maximum value of the flux density* the hsrsteresia ia greater 
with a flat wave of flux, but the effect is small, and from the industrial atand- 
point negligible, even with very distorted waves. If, however, the wave of 
nux ia dimmed, the hysteresis may be much increased. 

"The hysteresis determined by the balliatio method may be amaller than 
that whicn obtains with the use of alternating current, but the differenoea 
are am all. 

" The aeparation of hysteresis and eddy-current lessee by means of runa at 
two fie<iuenciee, using the Steinmets formula, is not accurate, but is a dose 
f^proximation when the sheets are thin." 

til. Xffoet of form-factor upon the iron loss was investigated by 
Dr. M. G. Llovd (aee '*E£Fect of Wave Form upon the Iron Losses in Trans- 
formera," Bulletin of the Bureau of Standards. Vol. IV, No. 4, 1007; also 
Reprint No. 88), who reached the following oondusions. 

* With a given effective electromotive force the iron losses in a trans- 
former depend upon the form-factor of the e.m.f., and vary inversely with it. 
By proper deaign of the generator supplying transformers, the iron losses 
may be reduoea to a minimum." 

lia. Xffeot of unsynunotrloal parlodic cyolss on h^toresis loss. 
Mr. M. Roaenbaum in a paper entitled "Hyateresia Loss in Iron, Taken 
Through Unaymmetrioal Cycles of Constant Amplitude,'* before the I. £« £. 
(aee Jowr, I. E. £., Mar., 1912), presented the following concluaiona. 

"It ia Been that the hyatereais loss increases very appreciably as direct- 
current magnetisation is auperpoaed on the altematmg flux. This phenom- 
enon manifeata itaclf in practice in inductor alternatoia and atatic balancers. 
In some kinds of inductor alternators the flux does not reverse, but oscillates 
between positive maximum and positive minimum values, thua the iron losa 
per^ ou. cm. is much greater in inductor alternators than in the 
ordinary tyi>e for the aame change of flux in the armature coil. In static 
balancera thia effect alao takea place where the direct-current magnetisation 
is not neutralised. It is therefore important, if high efficiency be aimed at, 
to neutralise the direct-current flux." 

8HXET OAaSB 

Sit. Two sjitems of ffSflnff sheets are in use. the U. S. Standard Gage 
and the Decimal Gage. These two gagea are fully covered in the two 
Bucceeding paragraphs. Also sec Par. SO. 

tl4. An act sstabUshins a standard rac* for sheet and pUte Iron 
Uld steel. Be it eruicted bjf the SeiuUe and House of Repreaentatiteaofthe 
United SUUea of America in Congreaa asaembUd, That for the purpose of 
securing uniformity, the following ia estabiiahed aa the only standard gace 
for sheet and plate iron and ateel in the United States of America, namely: 
(See Par, Sli.) And on and after July 1, 1893, the aame and no other shall 
be used in determining duties and taxes levied by the United States of 
America on sheet and plate iron and steel. But this act shall not be con- 
strued to increase duties upon any articles which may be imported. 

Sec. 2. That the Secretary of the Treasury is authorised and required 
to prepare suitable standards in accordance herewith. 

»Bo. 3. That in the i>raotioal uae and application of the atandard gage 
hereby established a variation of 2.6 per cent, either way may be allowed. 

Approved, March 3, 1893. 



284 

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PROPERTIES OF MATERIALS 



Sec. 4 



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PROPERTIES OF MATMRIALS 



Sec. 4-216 



llimlmal far* for tbaet inm and ateel adopted by the 
Amc ol Amer. Steel Manufacturers and the Amer. Railway Maater Mechan- 
ic* Aiaoe. i« baaed on the f oUowinc atandard thiolcneaaea, ezpreaeed in in. 



0.003 


0.012 


0.023 


0.040 


0.065 


0.090 


0.136 0.220 


0.004 


0.014 


0.025 


0.045 


0.070 


0.005 


0.150 0.240 1 


O.OOO 


0.016 


0.028 


0.050 


0.075 


0.100 


0.165 


0.250 


O.OOg 


0.018 


0.032 


0.055 


0.080 


0.110 


0.180 




0.010 


o.oao 


0.036 


0.060 


0.085 


0.125 


0.200 





Tin decimal aystem, denoting the thielcneaa in thouaandthe of an inch, waa 
eadoraed by the A. 8. M. £. Committee on Standard Thiolcneoa Gage for 
Metale. Tne weisbta are ucually calculated on the baaia of 480 lb. per cu. ft. 
lor iron and 490 lo. for ateel. 

OOmCBBCIAL BHntTS 

HT. Baetrteal shaata ia the ttade term for iron and steel aheeta ueed in 
the maanfactura of puaohinga for laminated cores or magnetic circuits. 

tU. Otmitm. There ace usually but two, or at the most three, grades of 
coBunercial aheeta. The ordinary grade is a soft or low-carbon steel, used 
enenaiTely for laminated rotors and stators in electrical machinery. The 
special grade ia a silicon ateel, which has low core loeaea and is non-aging, 
ased eztensiTely for transformers. 

n9. Data on Amarican Shaat and Tin Plata Comi>«n7'i eonunarelal 
ihaata 



Regular 

dynamo 

and 

motor 

sheets 



Special 

dynamo 

and 

motor 

sheets 



Trans- 
former 
sheets 



Grade of steel (iven hearth) 

^icciSe giBTity, in sheets 

Tcaaile strengtli. parallel to grain 

Yidd point. paraOel to grain 

ESong. in 8 in., parallel to grain 

TanJe strength, transverse to grain 

Tidd point, transverse to grain 

Brag, in 8 in., transverse to grain. 

Besjativity, microhm-cm 

Hysteresis loss at O— 10,000 in ergs per cu. 
cm. per cycle. 
Hystereaia coefficient 



Soft 
7.79 



Soft 
7.72 



4% 
silicon 
7.5 



48,000 
30,000 

21% 
55,000 
33,000 

22% 



62,000 
35,000 

25% 
61.000 
38,000 

19% 



96,000 
29,000 
2.4% 
102,000 
22,000 
2.1% 



8 to 12 
4042 



15 to 18 
3338 



0.001609 0.001328 



40 to 50 
1796 



0.000716 



The tcaaile teats given above represent only a few testa and consequently are 
•ot average results. On Regular Dynamo and Motor Sheets, the Bureau of 
StandardB obtained the following results, with No. 16 gage; tensile strength, 
BXMW lengthwise and 63,000 crosswise; yield point, 42,000 lengthwise 
asd 43.000 eroaswiae; elongation, 23 per cent, lengthwise and 28 per cent. 



The Regular and Special Dynamo and Motor ^radea are free from hardness 
sad brittleness and then is no difficulty in shearing or punching them. The 
Tt au a foiui er grade is generally harder than the ordwsry gradee, and in 
■aterial having the lowest iron losses there is usually more or less bnttleness. 
GsaeraDy speaaing, there is no difficulty in shearing it and not much difficulty 
iapooching it. 

The Regalar Dynamo and Motor grade is largely used in the construction 
sf laaiinated poles and intarmittently oparatsd electrical apparatus. The 
Special Dynamo and Motor grade ia used in high-effieiency dynamo and motor 



287 



dbyV^iUUyiL' 



Sec 4-220 



PROPBRTIBS OF MATKRIALS 



roton and BtAtore. The Traiufonnar grade is used very extensively In traB*- 
former cores. 

Curvee of averace induction, permeability and hysteresis in these three 
grades are given in Figs. 20 to 25. 

ItO. Aging of shaeU. The American Sheetand Tin Plate Company 
reports the following results of aging tests on their commercial sheets (Vmr. 
IK). Exposure to a temperature of 100 deg. cent, for 30 days resulted (on 



> 



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1000 








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4000 








son 


IWOS 

18000 


r 
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4S 




so 



Fia. 20. — Average induction and permeability curves, "Regular Dynamo 
and Motor Sheeto" (A. S. A T. P. Co.). 

■KB 



::::":2:" 


.Z.Z.I..I. 




.-- 1 --/ -- 


:z-':iVz::: 


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i/ 


- ^ - - +3? 






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i 'jii -I- - - - 


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■a 



21. — Average hysterpsis loop, "Regular Dynamo and Mulnr Sheets" 
(A. S. A T. P. Co.). 



the average of a number of samples of each grade) in a small increase in the 
iron loss (not exceeding 10 per cent.) in the Regular grade, a very slight in- 
crease in theiron loss of the Special grade, and a slight decrease in the iron 
loss of the Transformer grade. 

Ml. Iflaet of maehanieal working on ghMta. The only working tbs 
material receives is punching and compression in the finished core. Ths 



288 



iiiaxibyv^juuyic 



PROPBRTIB8 OF UATBRIAL8 



Sec. 4-222 



'act of puachinK is to daterionte the muoatio propertiai, which can be 
nwved by subsequent Mmealins, but if the cutting edgee are sharp the 
ifeet ia very small. 

HI. Date on Follanibae aUal thaeta are liven in Fi<s. 36 to 28. Nor- 
■tl induction curves are shown in Fis. 26. Curves of total core loss are given 
h RgL 27 and 28, all data being supplied by Follansbee Brothers Company. 



-(B- 










1000 








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-WO 3000 








4000 








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2 4 e 8 10 12 U It 18 :0 2S 30 39 40 IS X 

fia. 21. — Avence induction and permeaUHty curres, " Bpwial Dynamo i 
Motor Sheets" (A. 8. AT. P. Co.). 




Kio. 23.— Average hysteresis loop, ' 

(A. S. k 



'Smeial Dynamo and Motor Hheets" 
T. P. Co.). 



Both grades, carbon steal and silicon steel, are made by the basic open-hearth 
Pmna. Farther data may be obtained from articles by J. Q. Homan in the 
Bedrial ITarU, Sept. 7, 1912, pp. <S01-fl02, and the Iron Agt, Jan. 2, 1913. 

iU. Stalloy is the trade name for a commercial transformer steel. Ham- 
im and Rossiter (JSUetridan (London), Nov. 3, 10111 found the maximum 
PomeabiUty to be as follows: unannealed. 3,100 at S-4.fiOO: annealed, 4,200 
•t 0>7,000. Hystensis loss, 2,S00 eras per cu. cm. per cycle at ffl - 10,000. 



h,*^]i.)uyic 



Sec. 4-224 



PROPBRTISa OF MATSRIALS 



IM. CuTTU of total ear* lowMi in tlaotrieal ih««ta are ciTen in F^ 
iM, taken from the article on "Tranaformen," by Dr. A. S. MoAttieter in tfaa 
8ra edition of the Standard Handbook. 



-(B- 








1000 








2 


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WO 3000 








4000 








500 


































































































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Fio. 24.—. 



'Average induction and permeability ounre, "Transformer 
(A. 8. * T. P. Co.). 



Sheets" 






10 30 30 M W ■• 3t 


1«,C00 








^ , 







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Flo. 25. — Average hysteresis loop, Fio. 26. — Normal induction curves 
" Transformer Sheets " ( A. S. & T. P. of FoUansbee steel sheets. 

Co.). 

MAQNET 8TUL 
111. Desired eharacteristies in permanant macnata are maximum 
retentivity, coercive force, and permanence or non-aging eharaoteristie. 
These characteristics are beet obtained in carbon steel and certain alloy steela 
hereafter mentioned. 



290 



y Google 



PROPBRTIBS OP MATERIALS 



Sec. 4-226 



tM. ICacnat staal uiually eonteiu about 3 to 7 per cent, of tunsitea mad 
0^ to 0.70 per cent, of oarbon. The average tuDgsten content ia about 
S pv cent. U quenched in water from a temperature of about 800 dec. 
ernt. It will retain ita macnetiam better than carbon-steel. The addition 
•f about 0.50 per cent, m chromium will increaae the permanency, but 
the masnetio foree. Alao aee See. 5. 



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ftta4aca0 lo lsl4 L«Le £.02.2^4 Lfiisaois 
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Fig. 27. — Total core loea in Follansbee improved electric iteel ahceU. 

SST. Carbon msflivt ttaal is a hi<h-oarbon steel, and must be hardened 
by quenchins after it has been forged and machined to shape. Fig. 30 
shows the normal aaturation curve and the hystereaia loop of a glass-hsrd 
ptanoforte steel wire (Ewing, J. A. " Magnetic Induction in Iron and Other 
Metsls;" London, IDOO; 3rd rev. ed., pp. 83, 84). The maiimum per- 
meability in Fig. 30 is only 118. For information relative to the effect of 







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Fig. 28. — Total core loas in No. 29 gage (0.014 in.) Follanabee transformer 

steel. 



<lifferent degrees of temper on the retentiveneas see Bulletin No. 14, by 
Barua and Stronbal, U. 8. Geological Survey, 1886. 

Extensive experiments by G. Mars (StoAfumf £i<m, 1909, Vol. XXIX, p. 
^7W> indicate that retentivity is a function of the hardness and compoaitioa 
fi the metal. Fig. 31 shows relations between carbon content, hardness and 



391 



h,v^ji.)uyLC 



Sec. i-228 



PROPBRTISS OF MATSRIALS 



retentivity of oubon steel. The hardnen tnta were made with a lO-nim. 
Brinnell ball and a pressure of 3,000 kg. The retentivity increases with the 
carbon content and hardness up to a point where further increase in carbon 
is not accompanied by increase in hardness, then the retentivity deoreases 
due to displacement of effective iron by the carbon. Similar experimenta 
with various alloy steels sive results shown in Par. ISO. 

SS8. Tuiurstoii magnet Itoel ordinarily contains about 5 per cent, of 
tungsten. One satisfactory magnet steel analysed S.47 per eent. of tung- 
sten, 0.57 per cent, of carbon, 0.18 per cent, of silicon, and 0.20 per cent, of 
manganese. Tungsten-vanadium magnet steel analyses about 7.00 per 
cent, of tungsten, 0.30 per cent, of vanaidium, and 0.60 per cent, of carbon. 



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Fio. 29. — Curves of total core 
losses in electrical sheets. 



Fio. 30. — Hysteresis loop of gla 
hard steel wire. 



The addition of tungsten to steel increases the coercive force, and acoordins 
to Hoplunsoa, the value of the coercive force in tuDSBten steel may exceed 
50 (Ewing, J. A. " Magnetic Induction in Iron and Other Metals;" London, 
lOOO; 3rd rev. ed., p. S3). Comparative tests of four tungsten steels con- 
taining respectively 3, 6, 8 and 12 per cent, of tungsten, quenched from 900 
deg. cent., showed remarkably similar reeulta and indicated that a high 
percentage of tungsten is unneceoaary. In fact as much as 12 per cent, may 
produce inferior results (see Moir, M. B. Philoaophieal Magazine^ Nov., 1014). 
Also see Sec. 5. 



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Fig. 31. — Hardness and retentivity of carbon-steel. 

lit. Chrome nucnet iteel. According to Hopkinson the addition of 
chrome to oil-tempered steel may increase the coercive force to as much as 
40 (see PhUoaophxcal Tranacuiions, 1885). Chrome-steels containing up- 
ward of 8 per cent, of chromium possess superior permanency compared 
with tungsten steels, but are inferior in magnetic intensity (see Moir, M. B. 
PhilotojAicalMagannt; Nov., 1914). 



292 



V Google 



FROPgRTlSS OF MATERIALS 



IM. Compoiltlon snil 



lurdaniiur t«inp«ratur« 
rttonmlty 
(O. A. Kenyon; 3rd edition, standard Handbook) 



S«c.4-2S0 
for nMaimam 



Steel 


Compodtion per cent. 


Hardening 

tamp. dec. 

eent. 


C 


Si 


Mn 


W 


Cr 




0.97 
0.S8 
1.05 
1.22 


0.20 
0.18 
O.IS 


0.15 
0.26 
0.24 






810 
•30 
750 
760 




5.47 


1.23 




Chronie-tuDCSten 







m. Von-nurnetie (t««li. Hadfield found the presence of Urge 
pcoportioni (12 per cent.) of manganeee in steel deprived the metal of 
aesri^ all of its susoeptibility. Hopkinson found that a specimen of steel 
emtaining 25 per cent, of nickel was practically non-maf netic at ordinary 
tenperatiirea, but after eotJing to a very low temperature it became strondy 
aiaspiatic and remained so upon returning to normal temperature. The 
•df-iiardening steels (see "Structural Materials," Sec. 4) are also jpracti- 
olly non-macnetic. Any steel in the austenitic state is non-magnetic. 

BIBLIOa»ArHT 

Sn. Th* ftatborlt^tlT* litarature on the magnetic properties of iron, 
itcd and other metals is for the most part scattered through many books 
Am^\^ primaril^r with other topics, and through the transactions of the 
kadiof engineering and scientific societies and 'the technical press. Th« 
followinc is a selected list of the more important works and sources. 

£wixo»J. A. — ''Magnetic Induction in Iron and Other Metals." London, 
1900. 3nl i«v. ed. 

SnisiiKTS, C. P. — "Alternating-current Phenomena." McGraw-Hill Book 
Co., Inc., New York, 1S08. 

KamarsiOFr, V. — "The Magnetic Circuit" MoOraw-HUI Book Ck>., Inc., 
New Tork. 1911. 

Pmmdkk, H. — "Principles of Electrical Enipneering." MeOraw-EQII Book 
Co., lac. New York. 1811. 

GSAT, A. — "Electrical Machine Design." McGraw-Hill Book Co., Inc., 
-Vew York,. 1913. 

Tnnu. A. I.E. E. Jour. I.E.E.; rran*. Faraday Society; Bulletin of the 
Bueau of Standards. 

INSULATING HATERIALg . 

OLABBinCATIOir 
Bl Kathodi of elaaaifiektton. Dielectrics may be classified in a 
Bttmber of ways: (a) physical grouping, under solids, plastics, liquids and 
gMca; (b) according to working temperature limits; (c) according to the tsrpe 
of applicstion. 

>M. CUaUlekttoa of dlalaetrlei aeeordinc to Iwftt-reilgtiiic Pfop- 
mMm. Messrs. Steiiunets and Lamme in their A. I. E. E. paper on '^em- 
pBstunmnd Electrical Insulatbn" (1918, VoL XXXIlTp. 79) classify 
tlw naaal T"tTi^*t«r'^g materials aa follows, in three general classes. 

Clan A. This includes most of the fibrous materials, as p^>er, cotton, 
ftCL, nost of the natural oil resins and gums, etc. As a rule, such materialB 
beeome dry and brittle, or lose their fibrous strength under long-continued 
aodsrstdy hi^ temperature, or under very high temperature for a abort 
tiaie. 

dox B. This includes what may be designated as heat-reaisting materials, 
«1^ eonaiat of mica, a a bo stoe, or equivalent refractory materials, freauently 
Med in combination with other supporting or binding materials, the aeterio- 
ntioa of which, by heat, will not interwe with the insulating properties 
s< the final product. However, where such supporting or binding materials 
■« is such quantity, or of such nature, that their deterioration by heat will 
(raady impair the final product, the material should be considered as belong- 
ngtodaas A. 



293 



l.jV^iUUyiC 



Sec. 4-235 



PROPBRTISa OF MATERIALS 



I 



CIoM C. Tbia a repretentad by firaproof, or heat-proof mktaiials, cueh •■ 
mioa,^ Ui uaembled that very high temp«raturea do not produce rapid 
deterioration. Such materials are uaed in rfaeoatata and in the heatins 
elements of heating appliances, etc. 

The temperature limits specified by the A. 1. E. E. Standardisation Rules 
(Sec. 24, Par. IM) are as follows: 

(A— 1) Cotton, siUc, paper and other fibrous materials, not so treated aa to 
increase the temperature limit, OS deg. cent. 

(.A-2} Same as A-l, but treated or impregnated, and including enameled 
wire, IWS deg. cent. 

{B) Mica, asbestos or any other material capable of resisting high tem- 
perature, in which any class A material or binder, if used, is for struotural 
purposes only, and may be destroyed without impairing the insulatinc or 
mecnanioal qualities, I2fi deg. cent. 

(C) Fireproof and refractory materials, no specified limit. 



m. 



Phjraleal CUHMoktion of IMelacte'iea 

Qums and reaina 



[Solids 



Dielectrics 



Natural., 



Fabricated. 



Plastics. 



Liquids 



Oases. 



Used as such. 



Solidified on application 



Asbestos 

Wood 

Soapstone 

Slate 

Marble 

T,,ava 

Mica 

Papen and sheets 

Fabrics and yarns 

Hard rubber 

Synthetic .resins 

Molded compositions 

Glass 

Vitrified materials 

Caoutehooo 

Outta pereba 

Pitches 

Asphalts 

Waxes 

Compounds 

Mineral oil 

Animal oil 

Vegetable oil 

Varnish 

Shellac 

Paint 

Enamel 

Japan 

Atmospheric air 

Hjrdrogen 

Nitrogen 

Carbon dioxide 



IM. ClauiflMtton of dlaleetrlei aoeordlnc to tjiM of appUeatlon. 

Under this classification can be named: (1) Wire insulation; (2) cable insu- 
lation; (3) insulating supports, combining dielectric properties with mechan- 
ical strength: (4) coil and slot insulation for electrical apparatus and machin- 
ery: (5) insulating sheets, slabs and barriers; (6) molded insulation, shaped 
under the application of heat and mechanical pressure; (7) imoregnating and 
filling compounds; (8) superficial paints and varnisbea; (0) fluia insulatora; 
(10) gaseous insulators. 

1ST. Use of trade names in connection with insulating materials has 
unfortunately become very common. On account of the great number of 
such names no attempt has been made to state or define them all. Wherever 
feasible, insulating materials have been grouped and described in accordance 
with a rational elassifioatian, and adhering if possible to the natural or de- 
scriptive name of each thing instead of its trade name. 



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PSOPBRTIK8 OP UATBRIALa S«C. 4-238 

DnOVMIOH OF »»onKTm 
nc. P mIi »ble oharaetarlitiei of diaMetrlai may be enumerated as 
foOowa, under four heads; (1) electrical, (2) mechanical, (3) thermal, (4) 
chemical. 

(1) XlMtrloal (3) Tharmal 

Orest reajstiritr. (a) Larce apedfic heat. 

Small surface leakage. rb) Small tnermal reaistirity. 

Qraat diaruptire strength. (o) Small ooeScient o{ expansion. 

Deairable magnitude of dielectrio Id) High softening temp, 

cooatant depends upon types of It) High melting (Knnt, for solids, 

sppiieation. (f) High boiling point and low fraes- 

|e) Small dialecftric absorption. ing point, for liquids. 

Small dielectric hysteresis. (g) Low viacodty. 
:) Minimum power factor, 
i) Mimmum temperature coeffi- 
eienta. 

(2) MeohsniiAl (4) OlMiBl«a 

,) Great tensile strength. (a) Stability. 

,j) Great shearing strength. (b) Insoluble in adds, alkalies and 

e) Great oompreasiye strength. oils 

fit Pi«ii sble magnitude of modulus (e) High flash point, 

of elasticity depends upon type of (d) High On point. 



[S», 



i 



application. 
Dciriri 



(e) Dcairabia degree of hardness- 
ditto (d>. 

(f) Not brittle. 

(g) Denae non-porous structure. 
Va) Non'hygroscopie. 

0) Readily workable, 

nt. Inanl»tlon mdrtanea is separable into two eomponenta, volume 
leaiatiTity and surface resistivity. The leakage path through the substance 
or interior of the dielectric is electrically in parallel with the surface leakage 
path composed of a film of moisture or oil (with the frequent addition of dust 
or foreini matter) on the surfaces of the dielectrio. For exhaustive discus- 
■on of Uie characteristics of insulation resistanoe and the insulating proper- 
ties of dielectrioe see the following: 

Erershed, 8. **The Charaotaisties of Insulation ResistaDoe:" Jour, 
I. E. E., 1913. 

Curtia, H. L. "InsuUtting Properties of Solid Dielectrioe;" Scientific 
Paper No. 334, Bureau of SUndards, 1915. 

Flaming and Dyke. "On the Power-factor and Conductivity of Dielec- 
trics;" Jour. I. E. E., 1912, Vol. XLIX, No. 216, pp. 323 to 431. 

140. Volnma laanlntlon raiirtuiea of dielectrics is dependent upon 
the resistivity, usually expres sed as volume resistivity in ohm-cm., or ineg- 
ohm-cm. for greater oonTenieooe. Practically all dielectrics have a negative 
temperature ooefflelant, or decreasing resistance with rising temperature. 
When the volume resistivity becomes very high, on the order of 10^' ohm-cm., 
the dieleetiie absorption current is likely to be i^ sufficient relative magnitude 
to influence the olieemd value of volume reeistivity unless sufHeient time is 
allowed for complete dectrifioation. la the case of two materials having a 
rwistiiritr of 10" ohm-em., hard rubber and fused quarts, the apparent resis- 
tivity uBdcr continuous deotrifieation increases tor a long time. 

For most practical cases, however, that portion of the leakage current 
which flows through the body of the didectric is negligible in comparison with 
the portion which flows through the surface film. But when the volume 
resistivity is less than 10>' ohm-em. and whea the insulator is placed in an 
atmosphere having a humidity of less than 25 per cent., the greater part of 
the current may flow through the body of the insulator. 

In porous materials or those containing appredable moisture, such as 
slate and marble, the volume resistivity decreases somewhat withincreaae of 
applied vdtage. In all such oasee the volume resistivity increases rapidly 
as the moisture is dried out. 

The eifeotive resistance with alternating currents is usually leaa than with 
continuous currents, and decreases progresdvely as a rule with Increase in 
frequency, owing to dideotrio energy losses (Par. Ml), 

296 

Digitized byGoOgle 



Sec. 4-241 



PROPSRTISS OF MATBRIALS 



S41. Bnrfaoa tnttilatlon rerietanod. The surface conductivity ia tho 
reciprocal of the surface rraiativiiy, and the lurfaoe rotUtlTity is the reeist- 
ance between two oppoeite edges of a surface film which is 1 cm. square. 
Since for most materials under ordinary conditions of humidity the surface 
resistivity is much lower than the volume resistivity, the resistance per 
centimeter length between two linear conductors 1 cm. apart, pressed upon 
the surface of a slab of the material, is approximatdy equal to the surface 
resistivity. 

The relationship between surface resistivity and humidity, for a number of 
different materials, is given in Fig. 32. These curves are generally typical 

of solid dielectrics. The sur- 
face resistivity is often a 
million Cimes as e^eat at low 
humidity as at mgh humid- 
ity. Measuremonta made on 
various molded composi- 
tions at the Bureau of 
Standards (Scientific Paper 
No. 234) gave values ranging 
from 10>« to 10>T ohm-cm. 
(between opposite edges of a 
film 1 cm. square), at 22 
deg. cent. 

S4S. Dieleotrto eonstaat 
ia defined in Sec. 2. Th« 
customary medium of refer- 
ence is almost universally dry 
air at normal temperature 
and oressure. For most ma- 
teriala the temperature coeffi- 
cient is positive, but for 
india-rubber it appears to be 
negative at ordinary tem- 
peratures. The coefficient 
for celluloid at 15 deg. cent. 
is approximately 0.005 per deg. cent., whereas for mica it is about O.OiOOO. 

545. DiMeetzie abiorption is the term applied to the apparent soaking 
up of electric charge within the body of a dielectric when the electric stress is 
IMY>longed for an appreciable time. In other words, it requires appreciable 
ume for the dielectric to become fully saturated with electric charge or dis- 
placement, when a steady stress is applied. In some materials this phenom- 
enon is marked, while in others it is slight. Due allowance should oe made 
for it, however, in certain classes of measurements, notably insulatioa 
resistance. 

S44. Dletoctric itroncth, usually expressed in volts or kilovolts (kv.) per 
mil or per mm.,* is a property whion it is impossible to determine with high 
precision, and which is affected by numerous variables such as the site and 
shape of the test electrodes, the time rate at which the teat voltage is raised to 
the disruptive point, the order of frequency of the teat voltage and the 
thickness of the teat specimen. Furthermore, disruptive discharge requires 
not merely a sufficiently high voltage, but a certain niininium amount of 
energy. There is no accepted standard apparatus or method for testing 
clielcrtrics, and honcc the results obtained by different inveatigatorsarc com- 
parable only as to gnneral nrdcr of magnitude, if at all. Moreover the prob- 
able error in ineasureraents of disruptive strength is unusually large and any 
one set of observations is likely of itself to be in error by as much as plus or 
minus 10 to 20 per cent. Consequently the values of disruptive strength 
stated in this section are to be considered as purely approximate and not 
accurately comparative. 

546. The fftotors affecting dielectric strength may be stated as fol- 
lows: internal or external heating, chemical change, absorption of moisture, 

• 1 volt per mil— 39.4 volts per mm. 
1 volt per mil — 0.394 kv. per cm. 
1 vc^t per mm. — 0.0254 volt per mil. 
1 kv. pw cm. — 2.54 volts per mil. 




Fio. 



see 



yGoogle 



PR0PXRTIS8 OP MATERIALS 



Sec. ^246 



uUore of wnTOiimting medium, rite and Bhape of t«flt eleetrodM, thiekneM of 
teat apeoimeii. time rate of applying the t&ruptive voltase, whether oon- 
tiaoous or altarnatinc teat preasure ia employed, and order of magnitude 
of the teat frequency. 

>M. Uaot of aUe of aleotrodM. Farmer concluded from hia teata that 
the average dielectric strength of insulating materiala in thin sheet form ia 
materially higher with small electrodes than with large ones; upon making 
the electrodes very small, such aa needle points, however, the dieleotrie 
atreogth apparently decreases again. See Farmer, F. M., "The Oielaetrio 
Stocngthof Thin Inaulating Matariab;" Trmu. A. I. E. £., 1913. Vol. XXXII, 
uf. m7 to 2131. Alao see FranUin. W. 8., "Dielectric Stresses from the 
Mechanical Point of View;" Jour, franklin In»t., 1913. 

MT. Uaot of tlileknsii of test ipoelinen. It is comparatively rare to 
find an insulating material whose dielectric strength varies uniformly with its 
thjekneas. In the case of fibre, for example, the disruptive strength in- 
ma s ui very slowly with increasing thickness. On the otner hand, tne die- 
mptive strength of multiple layers of glass with intervening oil films is nearly 
proportional to the thickness. A law was proposed by Baur which can be 

ii|«i«siii1 B — ki^, where B is the disruptive voltage, I is the thickness of the 
J i ffa'tii c and jfc is a constant; in other words, the disruptive voltage varies 
as the two-thirds power of the thickness. This law ia a rough guide Tor some 
"— **-^-'- Anotnw law proposed bsr Walter, for air, ia B — a+bl, where 
a and friars constants and I is the thicknesa; thia law holds for needle gaps 
froBi 50*to 4S0 mm. under ordinary preesuree and temperatures. 

Mg, T.«iitlii»tlon. Hendricks* statea that a finel]^ laminated structure 
improrea the dielectric strength. This is partly explained aa follows: weak 
spots in succe s si ve layera very rarely coincide in position, rupture at some 
wcaJ internal point^may be confined to one lamination, and thla materiala 
are in general auperior in point of electric and mechanical unit strength. 

Mt. ISoet of t^equonoy. There is usually considerable difference 
between disruptive strengths aa determined by alternating e.m.fs. and by 
eoatinoous e.m.fs. In the case of continuous e.m.fs. there is much less in- 
ivaal heating than there ia with alternating e.m.fs. Disruptive strengths 
of solid dielectrics measured with continuous e.m.fs. are about one and one* 
balf to two timea the strengths meaa- 
■tcd with alternating e.m.fa under 
ike conditions. When the order of 
frsqneney is inereaaed from commas 
aal power frequencies to those repre- 
WBtatiTe of high-frequency high-power 
•argea, aay «)0,000 cycles, there is 
reason to believe that the disruptive 
sttength is reduced. Creifhton haa 
shown that this is the fact in the ease 
of porcelain (ase Free. A. I. E. E., 
Hay. I91S, p. 819, Fig. 39). where 
dMnqitive valuea at very hidi fre- 
qgrncy ware on the order of 60 to 80 
per cent, of the 60-oycls values. 

SM. BKaot of tho ttmo etoiiMiit 
ia applying the dismptive presauro is 
proBonaeeo. For very brief periods 
Aeketrica will withstand muoligreater 
potentiala than for longer periods. 
Tkis is apparently a eonaequenoe. in 

psit at least, of the fact that disruptive discharge requirea a certain minimum 
sawant of auxfy in each inatanee. Thus the disrufitive energy required in 
the case of oil la about 30 times that required for air. It is characteristic 



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Fia. 33. — Typical curves of dis> 
niptive voltage with respect to in- 
terval required for puncture. 



•f cil and of materials impregnated with oil that the dielectric strength is 
(reatsr for insta, ' 
proloagsd stress. 



for instantaneous or very brief applications of stress than it is under 
The brief time into-nu required to energise the dielectric 



* Hendricks. A. B.. Jr. "Hi|^-tenaon Testing of Insulating Materials;" 
Tnn. A. I. E. E., 1911, Vol. XXX, p. 187. 



107 



,y Google 



S«C. 4-2S1 PROPBRTIBS OP MATSRIALS 

befoni breakdown oooun ia sometimM referred to w the dieleotric apark lu. 
A good illvutration of the eompantive effeeta of alow veraua faat rata of appfi- 
cation of the diaruptive roitage ia given by Creighton for porcelain (aee Pfoe. 
A. I. K. £., May, 1916, p. 818, Fig. 28). Alao aee Hayden and Steinmeta, 
"Diaruptive Strength with Tranaient Voltagee;" Tnnu. A. I. E. E., 1910. 
Vol. XXIX, pp. lT2S to 1158. Fig. 33 ahowa typical ourrea (plotted from 
Rayner'a 1912 paper. Jour. I. E. E.) of diaruptive voltage with reapeot to th« 
time required for puncture. 

tSl. Dlalaetrlo hTltaretU ia a form of energy loaa in dieleotrioa, and ia 
independent of any loaa due to pure oonduetion. The latter loaa ia«xpreaaed 
by pB', where g ia the total conductance in mhoa oia given body of dielectrio 
ancf S 18 the impreaaed difference of potential in efteotive volta, the power loaa 
given thereby being expreaa c d in watta. The Itotle OOmpoiMIlt of dieleo- 
trio hyatereeu prol»bly ia proportional to the 1.6th power of the mazimura 
dielectrio flux denaity. The Tiieoiu eomponant of dielectric hyatereaia 
followa the aquare law. The latter component ia probably the predominating 
one, ainoe experimental evidence* from condenaer teata with alter nating 
currenta goes to ahow that the angle of phase difference due to hyatereaia ia & 
constant, for any particular condenser. It followa from thia that the power 
loaa in the didectno ia proportional to the aquare of the flux denaity and tho 
aquare of the frequency, wnioh correaponds to the viacous component of hys~ 
teresia. As a riue these electrostatic hysteresis losses in a condenser are 
much smaller than the loaaea oocasioned by magnetic hyatereaia and are rather 
diffictUt to meaaure. Frequently they amount to no more than a fraction of 1 
per cent, of the volt-ampere input of the oondenaer, at frequenciea from 25 to 
125 cyolea. Bee Kayner, E. H., "High-voltage Teata and Energy Loaaea in 
Dielectrics;" Jour. 1. E. E., 1912, VofXLIX, No. 214, pp. 3 to 89: also see 
Fleming and Dyke, "On the Power-factor and Conductivity of Dielectrics;" 
Jour. I. E. E., 1912, Vol. XLIX, No. 215, pp. 323 to 431. 

U>. Dlalaetrlo pewar-faetor. When a dielectric ia aubjeoted to a pe- 
riodic alternating e.m.f. leas than the diaruptive value there ia a loaa or expen- 
diture of energy within the dielectric from two cfkuaes: (1) the leakage con- 
duction current, (2) the dielectrio hyatereais. Conaequently, the volt- 
ampere input to the dieleetrio, inatead of having a aero power-factor aa in tha 
ease of the ideal dieleetrie of infinite reaiatance and aero hyatereaia, has a 
power-factor of finite value but usually small magnitude. Thia total dielec- 
tric loaa may, in aome oaaea, have conaiderable importance. Fleming and 
I^ke* made teata on eleven different materials at 920, 2,7flO and 4,600 oydea, 
and found that the powei^faotor was less than 1 per cent, in the case of dry 
Manila paper, paraffin wax, mica, ebonite, pure india-rubber, vulcanised 
india-rubbw and sulphur; about 2 per cent, for glasa and gutta percha; 
and 8 per cent, for 4ry slate. 

tlS. ISavta of tamparstura. It a dielectrio contains moisture, the 
application of heat will reduce the moisture content and simultaneously 
increase the resistivity and the diaruptive voltage. In the caae of a thor- 
oughly dry aubetanoe, however, increase of temperature hsa the reverse 
effect. Prolonged heating of a dielectrio, if in exceas of the aafe or conserva- 
tive limit of working temperature, is injurious and tends to hasten the break- 
down of the material by disintegration or chemical change, and ensuing dia- 
ruptive failure. Exoej>t in the caae of fireproof and refractory materials, the 
working temperature is a most important factor in determining the life of 
insulation. Bee Par. St4 and also see the temperature limits apecified in the 
Standardisation Rulea of the A. I. E. E., Sec. 24, Par. 1(T to WW. 

SOLID HATUSAI. KATBUALS 

IM. AabaitM ia a mineral fibre compriaed of hydrous silicate of magnesia, 

rhieb mdts at a temperature in the range from 1,200 to 1.300 dag. cent. 

It ia useful aa an inaulating material becauae of ita heat-reaiating qualitiea. 



which mdts at a temperature in the range from 1,200 to 1.300 dag. cent. 
It ia useful aa an inaulating material becauae of ita heat-reaiating qualitiea, 
and ia fabricated into boards, paper, tape, etc., frequently in combination 



with a binder to make it atronger mecbanicaUy and less abaorbent of moi»- 
ture. It ia Dot inherently a good insulator, and for thia reason is frequently 
mixed with other fibres or loading material to impart greater strength, higho' 
insulation and better finish. The commercial varieties of aabeatoe often 

* Steinmeta, C. P. "Alternating-current Phenomena;" New York, Mo- 
Oraw-HiU Book Co., Inc., 1908- 4tli ed., pp. 212 and 218. 



, Google 



PaOPEKTISS OF ilATSRIALS S«c. 4-256 

Tmtif'" iron and other impurities, mitking it dmoet uaeleee •> an eleotrieal 
insulator. Aibestoe ia an excellent thermal ioaulator. Ita eiectrieal reeis- 
tivity ifl on the order of 16X10* ohm-cm.; disruptive voltage, 00 to 100 
volts p^ mil; maximum working temperature, SOO to flOO deg. cent. When 
used for are defector* in oontroilera, awitehes, etc., it is usually impref- 
uted with a solution of silicate of soda and then subjected to heavy 



A sb ca t oa is frequently oombinod with mfgnesium carbonate, or with finel^r 
^nyond iponge, or with wool felt, as a thermal insulation for steam pipss; it 
IS also mixed with cattle hair, for similar use, and known as ssbestos hair felt. 
Asbestos is also extensively employed in the manufacture of molded composi> 
tions desicned to withstand high temperatures. 

MB. Olialk Is a fine-grained limestone of marine origin, oomiiosed of finely 
coauninuted shells, particularly those of the foraminifera. The specific grav- 
ity may be as low as 1.8. A theoretically pure limeetone ia merely a massive 
form o>f the mineral calcite, consisting entirely of calcium (lime) carbonate, 
CaO + CX>t-CaCO<, or 66 per cent. CaO and 44 per cent. COt. 

SM. yira clay. Clay ia the term applied to fine-grained unoonaolidated 
natural materials which possess plssticity when wet, but lose it on being 
hcatod and becopie hard. The specific gravity ranges between 1.5 and 2.2. 
The days are composed essentially of silica and alumina, in a state of exceed- 
in^y fine subdivision, resulting from the decay of older rooks. Fire clay ia 
the variety of day which is moat highly refractory, containing much silica 
and Bttle Ume, iron or alkalies. As an insulator it is applied m semi-Iiauid 
form and baked, after the conductors are imbedded. It Is not affected by 
B<dda, <h1s or alkalies. 

UT. Onma and raalag. The natural gums and reains such as caout- 
chouc, gutta-percha, pitch, etc., are^aeldom if ever employed for insulating 
purposes while in their native condition, but are treated, or mixed with other 
materials, or adulterated, in a ^reat variety of ways. They form the bsaes or 
cosatituents of many different inaulating eompoiinds, but undergo numerous 
chemical or phyuoal changea in manufacture. 

lik. loa. The disruptive strength of ice is 1 1 kv. (max.) per cm. ; dielee- 
trio constant, 86.4; resistivity, 7.2X10' ohm-cm. Bee Thomas, P., "The 
Dielectric Properties of Non-oonductors;" Jimr. FrmlUin lift,, 1918, Vol. 
CLXXVI, pp. 283 to 301. According to Whittaker's Pooketbeok, par* 
water haa a resistivity of 7X 10" ohm-cm. 

SM. iTory has a resistivity at 22 deg. cent, of 2X10* ohm-em. 
MO. KaoHn is a white china clay whose chief ingredient is the mineral 
kaoUnite, and the latter has the chemical comoosition HiAlt8iiO< + lHiO, or 
hydrous silicate of aluminum. Kaolin is highly refractory and is one of the 
prinoipal materials employed in the manufacture of porcelain. It is some- 
Umes employed for insulating purposes. 

Ml. Lava is a mineral tale, which has the chemical composition HiM^ 
SiiOu, or faydrated magnesium silicate, and ia similar to soapstone, pumice 
and tale, it is slightly soluble in hydiochlorio acid, but is not attacked by 
other acids or alkalies. Wldle in the natural state it can be machined with 
the same fadtity as brass. It neither shrinks nor expands under the in- 
fluence of moisture and has a very small coefficient of expansion. 

After machining, it is baked at about 1,100 deg. cent, which renders it 
extremely hard. Its insulating resistance is high and according to tests 
made by the American Lava Co., its dielectric strength varies from 3,000 to 
10,000 volts Iter mm., according to the thickness. ^ Par. ITO and ITl, 

Mt. Lavite (also see lava) is a light buff or cream-colored insulating mate- 
rial invented and patented in 1886 by D. M. Steward. The manufaoturem 
supply the following information: Density, 2.5 to 2.7; electrical reeistivity, 
SOO to 2,500 m«gohm-em.; disruptive strength, 200 to 250 volts par mU; 
modulus of niptnre, 6,000 to 12,000 lb. per sq. in. ; compressive strength. 
20,000 to 30,000 lb. per aq. in.; eompares with glass in hardness; not affected 
by temperatures up to 1, 000 deg. cent.; unaffected by acids except aqua regia. 
MS. Marble is a limestone of the cryatslline variety which will take a 
high polish and exhibit pleasing color effects. Ita chief coDstituenta are 
lime and magnesia, or their carbonates; it also contains water of formation 
and ■ometime* met^e veina. It is used very extensively for low-tension 



Sec. 4-264 



PROPBRTIE8 OF MATERIALS 



Bwitohboard panels. Its properties can be imx>roved by treatment in molten 
paraffin wax or Unseed oil, after all moisture has been expelled, but such 
treatment results in discoloration. The resistivity is on the order of 10' 
to ICH megohm-om. and the disruptive voltage is in the vicinity of 50 to lOO 
volts per mil. See tests in Par. SM. 

M4. Mlea is generally recognised as the most superior insulating material 
known to the art, that which is imported from India bein** the best, the 
Canadian grades next and domestic varieties last. Either domestic or 
India mica is satisfactory for nearly all insulating purposes except for oom- 
mutators, where it is too hard to wear down as fast as the copper bars. For 
the latter service Canadian amber mica is considered more satisfactory, 
being softer than the other grades. All grades of musoovite (white) mica 
are considered suitable for electrio heating appliances. Mica sheets and 
washers are used in electrical apparatus and appUances in almost innumer- 
able shapes. Cut mica in sheets becomes very expensive in the larger sises,. 
the largest commercial listed sise being 8 in. by 10 in. On thiB account it 

is customary to build up larser 

«-__- , , , 1 — I , , 1 — I siies by connecting together thin 

'' III layers of mica. Such manufac- 

tiu^ mica plate takes a number 
of forms. 

SU. Composition and prop- 
erties of mioa. Mica is a 
refractory mineral constituted of 
the double silicate of alumina or 
magnesia, and potash or soda* 
combined with varying propor- 
tions of potash, soda and other 
impurities. Iron in excess colors 
it gray and black ; magnesia tends 
to darken the color; aluminium 
and potassium silicates 'tend to 
make the mica transparent. 
Mioa crystalliiea in laminated 
form and may bo split along its 
axis to sheets as small as 0.0O6 
mm. 

It has a high didectric stren^h 
and is suitaDle to withstand hiyh 
temperatures. However, in its 
natural state it is not flexible nor 
uniform, and permits large sur- 
face leakage; so that most mica 
is reeonstnioted and put on the market in the form of micanite, megomit, 
megotalc, ete. ^ 

The properties of mica are very fully covered in a publication by Zeitler, H, 
**Mica: Its History, Production and Utilisation^' D. Jaroslaw. London. 
1913: also in the 1912 edition of " Mica," by the Canadian Dept. of Mines. 
These sources wots utilised in the preparation of the following table. 




att aio au flkss aj» QLM a» aw a« (uo 
Tliidcnflss In mm. 



Fio. 34.- 



-Disruptive strength of mica in 
air and in oiL 



Origin 


ResUtivity 

in 10" ohm 

-cm. 


Dielectric 
conatant 


Disruptive strength 

in volts per 

mm.* 


Mftdru 


15 to 133 
7 to 118 
0.44 to 22 
39 


2.5to5.6 

2.8to4.7 

2.9to3.0 

5.9 


50,000 to 80,000 
40,000 to 120,00 

80.000 
40,000 to 90,000 


Bengal. 


Canada 







Fleming and Johnson give the dielectric strength, in sheets 2 to. 3 mils 
thick, as about 2,000 volts per mil for amber mica and about 3,000 to 4.000 
volts per mil for the white, ruby and soft green varieties; Fig. 34 shows the 

• Note. — Test thickness, 0.3 mmi 



300 



yGopgle 



PROPBBTISS OF MATERIALS SeC. 4-266 

Msalts aS teats nuule by Rayner at the National Phyaioal Laboratory (Jour. 
LB.E., 1912, Vol. XLnC,No.212). Power-factor at 820 eyolea, 0.001. The 
dmaity of mica ia from 2.7 to 3.1. Specifio heat, 0.206 to 0.208. It ie not 
affected by heat until a temperature of several hundred defjeee oentiKrade 
B raaehed. when the lamine separate in the harder varieties and tend to 
ifc'ntm ate into small scales or flakes; amber miaa ia leas affected. Meltinf- 
ptint, l.Mnto 1,300 dec oent. It will withstand (Teat meohanical pressure 
usqwrniticular to the plane of oleavace. - 

IM. ma* prodneta. Many products are manufactured from mica, in- 
tladins paper, cloth, plate and molded insulation. In some cases the strips 
of mica are moonted on paper or doth, in alternate layers, usinx an insnlatina 
binder sneh as shellac. Molded products are usuuly made from ground 
abea mixed with a binder, and sometimes mixed with other insulating mate- 
risls such as aabestos, or a gum or compound. 

Quarts ia a form of illiea (SiOi) occurring in colorless transparent 
_jaal crystals, but sometimes yellow, brown, purple, green and 
r eolors. It abo occurs in crystalline masses of vitreoua luster. Dens- 
T, 2.65. Dielectric constant 4.3 to 6.1. The resistivity is from 10>< to 10" 
otUB-em. Silica is the principal constituent of glass. Quarts fibres of very 
mall lateral dimensions are sometimes used for suspensions in delicate 
dietrieal inatmments: such fibres have a tensUe- strength of about 10X10* 
dynes per sq. em. Also see fused silica (Par. ITS). 

IM. Mate ia a roek of day compoaition, in which preesure has produced 
a verjr perfect deavage, so that it mav be qdit into thin tough plates. The 
principal i»nBtituents are silica and alumina, with small percentages of iron 
axidss, lime, magnesia, potash and soda. It freaoently contains metallic 
Taai, which make it worthlees for deotrical worV, It is hygroecopie, in 
sikfition to containing water of formation, and is therefore far from 'an 
idta] insulator. The resistivity of a good grade of slate at normal tempera- 
tirsiaof the order of 10* to 10* me^onm-cm., and decreases rapidly at nigh 
tenperatores; hi|lier values of resistivity have been obtained with very 
dqr spedmens. The dielectric constant is between 6 and 7. Power-factor 
at (30 cycles, 0:086. The disruptive voltage fo> 1 in. of thickness ia from 
UOO to 10,000 volts, or 6 to 10 Volts per mil. See testa in Par. tM. Spedfic 
bsat, about 0.2; thermal conductivity, 0.0036 g-cal. per em-cube per 
dag. cent, per see. The density is from 2.7 to 2.S. Slate is a satisfac- 
tsry insttlator where a non-comoustible, low-tension material having fair 
issalslim properties is required. It ia sometimes varnished or enamdled to 
keep oat moisture. 

IM. Fnnetar* teata of Varment lUte and marbia,* made with flat 
tai culai farasB deetrodes 0.78fi in. in diameter having slightly rounded edges, 
isdiratad valiies rangins from SO volts to 100 volts per mil for marble (test 
fiseai 14 in. square ana about 1 in. thick) and roughly on»-tenth of these 
Tslaea for slate. Blue marble was considered superior to white marble. 
Marked hratinir of the specimens wss noted at or near the rupturing voltages, 
kai^ lesB marked in the case of blue marble, and eepedally marked in slate; 
the test pieces were air dried in a warm room for several weeks before 
tertiag, but undoubtedly retained a certain amount of moisture. Corona or 
brash discharges were very noticeable during the tests, at pressures in the 
nciaity ct the rupturing values. 

m. Boapatooa ia a kind of soft stone, which is soapy or slightly oily to 
the toneh. It is also known as itaatita, or massive variety, of tala, of 
Paykh g re an or brown color. It forms extensive beds and is mined for 
Mtfths, sink K«w*«e«, ete. It is oecanonally used for dectrioal insulation, in 
tlM ioni of slabs or bairiers and will withstand very high temperatures. It 
•a asft. not very strong, not affected by adds, oils or alkalies; can be ma- 
tbiaed, drilled and sawed, and absorbs moisture. 

flfl, Tala is a hydroua magnesian silicate, HtMgs(SiOf)f, containing when 
awe 03 per eent. of silica, 32 per cent, of magnesia and 5 per oent. of oom- 
■aeil water. It haa a specific gravity of 2.6 to 2.9. Soapstone and French 
•Mk are varietiea of tale; other varieties are used in making soap, paper, 
Wriraata, eie. Bae Par. Ml. 



'Beport of the Vermont SUte Geologist, 1912, pp. 106 to 219. 

801 ' ■ Digiiizedb, Google 



I 



Sec. 4-272 ' propertibs of materials 

ITS. Wood is uaed as an insulatiiuc material to a considerable extent. The 
varieties of wood employed are usually the hard woods, such as maple and 
hickory, impregnated with oil, paraffin wax, or clear air-drying varnish. The 
resistivity of paraffined wood, at 22 deg. cent, is of the following magnitude: 
mahogany, 4X10i* ohm-cm.; maple, 3X IQi^; poplar, 5X IQU; walnut, 
O.OQX10^o to lX10>o (Scientific Paper No. 234, Bur. of Standards). The 
dielectric constant and the disruptive voltage are both dependent upoa 
whether the electric stress is parallel or perpendicular to the grain. Paral- 
lel to the grain the dielectric constants of red beech and oak are between 
2.5 and 4.8; perpendicular to the pun, 3.6 to 7.7. 

In maple boilcKl in transformer oil under vacuum, dried under vacuum and 
boiled iMC&in at atmospheric pressure, the flisruptive voltage along the ^ain, 
at 1 in. of separation, was 70 kv.; at 2 in. it was 90 kv.; across the grain, at 
0.5 in., it was 60 kv.; at 1 in. it was SO kv.; dielectric constant, at 20 to 25 
deg. cent., across grain, 4.1. Well-dried wood should stand 10 kv. per in. 
without signs of burning or heating. It is extremely important that the 
wood should be well dried before inipr^nation, because it is very difficult to 
remove the moisture subsequently. When wood contains moisture it is a 
relatively poor insulator and the water contained in the cells conducts elec- 
trolytically. Wood treated with sine chloride to protect it against decay has 
comparatively low resistivity; see Electrical World, 1911, Vol. LVII, p. 828. 
For curves of disruptive strength of maple see Hendricks* A. B., * High- 
tension Testing of Insulating Materials;" Trans. A. I. E. E., 1911, Vol. XXX, 
pp. 167 to 218. 

VITEZraD BCATSBIAL8 

ITS. OUm is an insulating material in very extensive use, posscssizig high 
resistivity and dielectric streiurth at ordinary temperatures. The principal 
constituent is silica, ranging xrom 50 to 75 per cent, of the total contents; 
potash* soda, lead oxide and lime are also present, in various proportions. 
The resistivity at ordinary temperatures is on the order of 10^' to lOi' ohm- 
cm. and decreases with great rapidity as the temperature increases. Gray and 
Dobbie found that potash ^lass has higher resistivity than soda glass, and 
annealing increases tne resistivity (Proc. Royal Soc, 1900. Vol. LXVII, p. 19^, 
At very high temperatures gloss becomes a fairly good conductor. Moisture 
readily condenses upon its surface and it has consequently a high surface 
fieakage. It is also soluble in water to a slight degree and under weather 
exposure the surface tends to roughen. The dielectric constant ranges from 
about 5.5 to 10. The dielectric strength ordinarily ranges from 150 to 300 
volts per mil, and is higher in very small thicknesses. At 920 cycles crown 
glass has an apparent resistivity of 17X10* ohm>cm.; dielectric constant, 
6.60; power-factor, 0-018. _ Mechanically glass is unreliable and brittle; the 
tensile strength is uncertain and anywhere from 1,000 to 10,000 lb. per sq. 
in., with somewhat higher compressive sb^ngtfa. Coefficient of linear cit- 
pansion. 0.000008 to 0.0000095 per deg. cent. Density 2.5 to 4.5. For 
information on glass manufacture see Roeenhain, W., *'Qlaas Manufacture,*' 
D. Van Noetrand Co., New York. 

ST4. PoroeUdn. The three principal constit^uents of electrical porcelain 
are feldspar, cla^ and silica, ^ There are three feldspars: orthoclase, or potash 
feldspar, which is the most important; albite or indianite, which is soda feld- 
spar; anorthite, or lime feldspar. The two clays used are ball clay, and china 
clay or kaolin. A standard mixture of these constituents for testing pur- 
powa is 20 parts feldspar, 50 parts kaolin and 30 parts quarts. The func- 
tion of the feldspar is to act as a flux to unite the oth^ constituents into a 
vitreous mass when fired. There are two processes of manufacture, the 
dry process and the wet process. For details on the manufacture and proper- 
ties of electrical porcelain, see an exhaustive paper by G. E. F. Creigbton, 
••Electrical Porcelain ;"Proc. A. I. E.'E., May, 1915, pp. 763 to 841. A&osee 
Perrine, F. A. C, "Electrical Conductors:" D. Van Nostrand Co., New 
York, 1903; Chap. XIII. 

ITS. Drj-prooeM pcuroelain is manufactured by molding the moist raw 
mixture under hi^h mechanical pressure and then vitrifying by the usual 
firing process. This grade of porcelain is usually very porous and consequently 
has a disruptive strength on the order of atmospheric air, or less. At or near 
disruptive pressures, however, it heats rapidly and is not suitable for high- 
voltage insulation. The safe dielectric strength is on the order of 1,000 volts. 



PBOPSRTISS OF MATERIALS SeC. 4-276 

tn. Wo^proean poroelaln is made by mixing the raw insredienta with 
water. The mixture u placed in a filter preaa and the lurplua water ex- 
traeted, leaving a wet plastic cake. The cake ia re-mixed in a pug mill to 
Bake it more bomogeneoua, then molded or jiggered into a blank ol approxi- 
■ate final shape, and allowed to dr^. When fairly dry it ia turned in a 
lathe or tooled to final shape, dipped in the glaxing bath and placed in the 
kilii preparatory to firing. The glasing mixture ia the aame as the porcelain 
exeept wMl it containa more flux, and thus melta at a temperature barely 
aaffieient to vitrify the porcelain. The finished glase ia virtually a species of 
^aaa. During manufacture porcelain ahrinka from 10 to 20 per cent, and 
much care ia required to proportion the parte so that craclun^ will not 
nauH. The thickneaa is limited both b^ the shrinkage and the difficulty of 
obtaining satisfactory vitrification. High-voltage porcelain ia made in all 
cases by the wet process. 

m. FiupM tl sa of hlfh-TOltlf* porealaia. The densit^r ia from 2.3 to 
2.5. It is not affected by oils, sads or alkalies; the glase la said by some 
snlltoiitiea to be very sli^tly soluble in ordinary water. XJnglased porcelain 
afaoQld be non-hy^oscopic and on immersion should not incresse in density. 
A good rough test is to place a drop of »nk on the porcelain and note whether 
it ^ireads or penetrates; alcohol solutions are still Detter. The linear expan- 
■on eoefBeient is from 4.5 to 6.S X 10~* per deg. cent. The specific heat is 
Oil? and the thermal conductivity is 0.045 per cent, of that of silver. The 
ileetrieal reactivity of unglaaed porcelain is on the order of 10" to 10" obm- 
rm. at ordinary temperatures, and decreases very rapidly with increaung 
tenperatuTes; at ver^ high temperatures porcelain becomes a fair conductor, 
and Is therefore unamtable for electric furnaces. 

TIm <fi«leetric constant ia from 4.4 to 6.8 with continuona e.m.f. and about 
10 per cent, less at 50 cydes per see. At low frequenciee the disruptive vol- 
ts^ is about 30 kv. for a thicknees of 0.1 in. and about 110 to 120 kv. for a 
thwkneas of 0.5 in. At frequencies of the order of 300,000 cycles the flisrup- 
tive atrength, for a thickness of 0.5 in., is on the order of 80 to 90 kv, and if 
the test voltage is appKed rather slowly the disruptive atreuftth varies in much 
aataller proportion than the thickneaa (aee paper by Creighton mentioned 
bcimr). In some cases mechanical stress has been observed to reduce the dia- 
la p ti sa strength, but in other cases had little effect. 

American porcelains have a tensile strength which ia variously stated from 
•50 to 2,200 lb. per sq. in., with an average of about 1,400 lb. per sq. in. 
The compressive strength is about 10 times the tensile strength. Modulus 
of dastiaty, 2,500,000 in-lb. European porcelains are generally reported 
as fasvinc a tensile strength of 4,500 to 6,300 lb. per aq. in. and a compres- 
mn strength of about 65,000 lb. per sq. in. The following references on 
peredain are given for the convemence of thoee who wish more complete 
i^ormation. 

Kempton, W. H, " The Application of Porcelain to Strain Insulators;" 
Tnw.. A. I. E. E„ 1910, Vol. XXIX pp. 967 to 974. 

Lastgarten, J. "High-tension Porcelain Insulators;" Jour. I. E. E., 
Jidy, 1912, pp. 235 to S»8. 

lin]ay,L.£Tand Thomas, P.H, "High-frequency TestsofLinelnaulators;" 

Sothman, P. W. "Comparative Teets on High-tension Suspension Insu- 
latois:" Trxnu. A. I. E. E., 1912, Vol. XXXI, pp. 2143 to 2226. 

An^in, A. O. "Factors Producing Reliabihty in the Sns^nsion Insula- 
tor;" Proe. H. E. L. A., Hydroelec. and Transmission Sessions, pp. 201 to 
223: 1913. 

Creigbtoii, E. E. F. "Electrical Porcelain;" iVoc. A. I. E. E., May, 1915, 
|i(k 753 to 841. 

Abo see Tran». American Ceramic Soeiety. 

tn. UUOi. The properties of fused fUiea are as follows: Resistivity at 
crdiaary temperatures, on the order of 10>* to 10** ohm-cm., decreasing rap- 
idly at higher temperatures; dielectric constant, 3.6 to 3.6; dielectnc 
amngtfa. above 600 volta per mil; mdting-point, 1,700 to 1,800 deg. cent.; 
eoefident of expanaion, 0.0000006; denaity, about 2.07. Also aee Chemical 
ituntu, VoL rV, p. 866, and Vol. VII, p. 3443. 

nt. TUa. Vitrified clay tile ia very extenaively uaed for underground 
faadaits. Although it poss e ss e s very fair insulating propertiee, ita iiae for 
tUaporpase is owing very largely to its immunity from corrosion and diainte- 
rUMB under sub-soil conditions and also its Ability to withstand a great 

SOB 

DigilizedbyV^iUOyiL' 



SeC.4-2S0 PttOPSRTlSS OP MATSBIAL8 

ran^ of temperfttnres without injury. As a rule* it is sUshtlj absorbent, 
reoeiTiag as muoh as 3 or 4 per oeat. <u water, in some esses, in 24 hr. The 
puncture voltage, with a O.&dn. (1.5 om.) wall, after 24-hr. imm«rBion» 
ranees from about 10,000 to 30,000 volts. It ii not affected by arcs unleas in 
direct contact with thAn, and in that event wHl be likely to mdt looally and 
chip or fracture in the surrounding area in consequence of unequal heating 
and expansion. 

S80, yitrtooa anamel connsting of opaque white ^ass is extensively used 
for coating iron resistor grids and imbedding the resistor wires, thus forming 
non-inflammable and highly fireproof devices capable of withstanding unus- 
ually hi^ operating temperatures. Enamelled iron-'ware is made exten- 
sively by the process of sprinkling powdered i^aas upon red-hot metal, 
whereupon the glass fuses and forms a continuous thin coating. The 
fwmulss used for compounding the glass are quite closely guarded as manu- 
facturing secrets. What is desired is a thin, strong elastic coating which will 
expsnd and contract with temperature changes at as nearly as posuble the 
same rate as iron. 

raaOUB JKATXRXALB 

Ml. CalluloM is the base of practically all fibrous insulating materials and 
Is an organic compound eompoMd of 48 per cent, carbon, 46 per cent, oxygen 
uid 1^ cent, hydrogen. It is a carbohydrate of the formula (CiHtsOt)., 
mmilar in composition to starch. When pure it is a white amorphous mass; 
unsised. well-bleached linen paper is nearly pure cellulose. It has a resistive 
xty on the order of 10* to 10** ohm-cm. at ordinary temperatures and a dieleo- 
tric constant of about 3.9 to 7.5. All untreated cdluloae materials break 
down at about 120 deg. cent, and should not be subjected to a maximum of 
more than 05 deg. cent. A safe operating litpit is about 80 deg. cent. 

t8t. Vntraatad flbrona tnaWriali are as a whole hygroscopic and are 
therefore relatively inferior insulating materials. They are nevertheleas 
employed, some of them, to a fpe&i extent, but their use is very largely con- 
fined to ronditions under which rooiBture is restricted or expelleo. Their • 
properties are greatly improved by treatment or impregnation. 

tSS. Tha intpragnatlon of fibrous and asbastos produets with var- 
xushes, gums, bakdite, etc., produces several results: First, the treating 
materials fill up the pores of the basic material and eliminate moisture; see- 
ond, the dielectric strength is increased even where there is no moisture to be 
considered; third, most treating materials assist in producing smooth sur> 
faces; fourth, the heat^esisting quality of the basic material is often in- 
creased, and, fifth, the filling up of the pores may in certain cases reduce the 
tendency to shrink. Incidentally the treating materials increase the heat 
conductivity of the insulation, resulting in better radiation. 

IM. Pai>er is manufactured from wood pulp, ra^ or plant fili^e. The 
essential processes in manufacture are (1) the reduction of the raw material 
to the consistency of a thin pulp, by means of operations involving the use of 
chemicals and stttsm; (2) the running of this pulp upon a continuous sieve of 
fine mesh, which retuns the fibres that become felted together; (3) the 
removal, drying and finishing of the felt so formed, finished paper retains 
traces of the bleaching or coloring matter employed, and in addition fre- 
quently contains a certain amount of loading matter such as china day, cal- 
cium sulphate and other inert mineral matter. A sising of vegetaole or 
mineral solution is sometimes added to render the paper leas porous* and 
improve the surface. 

The mechanical properties of paper are derived in large degree from the 
basic fibres employed in its manuiacture; thus paper made from wood pulp is 
brittle and easily torn, whereas linen or Manila fibre jiroduces a much tougher 
and stronger paper. Owing to its porosity paper is hygroscopic and mtf- 
mally contains from 7 to 12 pet cent, of moisture. When thoroughly dry it 
has a very high resistivity, on the order of 10'* ohm-cm., but it eauly absorbs 
water and when wet descends to the class of a poor conductor. The dieleo- 
tric constant of dry paper is from 1.7 to 2.6. Dry Manila paper has a 
power-factor of about 0.007 at 920 cydes. The didectric strength of various 
kinds of untreated P*P«r» ranging m thickness from 1.8 to 28 mils, should 
average from 110 to 280 vdts pw mil; higher values are obtainaUs ^m 
extremdy dry paper. Ths tensile strength will range from a few thousand up 



804 

L;j,l,.ociby*^iOOgle 



PROPBHTIKR OF MATERIALS 



S«c.^285 



to many ihousaitd lb. per to. in., depending upon the oaality of fibre. The 
doncatton at frftoture u Blicht, about 2 or 3 per cent. For temperature Urn- 
ita He c^luloae. Par. ttl. There are numerous varieties of insuiatinc paper, 
meh as rope paper, Japanese paper, Manila paper, whale-bone paper, ftuler 
board, preasboard, etc., some of which are briefly mentioned in oUier 
paracraphs. 

tH. Tr«»ted paper is a clear dry paper impregnated with oxidised Unseed 
oil, or « mixture such as oxidised oil and asphalt, or a gum-base varnish. 
WeO-treaied papers in thicknesses ranging from 6 to 12 mila break down at 
&bout 50iO to 750 Tolts per mil. The \iica Insulator Co. gives dsaruptire vol- 



tagea for Empire oiled papers, in thicknesses of 1.5 to 18 mils, ranging from 
1.740 to 800 rolta per mil; these values include condenser, rope, bond aad 
eeroent p»per and fuller board. The same manufacturer gjvea for rope paper 
treated with a compound of oxidised oil and asphalt, disruptive voltages 
ranging from 1,000 to 000 volts per mil, cwresponding to tJucknesscs of 5 to 
15 mile. Acc<H-ding to Jona, the dielectric strength of imprei^nated paper 
cable insulation ia from 200 to 250 volts per mi], and the diriectnc eonstant is 
about 2.5 to 4. The value of the constant k (see Par. SfS) for impregnated 
paper ia uaually between the extremes of 1.000 and 3,000. 

tSS. BSbkaUsad pt^^m, known under the trade name of bakelite-micarta, 
is a dark, hard, homogeneous material considerably stronger than hard fibre. 
U can be w^orked with sharp tools, punched only in thin sheets, and cannot be 
molded. It will withstand continuously^ a temperature of 150 deg. crnt. and 
for short periods 200 deg. cent. It is infusible. The density is about 1.25. 
Moore givea the following properties of bakelite-rairarta, measurrd at 180 

Sirrle* (see Moore, R. W. K.. "Properties and Uses of Bakelitp-niirarta," 
Uetric Jtmrnal, 1013, pp. 645 to 050): resistivity. 2.13X10I" ohm-cm.; 
(fielfctric <^nstant, 5,2; power-fartor, 0.024; dielortric strpngth, 500 to 
1,000 volts per luil; tf^nuile strength, about 20.000 lb. per sq. in.; roeffirient 
of expanuon. 0.00002 per deg. rent. It is satd to be inwoluble in alcohol, ben- 
sine, turpentine, weak acids and alkalies, hot water ami oils and non-hy- 
_ irosropic. 

tST. Asbaitot pap«r, comprised of an asbestos base, is a soft, flexible 
niaterial of little strength and is hygroscopic. It will withstand an operating 
temperature of 200 deg. cent, without 
injury. The dielectric stretigth is on 
the order of 100 vc^ts per miL 

Treated aabMto* paper. A vari- 
ety of treated asbestos paper known 
M Delta aheetin^ is impregnated with 
a black insulating compound which 
softens at about 120 deg. cent, and 
nulU at about 200 deg. cent. It is 
daimed that from 2.500 to 5.000 volts 
' I required to puncture it, in thick- 
I of 10 to 25 mils. 



.(a .M .M .M .10 as oi 
Tblcknsu* Inches 

Fia. 36. — Dielectric strength of 
treated pressboard. 



a».iirfi.ii.i.iioiiM« 


,/ 


1 




y 










/ 


/ 




-, 


1 


> 




/ 


y 


<^ 








/ 


A 


'y 










/y 


r 













m. yrMsbomrdknilfalUr board. 
rrtMboard is xnAnufactured from cot- 
ton raff aod paper clipping, in a 
nnmlier of grades. It u similar to 
paper, but thicker and ^leee^ flexible. 
>n the untreated condition it is hy.. 
CMscoptc, and its properties improvs 
vithits dryness. Uppenborn gave the 
^vsietrTity as 11X10* ohm-cm. and 
Turner and Hobart cave the dielectric 
Mrength as 200 to 330 volu per mil. 
.rtawpalm is another name for pressboard, applied to a grade manufactured 
IB Germany. The qualities of pressboard are greatly improved by impreg- 
oation. 

M>. ftaated iirsiiboard. Extensive tests of oiled and varnished press- 
board are oven by Hendricks in "High-tension Testing of Insulating 
Materials," Trans. A. I. E. E., 1911, Vol. XXX, p. 187. The dielectric con- 
■tast of pressboard dried and boiled in transformer oil ranges from 4.3 at 
13 deg. cent, to 7.6 at 100 deg. cent. The dielectric constant of varnished 

» aoe 



Sec 4-290 propbrtibs of materials 

preesboard is About 2.9 at 20 to 25 des. cent., meuured on 0.1-in. board. 
Thedideotrio strength of trekted preaaboard ia ^ven in Fig. 35: curve (1) 
for presBboard dried and boiled intranflformer oil; curve (2) for preasboard 
dried, boiled in linseed oil and given two coats of varnish; curve (3),_ dried 
and given two to four ooats orUnseed oil and gum varnish, depenmng on 
thickness. When these sheets are laid together in laminations, the puncture 
v^tage per mil of complete thickness decreases, but in the case of verv thin 
laminations the puncture voltage does not appear to decrease in as raj>ia ratio 
as with single thicknesses. 

S90. Viiloanlsed fibre* is a hard, dense material of which the principal 
ingredient is paper or cdluloee made from cotton rag stock; the other ingredi- 
ents are sine chloride and coloring matter, the latter consisting of analine 
ccdors or mineral pigments. The finished material is heavily compressed into 
slabs, sheets^ tubes, etc. The water and chemicals are not oompletely 
removed during manufacture and the product is hygroscopic and not a supe- 
rior insulating material except for moderate voltages. It will absorb about 
50 per cent, of its weight ot water in 24 hours. The density ranges from 
1.0 to 1.5 according to the grade; average 1.4. The resistivity ia company 
tivdy low for dideotrics, or on the order of 10' to lO'** ohm-cm. Certain 
varieties are said to have a resistivity as high as 7 X lO** ohm-cm., probably 
in a very dry state. The measurements of dielectric strength by different 
observers are widely discrepant. Parsball and Hobart gave 10,000 volts aa 
the didectric strength of all thiokneeses from i to 1 in. Hendricks ^ave 
about 200 volts per mil at thicknesses of 50 to 150 mils, 100 volts per mil at 
0.4 in., 100 volts per mil at 0.7 in. and 90 volts per mil at 1-0 in. Oth^^ 
have found values ran^ng as high as 300 volts per mil; the results depend 
largely on the dryness of the material. The tensue strength ranges from 10,- 
000 to 20,000 lb. per sq. in, and the compressive strength is from 35,000 to 
00,000 lb. per so. in. lilbre is not soluble in water or oil, but is attacked by 
strong acicu, ana swdls when soaked in water; upon drying it shrinks appre- 
ciably and warps badly. Numerous grades of fibre are manufactured and 
known by various trade names, as horn fibre, hard fibre, indurated fibre, 
leatberoid, fish paper, etc. The flexible and more fibrous varieties have better 
insulating quahties. Impregnation improves the qualities in marked degree. 

m. Treated fibre. Theinsulatingpropertiesof bard or vulcanised fibre 
are much improved by treating the pulp with bakelite. A material of this 
character, known as bakelite-dielecto, is manufactured by The Continental 
Fibre Co. and is said to have the following characteristics. It is a hard, 
tough material, light brown or black in color, and manufactured in sheets, 
tubes and certain special f<H>ms; cannot be molded, but can be machined 
either with or against the grain; is non-hygroscopic and impervious to hot 
water, oils and ordinary^ solvents; will witiutand continuously a terap«'ature 
of 150 deg. cent.; resistivity, 1.1 X 10^' ohm-cm. at ordinary temperatures, 
increasing with temperature up to 100 deg. cent.; dielectric strength, 700 to 
1,150 volts per mil; average tensile strength, 18,000 lb. per sq. in.; compreaa- 
ive strength, 21,000 lb. per sq. in. 

SU. Xini>reffnated fibre duct is in extensive use for both inside and out- 
side construction. It is made in the form of a cylindrical tube by wrapping 
many layers of paper or pulp on a mandrel and impregnating it during the 
process with bitumen or a compound of liquid asphalt and coal tar, It is 
sometimes known as bitumemsed fibre. Tests made on a certain grade 
of this material show that it absorbed from 2 to 3 per cent, of water after 06 
hr. immersion; one manufacturer guarantees not more than 0.75 per cent, 
when the ends are sealed. The compound softens slightly at 55 deg. cent, 
and commences to break down at about 05 dec. cent. Manufacturer^ guar- 
antees on minimum puncture voltage, dry, tnrough a 0.375-in. walli range 
from 25 to 50 kv ; after prolonged immersion the dielectric strength will 
usually be lowered, depending naturally upon the amount of mmsture 
absorbed. 

Its. Tarnished cloth is a thin white fabric of cotton or linen muslin 
coated with a mixture of boiled linseed oil, resin and benxine. Upon drying 
the oil oxidises in contact with the air and leaves a smooth, hard surtaoe. 

*6ee*' Manufacture of Hard Vxhre*' Electrical World, Vol. LIII. p. 1437; 
a]M> see Vol. LV, p. 1342. 

^ r 1 

Digitized by VjOOQIC 



PR0PBRTIE8 OF MATnUTALS Sec4-2M 

I eoata may be added to weure the deeired thiokneM. This material 
also knowB aa Tamlabad eambHo and as Tamlalwd mvaUn. For 
Tmnnahecl cambrie the usual value of the oonstant k in the formula Ji ■* ife 
loci« iX^/dCi ia from fiOO to 2,000; R ie the iiuulaUon resistance of theiusidated 
wire in. zn«sohm-mi]es, d is the <tiameter of the oonduotor and D is the outaidn 
Aametflr of the insulation. Dieleotrio constant, 3.5 to 5.5. Dielectrio 
■trenKtlL, in commo'eiai thicknesses of 5 to 10 sdls, about 500 to 1.300 volts 
par mil; the Mica Mfc. Co. gives 1,000 volts per mil. Also see tests by Far- 
mer. F. M., *'The Dielectrie Strength of Thin InsulaUng Materials;" Traru, 
A. I. K. K.. 1913, Vol. XXXII. pp. 2097 to 2131. 

Varnished cambric is more elastic than paper and is very suitable for 
cable Izksalatimi. A separaUw of treated paper, cloth or rubber is applied 
to the copper core to prevent any action of the varnished cambric film on the 
copper. Then strips of varnished cambric are taped over the separator 
with applications of a plastic non-hardening compound between layers to 
exdude moisture and make the cable flexible. The core U finished by cotton 
tvaidinx e-t^d weather-proofing, or asbestos braiding and flame-proofing, 
or a lead sheath over tape. Inaome types of cable the insulation is graded, 
first using rubber and then varniahed cambric. The Qeneral Electric Co. 
recommends a working temperature limit of 80 deg. cent. (176 deg. fahr.) 
for vamiahed cambric cables. 

SM. Oiled cloth is a thin, white fabric of cotton or linen muslin coated 
with tiro or more applications of pure oxidised linseed oil. The insulating 
properties are derived chiefly from the oil or compound with which the fabric 
s impregnated. This material is known by a number of trade names, among 
them Smplra doth. Gray gives the normal dielectrie strength, with a 
lO-mfl thiokness, as 750 volts per mil; the Mica Insulator Co. gives 1.000 to 
1,100 v<^ts before baking and 1.100 to 1,200 volts after baking. Silk, linen, 
canvas and duck are trMited by the same process, with dielectric strengths 
ranginsfrom l.lOOto 1.450voltflper mil with silk, 1,250 to 1,375 voltsper mil 
with linen and 000 to 775 volts per mil with canvas (Mica Insulator Co.). 

tM. ZmprcglUbtdd cloth is similar to varmshed or oiled cloth, with the 
ihfference that the fabric is treated with an impregnating compound. One 
manufacturer employs a mixture of oxidised oil and asphalt; others use an 
saphaltum or a paraffin base, dissolved in a thinning material. The Mica 
Insulator Co. ^ves puncture voltages for " Kabak" cU>th (impregnated cam- 
brie) ranging from 1,065 to 1,050 volts per mil. 

S9t. Gompoalta insulation of fibrous materials and mica. In 
applying mica to coils or heavy strap conductors it is necessary to use some 
fiorous material like paper or cotton as a base for the mica. It is customary 
to build up mica on thin sheets of fish paper or Japanese paper, and to wrap 
the resultant sheet around the straii^bt parts of armature coils or heavy con* 
ductcva. It is also eustomarv to budd up mica on a thin cotton tape and to 
use the resultant material for taping ooils or heavy conductors. If the 
amount of i>aper or tape is small and if the material is applied in such a 
loeation. as in an armature ^t, that the mica will remain intact even after 
the paper or the cotton tape has deteriorated, these materi^ may be expected 
to withstand fairly high temperatures. 

99T. Paper and mtca* or mica paper, \b prepared from various n-ades of 
paper by coating them with thin mica scales which are made to adhere by 
means of a cementing varnish such as shellac. The lajrers of mica and paper 
are bmlt up in a variety of ways, depending upon the degree of flezibthty. 
or stiffness, desired, nrshall ana Hooart give puncture voltages for oompo* 
site lamina of alternate paper and miea^ ranging from 700 to 1.300 volts per 
rail, in thicknesses of 6 to 11 mils. Vanous combinations of paper and mica 
are manufactured, including Japanese, fiah and rope papers ana preesboard. 
198. Cloth and mica, or mica cloth, is prepared from various fabrics by 
ooatine them with a thin layer of mica, cemented together with a cementing 
TsroisH like shellao. A layer of paper is sometimes added to the eombina- 
tion. An extra flexible cloth is made by using rubber tissue as a binder, 
instead of cementing varnish. 

SH. Cotton Insulation for magnet wires, employed more extensively 
than any other material exceptenamel, is applied in one, two or three thick* 
ne«M. Untreated cotton is hygroscopic and breaks down at a temperature 
of 120 deg. cent. The thickness of covering varies with the sise of wire (see 

307 

Digilizedby^iOOyie 



Sec ^300 PROPERTIES OF MATERIALS 

tablea in See. 6). Gray gives the puncture voltage of a 7-nul thickaeaa 
(composed of two layers) as about loO v(dta; impregnated, about 600 volts. 

800. 811k IziBulAtlon for xnAffnet wlret is applied in one or two thick' 
nessee, ranging from 1 to 2.6 mus per layer. While it is somewhat hydro- 
scopic in the untreated condition, it has superior insulating properties com- 
pared with cotton, and is much improved by impregnation. Neither cotton 
nor nik are the equal of baked enamel (Par. SBlj in dielectric strength. 

SOI. AsbMtOt InsuUtion for nuiffnet niros. Asbestos insulation can 
be applied to wires and small straps with the use of binding materials, but 
in all cases, except in that of asbestos tape which c&n readily be used in tap- 
ing armature or neld coils, the mechanical qualities are quite poor. Asbestoe 
windings also require considerable space if used in sufficient thickness, they 
are not in themselves moisture-prooi, they have low dielectric strength, And. 
do not give a smooth surface. 

Deltaoeston magnet wire is insulated with asbestos fibre cemented to the 
wire with a special Dond. It is claimed that the maximum continuous work- 
ing temperature is 150 deg. cent.; for short periods, 260 deg. cent. The 
insulation thickness is about the same as double cotton and breaks down at 
300 to 600 volts. 

sot. TajMl. Insulating tapes are chiefly of four varieties: (a) thoso 
woven from cotton or silk and untreated; (b) those woven from cotton and 
treated with insulating varnish, or cut from treated cloth; (c) those cut from 
oloth which has been loaded with rubber or adhesive compound. The lay of 
the threads is arranged in three different ways, straight, biased and webbed; 
the last one is the strongest and does not stretch readily, (d) Paper tapes, 
treated and untreated, are out from finished stock. See " Specifications and 
Tests for Insulating Tapes," BUctrical World, Vol. LVII, p. 488; also Vol. 
LVI, p. 689. 

SOS. Untreated tApM sfe hygroscopio and for that reason are not entirely 
satisfactory unless finallv impregnated or protected from moisture. Gray 
states that a half-lappea layer of untreated cotton tape 6 mils thick will 
withstand about 250 volts when dry; about 1,000 volts when irapreenated. 
Precautions should be taken to detect the presence of bleaching ana chem- 
ical matter, such as chlorine, which ma^ attack copper. Webbina; is some- 
times used for mechanical protection, aside from its insulating qualities. 

504. VamUh-troated tapes are cut from sheets of treated cloth, such as 
Empire doth, varnished cambric and the like, and are used for taping wind- 
ings whioh -cannot readily be impregnated. They are cut straight or on the 
bias, the latter being sometimes prefwred for taping uneven surfaces. See 
treated cloth. Par. S9S to Iti. 

505. Bubber-treated tai>ea are comi^osed of fabric loaded with plastic 
rubber gum or compound in a soft adhesive state. Such tapes are used ex- 
tensively in making water-proof joints on underground rubboMnsulated 
cables, or in other locations where a moisture-repellent wrapping is desired. 
They are frequently used in conjunction with a splicing gum of similar com- 
{>osition, and protected by water-proof insulating compounds and outside 
wrappings of adhesive tape with insulating paint over all. In the case of 
underground cables a lead sleeve is ^i>ed over the whole joint, making it 
completely water-tight. 

sot. Adhaglve or friction tape is composed of fabric loaded with a 
•ticky or adhesive compound. The base of the compound in the more 
expensive grades is rubber gum, adulterated with fillers in various well- 
known ways, while the len expensive grades contain little or no rubber and 
its place is taken by one of the numerous bituminous compounds. This kind 
of tape possesses fair instilating properties and is very extensively used in 
low-tension work. 

SOT. P*p6r tap«a of both the treated and the untreated varieties have a 
most extensive use in the manufacture of paper-insulated cables for power 
and communication service. See paper, Par. 184, 

SOS. Asbestos tape, or a tape having a base of asbestos fibre, is superior 
in its heat-resisting properties to cellulose materials such as paper and cloth. 
Such tapes are usually known by trade names, among them being deltatape. 
The latter it is claimed can be raised to 260 deg. cent, before breakdown oe- 
ears; puncture voltage, about 250 volts per mil. 



yGooglc 



PBOPSRTIBS OF MATBRtALS 



S«e. 4-309 



HOLDXD OOMPOSrriOITB 
IfoMed insulfttion embraces a great number of different com- 
aad eompouade, which are difficult of claesifioation. The chief 
a of aome of these materials are well known, while others are made 

RKCRt foriQiilaa and Droceeses. Amons the raw materials employed in 
^Banufaetare of molded materials are nuoa, asbestos, rilics, clay, alkaline 
!*tks, wood pulp, cotton, hemp, flax, asphalt, camphor, hydraulic cement, 
"ihtt. sfadlac, oo|m1. dammar gum, rosin, paraffin wax, linseed oil, turpen- 
^fc b eniine, alcohol, phenol and formslaehyde. The following general 
■■fieatioti of molded materials has been adapted from " Claasincstion 
■4 Characterisation of Molded Insulations," by E. Hemming (Bkctrical 
ImU, 1014. Vol. LXIII, pp. 761 to 782, 70a to 709, 813 to 817). The 
■Mine pmiierties given for each class of material Iwlow should be oon- 
Jnad in eonneotion with more specific particulars in the paragraphs 
■nediaialy following. 



Claas 



Allowable 
temperature - 
(deg. cent.) 



Continu- 
ous 



Ot^aie, hot- molded . . . 
cold-molded. . . 
ie. cold-molded . 
compounds- . . ■ 



iMhstie reainous'prod- 

sets 
Vdded 



80 
300 
900 

SO 

80 

150to2SO 
8D 



Mo- 
men- 
tary 



500 

1,500 

100 



300 
173 



Meg- 
ohms 
peritt' 
cube* 



513 
380 
900 



40 



Dielectric 
strength 

(volts 
per mil) t 



143 to 361 
84 to 1«7 
70 to 72 



42 to 333 



Tensile 

strength 

(lb. per 

sq. in.) 



940 to 2,000 

920toI,SS0 

1,985 to 2,920 



2,880 to 4, 750 



* Minimum observed value after 72 hr. immersion in water. 
i^T Tests made between blunt needle points; thicknesses of test pieces. 
Its lis.: tested dry. 

tit. AatOA material is a hard composition employed chiefly for strain 

^riatcrs. Tests made by Symons (Jour, I. E. E.j 1904) on a strain insula- 

tei this material gave tne Mlowing results: Resistance, 20,000 megohms; 

. 11,000 vuts; tensile strength, 5,500 lb.; absorption of water, 3.2 

•nit. of its own weight after 1.5 hr. immersion at 49 deg. cent. Other 

J nade on this material gave a dielectric strength of about 90 volts per 

I; tensile strength, 1 ,400 lb. per sq. in. It will withstand great heat, but 

Ml to become Drittle at high temperatures. 

Bl. Ambrottk (made in Berlin) is a heat-resisting molded material manu- 
in nn m cfo us grades, some of which are claimed to be fireproof, 
^-.^ ..~av are suitable for temperature limits of 100 de^p. cent, and some 
'B deg. cent. The msnuifacturers claim that it is moisture-proof, does 



ndeg. 
'ihrinK. 



, and can b« worked and machined. The density ranges from 

i t» 1.8, according to quality. Tests made at the Reiohanstalt on grade 

give a dieleetrio strength of 800 volts per mil, in a thickness of 13 mils. 

itnsile strength is abont 2,100 lb. per sq. in. and the compressive strength 

•t 2,700 lb. per sq. in. 

At. JUbsatoa-mioa comprised of asbestos and mica bound together 

ki ibdlae, is manufactured by the Johns-Manville Co. under the trade 

of "molded mica." In appearance it has a dark color and a smooth 

,_. It can be molded into any shape, either with or without metal 

It softens at about 65. deg cent, and has a safe working tempera- 

of 55 to 00 deg. cent. The manufacturer gives the dielectnc strength 

It 335 volta per mil in a thickness of 0.36 in.; tensile strength, 8,500 

•q. in.: bat slightly affected by moisture; attacked in some depee by 

■E-. depmdlBS upon their character and concentration, flee £i«c<n<xil 

*i»R UuTToI. tX, pp. 803 and 804, 



309 



Digilized by 



Google 



Sec. 4-313 



PROPBRTZBS OF MATERIALS 



aiS. AtbostM molded with & binder, known under the tnule names c 

?;ummon, faemit and tegit, u manufactured by the Hemminc Mfg. Co 
rom whom the following data waa obtained. Gummon la black and caQ h 
highly polished; tegit is dark brown and can be polished, though less hiehl 
^ian gummon; hemit is made in both ^ay and black and will also take 
polish. The density varies, in the neighoorhood of 2. These material 
are suitable only for molding; are infuaiSle, but will gradually carbonise a 
higher than working temperatures; will not resist concentrated add; are nc 
recommended for working pressures above 1,000 volts. 



) 





Ohm-em. 

at 23 

dec. cent. 

(Bur. of 

Stda.) 


Max. 

worldns 
temp 
(de, 
cent.) 


Dielectrio 

strenctb 

(volta per 

mil) 


Strength 
(lb. per »q. in.) 


Absorp- 
tion of 
moisture 
(per 
cent.) 


Tensile 


Com- 
press- 
ive 


Hemit 

Qummon 

Te«it 


1X10'» 
3X10»« 
2X10" 


1,100 
320 
200 


50 
75 
50 


2,000 

600 

1,200 


1,000 

6S0 

1,100 


5 
2 
5 



Also see Hemming, E. "Molded Electrical Insalation and Plastioe;' 
Clausen and Co., New York, 1914. 

514. Asbdstoi wood or lumber, known also by the trade names " Trana 
ite Asbestos Wood" and "Asbestos Building Lumber,** consists of asbesta 
fibre and hydraulic cement, and is used as a substitute for wood in building 
construction. It is also used to some extent as a substitute for slate ani 
marble in electrical construction. The following data (Par. Sli and SIS 
was furnished by C. L. Norton; also see hispaper entitled, ** Some Refractor] 
Substitutes for Wood " Jour. A. S. M. E., 1912; and "The Manufactun 
and Use of Asbestos Wood," on pp. 375 and 379 of "Technology and la- 
dustrial Efficiency," McGraw-Hill Book Co., Inc., New York, 1911. 

815. Trandte aibeatoi wood is light gray in color and is manufacturei 
in sheets up to about 4 ft. by 8 ft. by 2 in. It has a density of about 2.0 
It can be sawed and bored like wood but is harder and slower to cut. Al 
600 deg. cent., partial dehydration and partial loss of strength occurs, but 
it does not soften. At 1,100 deg. cent, the material holds shape and con- 
siderable portion of its strength, but it will not stand temperatures above 
1,400 deg. cent. The temperature coefficient of expansion at ordinary 
temperatures ia about 0.000008 per deg. cent. The thermal conduotivitji 
is 0.0005 etd. per om-cube per sec. per deg. cent. Transverse breakini 
tests i^ve a modulus of rupture of about 5,000 lb. per sq. in., and the erushini 
strength is from 20,000 to 25,000 lb. i>er sq. in. When dry, at or near 20 
deg. cent., it has a resistivity of about 150,000 me^ohm-cm. It is dissolved 
slowly by acids. When used in dry or hot places it is suitable for electrical 
insulaUon and is tougher than slate or marble. Since it absorbs moisture il 
is not suitable for damp locations. 

515. Bbony esbeatoi wood is asbestos bonded with magnesia, cement 
and saturated with an insulating compound. It is black, smooth and glossy 
and has a density of about 1 .9. It can be worked the same as slate, but more 
rapidly and easily. The working temperature limit is about 200 deg. cent.; 
it does not soften; the melting-point is above 1 ,400 deg. cent. The coeffioieot 
(^ e:q>ansion is 0.000010 per deg. cent. The thermal conductivity is 0.00065 
cal. per omniube per sec. per deg. cent. It has a modulus of rupture 
<rf about 5,000 lb. per sq. In. and a crushing stren^h of 15,000 lb. per sq. in. 
At 20 deg. cent, after 96 hr. immersion the resistivity is above 3X10* meg- 
ohm-cm. and changes 5.3 per cent, per deg. cent. The disruptive strength 
is greater than that of slate or marble, and it also withstands better the 
effects of surface arcing. It is also tougher than slate or marble. 

SIT. Bskkelite and b&kelite compoaitioni. Bakelite is a condensa- 
tion |>rodttct of phenol, manufactured in three grades. Bakelite "A" is 
the initial raw material and exists la liauid, pasty or solid condition; upon 
heating it ia converted into "B" which is an intermediate solid product. 



310 



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PKOPBRTIS8 OF UATBSIAIS 



Sm. 4-318 



nMemiis undar knilioation of haat and (oitable for moldint; bakaiito "C" 
■ the fixwl produot. produoed by h«»tin« "A" or "B," and u a hard, noit- 
raaBoa>, infnaibla aond, in appaaranee rcaesblinc amber or hard rubber, 
la eolar it ean ba mada tranaparant or opaqua; oolorlaaa to jrallow, brown, 
led and blAok. The oolcriajEmattar, when any ia uaad, ooaaiata of oraanie 
djpaa or miiMral picmenta. The raw material la aold in diaaolvad, Uqvid or 
aKd oomdition, and ia uaed for rarniah, lacquer, enamel, impraanation, ad- 
h aa i t a cement, plaatie moldins eompoaitiona and molded artielea. It ean 
ba molded into any ahapa by eaatins or by forminc in the hot preaa, and will 
nwiw a metal inaerta. In condition of final hardneea it can ba worked, 
leartiined and poUahed like amber or hard rubber, and ean be iwed at eon- 
tinnoroa temperatnrea eoaaiderably above 100 deg. eent. It ia not a good 
andactor of heat. For abort paiioda it will atand UO to 300 det. eent. 
BwobodA sivaa 280 dec. cent, aa the maximum worUnc temperature of 
bakelite-aabcatoa. At higher temperaturea it ia infuaibie, but ehara. It ia 
not attacked by the aolventa or many of the acida, but will not withatand 
hot aulpburic aoid, nitric add, bromine or atrong alkaline aolutiona; the 
elect M ehemicala ia dependent in aoma degree upon the grade of material. 
It ia noD-hygroacopio, and ia aaid to reeiat ateam and boiling water. The data 
pvan below were lurniahed by Dr. L. H. Baakeland, the iuTentor of bakeUte. 





Oen- 
aity 


Dielectric 

atrength 

(voltaper 

mU) 

fiao 

2,800 

MO 

200 

9W to 1,120 

635 to 1,130 


Straogth, 
(lb. par aq. in.) 

Ta«-1. pCom;, 


Coaf.ot 

expan- 

aionpar 

deg.oent. 


Bakelite''C" 

Baked fam of bakeUte 
Tamiah No. 2. 


1.2« 


5,000 


20,000 


0.00011 


Bakdite-wood fibre 

Bakelite-aabeetoa 

Bakelite-miearta (aheet) 
BakeUte-dielecto (aheet) 


1.34 
1.90 


4,200 

4,200 

10,500 


27,000 
24,000 


0.000034 
0.000023 













Reaiativity of "C" at 26 deg. cent., 5 X 10" to 3 X 10" ohm-em. ; dielectric 
roaitant, 4.1 to 8.8. The reaiativiW and the dielectric atrenjrth decreaae at 
temperaturea abore 75 deg. cent. For further data on bakehte aee ; Journal 
»f Ind. and Bng. Chem.,1906, Vol. I, No. 3 and No. 8; 1811, Vol. Ill, No. 7 
and No. 12; 1012. Vol. tV, No. 10: 1913. Vol. V, No. 6. Tram. A. E. S., 1909, 
Vol. XV. EUt. World, 1911. Vol.LVII, pp. 632 to 634. Mt. and Chtm. 
Bng., Jan. 1912. Jour. 3oe. Chtm. Indvtry, June 16, 1913, Vol. XXXII. 

lU. Cellnloid, formerly known aa xylonite, ia compoeed eaaentially of 
aoluble guncotton (pyrolin) and oil (camphor). In texture and color it 
raaemblea ivory, and ia varioualv colored in imitation of amber, coral, 
tortoiae ahell, etc. It ia very aligfatly hygroecopic and can be molded into 
any form by aoftaning in boiling water. It ia highly inflammaUa. The 
denaity ia 1.44. The reaiativity at ordinary temperaturea ia from 2X10'* 
to 8X10^* ohm-cm. According to Thomaa (Jour. Franklin InttUuU. 1913, 
Vol. CLXXVI, pp. 283 to 301), celluloid teated at 1,000 cyclea baa an 
affective reaiativity of 2X10* ohm-cm. and a dielectric constant of 13.3. 
Clear celluloid haa a dielectric atrength of 250 to 700 volta per mil at 20 
deg. cent., and ICX) to 300 volta per mil at 100 deg. cent. ; colored aamplae, 
250 to 470 v<^ta per mil (Turner and Hobart). Thomaa givea a puncture 
voltage of 1880 volta per mil, at 1,000 cyclea. At 920 cyclea the effective 
raaiatance ia 28X10* oom-om.; dielectric conatant, 4.02; power-factor, 0.012 
(Fleming and Dyke). 

lit. Oondenalte ia a molding material of which the chief conatituent ia 
a eompoimd reaulting from chemical reaction between phenol and formal- 
dehyde, riaaaad aa a phenolie oondenaation product. It can be prepared in 
many forma, tranaparant or tranalucent, in a variety of color*; it ia adaptable 
aa molding material, vamiah, enamel, impregnating material and cement. 
The bat atap in ita manirfaetur* la the iwodootion of a reainoua gum-like 



Sll 



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> 



S«C. 4-320 PROPSRTJBS OF MATBRIALS 

•ubstanee which will not harden ondar heat; this produot i« haatad and than 
eombinad with a hardaning acent, producing a hard, infuaible andpractiomlly 
insoluble subatance which the manulacturer (Condenaite Co. of America) 
daima ia high in dielectric and mechanical atrength and heat reaiatanea. 
The following data on the properties of molded condenaite were f urniahed 
by the manufacturer: Denaity, 1.25 to 2.0; not hygroacopie. unaffected by 
water, insoluble in the ordinary solvents and oils, attacked by atron^ nitric 
acid and caustic potaah, slightly attacked by sulphuric acid. The resistivity 
at 23 deg cent, is about 4 X W* ohm-cm. (Bur. of Stds.) : dielectric strength, 
about 300 to 400 volta per mil at a thickness of O.IS in. and 500 to 600 volta 
per mil at a thickness of 0.04 in.; tensile strength, 4,300 lb. per sq. in.; com- 
pressive strength, 29,000 lb. per aq. in.; not perceptibly affected by 48 hr. of 
ezpoeure to a temperature of 200 deg. cent.; maximum working temperature, 
300 deg. cent. (Swoboda, BUe. Jour., May, 1013). Also ace Slidrical 
Rtviea and Wat BUc, Vol. LX, p. 199. 

SflO. IHalactrlte is a black molded composition composed of vegetable 
fibre and mineral filler. It is molded and vulcanised by the application of 
heat. Resistivity at 22 deg. cent., 5X10'* ohm-cm. 

Sfll. Blactroae is a dark brown or blacky oompoaition of hard, tough 
quality which it is claimed is non-hygroscopic and not alfected bv water 
or oil. It can be molded in any form, will hold metal inserts, ana can be 

S'lven a smooth glossy finish. The working temperature limit is about 95 
eg. cent. Resistivity at 22 dei^ cent., 1 X10'< to 23axi0« ohm-cm. The 
manufacturer ^Electrose Mfg. Co.) claims a dielectric strength of at least 
AOO volta per mil, in a thickness of i in. Elertroae is used in the manufacture 
of many different forma of Insulators and bushings and is also made in pliable 
insulating flooring. aeeBlecCHctd World, Vol. LIVTp. 797 and Vol. LVI, p. 887. 
Its. Oohmak is a molded substitute for hard rubber made by the Vulean- 
is«l Products Co. The density ranges from 1.4 to 1.8 according to compo- 
sition. The claim is made that it is non-hygroscopic and insoluble in oils 
and weak solutions. Resistivity, on the order of 2 X 10" ohm-cm. at ordinary 
temperatures, decreasing with rising temperature. Dielectric strength, on 
the order of 400 volts per mil, at a thickness of 0.25 in. Tensile streDgth, 
9,000 to 12,000 lb. per sq. in. Softens slightly at 100 deg. cant. 

SIS. Insulate is a black molded composition composed of mineral com- 
pound uid resembles hard rubber. It can oe moulded in any shape and can be 
worked and machined. The manufacturers (General Insulate Co.) claim 
that it ia non-hygroacopic, insoluble in all weak solutions and has a manmum 
working temperature of ISO deg. fahr. The resistivity of No. 2 grade at 
22 deg. cent, is 8X10" ohm-cm. The dielectric strength ia on the order of 
45 volts per mil, at a thickness of 0.4 in. 

SM. Moldad miMt is made of finely split mica scales held together by 
a atrong insulating varnish, binder, or cement, such as shellac, the sheets or 
forms thus built up l>eing subjected to heat and pressure. These composi- 
tions are more or less hsat resisting, dependent upon the nature and propor- 
tiona of the binder employed. They are known by a variety of favde namea 
such as micanite, mica plate, micabond, micabeston, turbomic, formica, 
roegomit, megotalc. etc. The less binding; material they contain, the nearer 
they approaco the properties of natural mica. Such reconstructed or molded 
mica ia made in three commercial forms, as follows: (1) Molded plate, which 
becomes flexible when heated and in that condition can readily be formed 
into various shapes such as rings, troughs, spools, and, in thinner sheets, 
rolled into tubes. Upon cooling it regains its rigidity. It can be used for 
any purpoae where very high temp^atures are not encountered, except for 
commutator bars. (2) For insulating commutator segments. It oannot 
be molded and offers great resistance to beat. Canadian amber mica ia 
preferred for this purpose. (3) Flexible sheets which may be bent to shape 
without application ol heat, for inaulating armature alota, magnet and com- 
mutator cores, etc. It is also used in conjunction with tapes for insulating 
wires and cables. 

Rsyner concluded from hia testa (National Physical Laboratory) that 
generally speaking, thin qualittea of micanite up to about 1 mm. will with- 
atand a stress of 20,000 volts per mm. (500 volts per mil^ in air tor 10 rain. 
Above this thickness, np to 2.5 mm., there is more difficulty in making 
material which will withatand thia streaa, and usually the material witfastaada 
the voltage longer under oil. 



•U 



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PROPBRTISS OF MATBRIALS 



Sec. 4-32S 



The Mi«t IiMuUtar Co. sivM the foUowinc dideotric strenstha for miesmte 
I ifdiflcrait sradee: 



Use 



Qrada 



Thioknen 
(mib) 



Volt* per 
mil 



For moldia^ 

Fcr eomznutstors. . 

For molding 

Phte for Bat work 
neiibfe 



India 

India 

Amber 

India 

India 



10. to 125. 
10. to 125. 
20. to 82.5 
62.6 to SOD. 
5. to 125. 



955 
955 
830 
800 
588 



Tike reaativity is on the order of 10^* ohm-cm. 

SU. Sozito ia a black moulded composition, the propertiea of which 
en as follows by the Northern Industrial Chemical Co. Density, 1.8; 
molded into any slume and will receive metal inserts; will take a high 
; infonble and insoluble; will not support combustion; afaeorba 0.5 to 
I per omt. of water after 24 hr. immersion; dielectric strength, 80 volts 
ftrmiL 

IM. Stamold (Dickinson Mfg. Co.) is a black, heat-resisting, molded 
■ateriai which the manufacturers claim has high dieleotrio and tensile 
•tacBctb and is heat-proof up to 260 deg. cent. The same manufacturers 
iha ivodnoe other molded materials known as Itam-aibalton, beat-proof 
^> to 200 dec. eent.; ■Um-aond«iialt«, heat-proof op to 176 deg. cent. 
•ad eapabla of being worked, machined and paished; rubber-substitutes. 



t np to 70 deg. cent, 
nr. TnleabMton (Johns-Manville Co.) is an insulating material made 
>l Mbartos and mbbiar, the latter being used as a binder. This material 
ii payiah brown in Mpearanee, can be molded into nearly any shape, and 
las a snrfaee wUdi wiu not take a smooth finish. The softening nnnt is 
' 175 deg. cent., with a safe working temperature of about 160 deg. 
The leaiBtiTity at 22 deg. cent, is about 2X10'* ohm-em. The 
rie 8ti«nsth ia about 90 volts per mil, the test pieces being 0.25 in. 
Chance in teinperature has no effect on the dielectric strength. 
Smo this material is of a fibrous nature, it is not suitable for use in damp 
lliem. Acids have a slight effect upon it. The transverse strength is 
MOO lb. per sq. in. See Slettrioal World, 1912, Vol. LX, pp. 893 and 894. 
ttS. Toleabeaton Ho. 101 (Johns-Manville Co.) is a material composed 
if aabaatna nnd a apaeimi gam used as a binder. In appearance it has 
* trawn mottled surface which will take a very hi^h finish. Intricate and 
TWipRratrd pieces can be readily molded from it, using metal inserts if 
dsHred. The softening temperature is between 260 and 300 deg. cent., 
aad the safe working temperature is about 230 deg. cent. The dielectric 
•tnncth ia about 116 volts per mil with test pieces 0.25 in. thick. Trans- 
«■■« strencth, 0,000 lb. per sq. in. Not affected by most acids, and not 
it s ct ed br oil or water. 

nt. TdlealOM is a molded material having the properties of hard rubber, 
oeept that it ia said to be considerably toui>(her. It can be molded in any 
farm and ia used, among other purpoees, for insulators. 

KUBBim AMD ITS DKBIVATIVSS 
nt. Bobbar or OMratehoue is the general name applied to a gretit 
swnber of different natural gums, the different varieties being of decidedly 
■oiike characteristics, but having among themselves certain common prop- 
etties and similar constituents. The synthesis of rubber shows that it 
J with the terpenes, having the formula (CmHh).', but thus far all at- 
I to show the sise of the molecule have been unsuccessful. In addi- 
i ot tbe crude rubbers contain proteids, resins, hydrocarbons, etc.; 
iaioBae eases it requires extensive treatment to obtain the pure gum. Crude 
nMcr is obtained by coagulating and drying the milky latex obtained from 
■rtain specieB of trees and plants, tbe principal sources being in South 
Aaerica. Central America, Africa and Asia, the Amason district of South 
>ia e r ii a beinc espeeially noted for its high-grade rubber. Crude rubber is 
■Ihcted in marked degree by temperature, being soft and sticky when warm 
bat itiC when oold. 

818 , 

D,J,!,.«1by^^JOOglC 



Sec. 4-331 PROPSRTISS OF MATERIALS 

til. Eaduetlon of orude nibb«r. The lumps or btsouita of orud< 
rubber are boiled in water, ground, washed, dried, mixed with sulphur, 
adulteranta and filler and then calendered. For details of the proe e— sec 
Perrine, F. A. C. "Conductors for Electrical Distribution," New York, 
1003; and Esch, W. " Handbook for India-rubber Engineers," Hamburg, 
1913. Owing to the high cost of pure rubber it is almost universally adulter- 
ated and many rubber products do not contain over 20 to 30 per cent, of 
pure gum, and oometimee much less. Among the numerous adulterants in 
use are rubber substitutes, osokerite, paraffin, pitch, oil, etc., and fillers suoh 
as sine oxide, white lead, red lead, barium sulphate, magnesium carbonate, 
barium carbonate, chalk, lamp-black, talc, alumin nakee, etc. 

Tulcsnlsatlon. When rubber and sulphur are heated to a temperature 
above the melting-point of the latter, 120 deg. cent., the two combine and 
form a new product termed vuleamied ruboer, which is stronger, more 
dastio and leas susceptible to temperature changes than pure rubber. The 
degree of vulcanisation depends upon the proportion of sulphiu', the tempera- 
ture and the duration of heating. 

M$t, Kubbsr substitutss in the true sense have not yet been produced 
on a commercial scale. There are certain so-called substitutes, produced 
from vegetable oils by processes of vulcanisation or oxidation, which can 
advantageously be mixed with rubber for the production of certain articles. 
Rubber substitutes used not infrequently in wire insulation consist principally 
of oxidised oils, paraffin, resins and rubber shoddy. The latter is a com- 
pound obtained by treating old rubber with steam, sulphuric acid and chlor-- 
ide of nne, thus removing most of the vegetable fiores and the sulphur, 
but leaving the meobanlcal admixtures of earth and oxides employed in the 
orimnal manufacturing process. Such substitutes are usually known under 
trade names. 

ass. Ueetrlcal propertias. The resistivity is on the order of 10" to 
lOit ohm-cm., varying greatly according to the composition and increasing 
with the content of pure rubber. The temperature coefficient is negative 
and unusually large, ranging from 2 to 4 per cent, per deg. cent. Del Mar 
states that at any given temperature the rate of change of resistance per deg. 
of temperature change is approximately proportional to the resistance at 
that temperature, values of the factor ranging from 0.02 to 0.03 for 30 per 
cent. Para compound. Values of k in the formula R'^klogitiD/d) for m- 
' sulation resistance of cylindrical wires in megohm-miles, are variable be- 
tween wide limits, ranging from about 1,000 to 20,000; d is the diameter of 
tiie wire and D is the outer diameter of the insulation, in the same units. 
The value of k is very much higher with alternating currents. 

The dielectric constant of pure viUcanised rubber is from 2 to 3; rubber 
compounds, 3 to 4. Jons gives values as high as 6 for certain compounds 
containing relatively large percentages of Para. 

The dielectric strength of high-grade rubber compound ranges from 300 to 
fiOO volts per mil; it decreases quite appreciably for long periods of electrifica- 
tion. Lufldn ststes (,EUctrieat World, 1913, Vol. LXI, p. 1310) that for each 
rubber compound there is a critical temperature at which the puncture vol- 
tafe is a maximum. This ranged between 40 deg. and 80 deg. cent, for five 
different grades, in a certain series of tests. One particular grade, or high 
quality, gave a maximum at 70 dec. cent., being 30 per cent, above the value 
at 20 deg. The range was carried to 100 deg. cent, at the upper limit, and 
deg. at the lower. 

Fleming and Dyke measured the power-factor of rubber at 920 cycles 
and found values of O.OOS for pure India-rubber and 0.002 for vulcanised 
India-rubber. For further data on electrical properties, consult the follow- 
ing: 

Jons, E. "Insulating Materials in High-tension Cables;" Tran«. Int. 
Elec. Congress, St. Louis, 1904, Vol. II, pp. 550 to 571. 

Fisher, H. W. "Rubber-covered Wires;" Trant. A. 1. E. E., 1907, Vol. 
XXVI, pp. 997 to 1025. 

Osborne, H. B. "Potential Stresses in Dielectrics;" Tratu. A. I. E. E., 
1910, Vol. XXIX, pp. 1563 to 1581. 

Hering, C. "Thickness of Electric and Thermal Insulation," EUctrical 
World. 1911, Vol. LVIII, pp. 1303 to 1305. 

I^ndi, J. H. "The Thickness of Insulation on Wires and Cables," Sin- 
trieal World, 1912, Vol. LIX, pp. 590 to 592. 

314 r- i ' 

DigilizedbyCjOOgle 



PROPKRTlSa OF ItATBRIALa 



Sm^ 4-334 



(M. Tg^iffc «»■««-« inropartiM. * The denaity of pure rubber is 0.03 to 
tM; rubber oompounda, 1.7 to 2.0. A properly valoeniaed oompouod of 
Mfh grede rubber suitable for the beet hoee end paekinc has a tensile 
Mrencth of about 2,000 lb. per iq. in. and may be stretohed to about seven 
times its oricinal length. The physical properties, however, are subject 
to wide variations depending upon the relative proportions of gum and filler 
lad tbe extent of vulcanisation. The real value of rubber depends upon 
the lenarth of time whieh it will retain its desirable properties. It often 
iJHeriorates lees rapidly when in use than when lying idle; deterioration is 
Koelerated by heat and especially by sunlight, probably as the result of 
nidation. Other things betng equal, the better grades are stronger, more 
dastic and more durable than the poorer gradea. 

Tlie following tests made by the Bureau of Standards indicate the proper- 
ties of six different grades of rubber (See Circular No. 38). 





Tensile strength 


(per cent:) 


flett 




Ob. per sq. in.) 


(per cant.) 


Sample 




















lx>ngi* 


Trana- 


Longi- 


Trans- 


Lontj- 


Trana- 




tudinal 




tudinal 


verse 


tudinal 


verse 


1 


3,730 


3,175 


830 


840 


11.3 


7.3 


3 


2,070 


3.080 


840 


870 


8.0 


5.0 


3 


1,200 


1.380 


480 


. S55 


33.1 


1S.3 


4 


1.8fiO 


1.700 


410 


480 


34.0 


34.0 


5 


800 


810 


330 


380 


37.6 


35.0 


e 


880 


000 


318 


SIS 


34.3 


35.0 



t After 300 per cent, elongation for 1 min.. with 1 min. rest. The set and 
the tensile strength were determined on different test pieces. 

SW. Tba lata wurUag tamparatore limit for eablea insulated with 
rubber gnm or rubber compounds is 50 deg. cant. 

tM. Chamical aeUvitj. Rubber compounds oontsining sulphur are 
injurious to copper. Ruboer-oovered oopper wires should be proteotad by 
a costing of tin. Rubber is sttaoked by oil and therefore ruobar-ooTerad 
amdueton should never be immersed in insulating oils, which appiiea to 
say form of rubber insulation. 

an. Ipaoiflcatlona and taata for 30 par oent. Hevea rubber-inaulating 
compound were prepared in 1914 by a Joint rubber insulation oommittaa 
upointad by a group of manufacturers and users of rubber eompounda. 
Ilie full report and Hpeoiflcatioos will be found in the Pnt. A. I. E. E., Jan., 
1014, pp. 121 to 140. Spedflcations for rubber-insulated wire ion* bean 
prepared by a number of aasooistions; see R. 8. A. " Manual." 

SSS. Ohattarton'i compound is com^oeed of 3 parts gutta-percha, 1 
part roein and 1 part Stockholm tar. It is used for filling the interfltioss 
between the strands of cable conductors before applying gutta-percha, in 
■ubmarine cables. 

tS9. Clark's aompoond consists of 60 parts mineral pitch and 40 parts 
of finely ground sand. It is employed to impregnate jute yam wrapping-on 
the outaiae of armored submarine cables. 

S40. Outtap-pareha is a natural gum, the best quality of which is obtaiasd 
from the Isonoa gutta-tree found in Sumatra, Borneo and Malacca. A 
cum known as B a i lata, which is quite similar to gutta-percha, is found in 
Venesuela. The density of gutta peroha is 0.07 to 0.98 and its properties 
srs esnenUIy the same as those of pure rubber. Crude gutta-percha is re- 
doeed in the same manner as crude rubber, but unlike the latter it is used in 
the pure stat^ principally for submarine cable insulation. Fleming and 
Dyke found tlutt at 020 cycles the effective resistivity is 34 X 10* ohm-cm.; 
apparent dielectric constant, 2.88; power-factor, 0.020. For extended infor- 
mrtion on gutta-pertsha and its properties see Clouth, F., " Rubber, Gutta- 

• The Testing of Mechanical Rubber Qoods; Circular No. 38. U. S. Bureau 
cf StandardsTlOlS. Also see "Reports of Tests of Metals" (Watertown 
Anenal), Gov. Printing Offioe, Wadi., D. C, 1909. 



315 



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Sec. 4-341 PROPBRTIBS OP MATBRIALS 

percha and BaUta," Colome. 1903; Seeiigmann, Toriilhon and Faloounet 
"India-rubber and Gutta Percha," 1010; Del Mar, W. A., "Electric Po^re 
Conductora," 2d edition, New York, 19U; Kempe, H. R.. **A Handbook o 
Electrical Testing," 7th edition, Ijondon, 1908. 

t41. Kard rubber <Hr ebonite is a rubber com^und containing a larci 
percentage of sulphur and highly vulcaniied. It u a bard dense materja 
poasesBing many desirable properties as an insulator at temperatures no^ 
greatly exceeding normal. The resistivity is on the order of 10'* to lO^' 
ohm-cm, at ordinary temperatures; the surface reeiativity is impaired \>y 
exposure to sunlight (See Scientific Paper No. 234, Bureau of StandardA. 
The dielectric constant is from 1.9 to 3.5. In small thicknesses, of 20 niila 
the dielectric strengthranges from 1,700 to 3,750 volts per mil, tested betweec 
2-in. spheres; 1,000 to 2.000 volts i>er inil> tested between flat electrodes. Aa 
020 cycles it has an effective reeistivity of about 1.5X10'* ohm-cm.; di- 
electric constant, 3.17; power-factor 0.005 (Fleming and Dyke). Mechanio- 
ally it is brittle, but can oe worked, machined and polished; tensile strenarth, 
about 1,1CX) lb. per sq. in. and compressive strength about double; density, 
1.2 to 1.26. It IS attacked by oils and oione, but is non-hygroscopic. See 
Parmer, F. M.. "The Dielectric Strength of Thin Insulating Materials." 
Trant. A. I. E. E., 1913, Vol. XXXII, pp. 2097 to 2131; bLo PaterBon, 
Rayner and Kinnee, "Notes on the Testing of Ebonite for Electrica.! 
Purposes," Jow. I. E. E., 1913, Part 217, Vol. L. 

S4S. Kerite is a vulcanised compound of oxidised linseed oil and nibl>er 
combined with various vegetable oils, invented by A. O. Day. Accordine 
to Perrine* it has a specific insulation resistanoe somewhat lees than purer 
rubber, but is said to be mechanically more durable than any insulation 
manufactured from pure rubber. It is employed in the insulation of wire« 
and oaUee aa a subetitute Ux the usual rubber compound. The valu« 
of the constant h in the formula R^k logio (DJd) is given b}^ the Koite Ins. 
Wire and Cable Co. aa 4,000 at 60 de^. fahr.; R is the insulation resistance of 
the wire in megohm-miles, d is the diameter of the eonduotOT and D it the 
outside diameter of the insulation. 

ti$. Sulphur has a resistivity of IQi? ohm-cm. at 22 deg. cent.; dieleetrio 
constant, 2.2 to 3.9; power-factor at 920 cycles. 0.0003. 
144. TuleaJiite. See hard rubber, Par. 141. 

▼ABNISHIS AND COMPOX7NDS 
S4i. ZoUdiifint nubtarlftU, such aa varnishes, which are applied aa 
liquids and emerge as s<^ds, are of interest chiefly in their final state. They 
are divisible broadly into two classes: (1) those employed to impregnate or 
treat basio roateriws, such as the fibres and the pulps; (2) those employed 
as filling compounds, to permeate or seal extensive vmds which otherwise 
would offer lodgment for inoisture and deleterious forrign matter. The 
properties of the farmer class are obviously of importance, principally, in 
association with the treated or impregnated base; while materials of tbe latter 
class constitute a species to themselves. 

S49. Insulating vamUhei are divisible, according to their applications, 
into four groupsif (A) For impregnating windings; (B) for treating papers 
and fabrics; (C) for cementing purposes; (D) finishing varnishes. They are 
also divisible, according to their properties, into (a) oxidising and (b) non- 
oxidising, and again into (I) air-drjring and (2) baking. Oxidising varnisbee 
of class A are frequently composed of unseed oil with a reeinous base of eopal 
or other fossil gum, and when thoroughly oxidized are almost impervious to 
oil and moisture. The drying action in linseed-oil varnishes takes plaoe 
first by the evaporation of the volatile solvent and then by the oxidation of 
the oil and the gum; the latter action is hastened by the addition of mineral 
drier^ the quantity of which depends upon whether air-drying or bakinjg 
varnish is desired. In another form of oxidising varnish the gum base ia 
replaced by asphaltum, but this is said to lower the dielectric strength and the 
resistance to attack by oil. Non-oxidising varnishes of class A contain a 

• Porrine, F. A. C. *' Conductors for Electrical Distribution," New York 
D. Van Noetrand Co., 1903, p. 106. 

t See fleming and Johnson. " InsulaUon and Design of Electrical Wind- 
ings;" Longmans, Qreen and Co., London, 1913; pp. 63 to 76. 

316 

Digitized by VjOOQIC 



PROPERTIES OF MATERIALS See. 4-347 

base of cum or Mphaltom with • ■pirit lolvcnt, iheUM Tarniah batnc ftn 
exajnple. Varniahc* of dua B are oompowd in loine insbuioai of liiuaed oU 
■ith B KOI" baae, and a minaral drier auoh aa mansaocaa borate or Iithar(e: 
is other eaaea linaeed oil alone ia iiaed. It ia eaaential that vamishM of 
da^ A and elaaa B ahould be aa nearly aa poaaible impervious to moiature, 
and. far oil-immeraed apparatua, not attaoked by tranaformer oil. In tb* 
ramiahea of elaaa C, ahellae is probably the moat extensively employed. 
Claaa D vamiahes are used mainly for the sake of appeaianoe and to provide 
a hard amooth exterior surface in the intereat of oleaiuinees. 

a4T. Impraciiatiiir. filUiac and Malinc eompounds are prepared from 
a mnltitade of different formulaa. In moat instances their oompoaition ia 
■narded aa a manufacturing secret and they are marlceted under various trade 
oameB, auch aa Ajax, Armalao, BenoUte, Inaulatine, Insulae, Ohmlac, Osite, 
Seaiatolae, S. V. W., Victolae, Voltslac, etc. Impregnating varniabea hava 
been superseded to some extent by compounds having an asphaltum or par- 
affin boae diaaolved in thinning materia], which are chemically more inert, 
more reaistant to moiature, better heat conductors and capable of filling the 
iateisticea of windiitgs. Tlieir uae is chiefly limited by their temperature 
characteriatics. The compounds oa the market offer a fairly wide range of 
eheiee in temperature characteriatics, the softening or flow' pointa varying 
from about SO to 130 deg. cent. The Minerallae Elec. Co. givea the following 
properties for Minerallae No. 2, a semi-aolid compound: softening point. 4fi 
deg cent.; melting-point, 63 deg.; flash-point. 202 deg.; burning-point, 218 
deg-; resistivity. l.SXlOi* ohm-cm.; dielectric constant, 2.1; dielectric 
strensth. 1,000 volts per mil. 

In the case of filling and sealing compounds, the thermal properties are 
rdatsTdy of more importance than the dielectric strength ; chemical inertness 
aad imperviouaneee to moisture are very important. These compounds 
sbookl be tested for softening point, evaporation, melting or pouring imint, 
flash-point, buming-j)oint. characteristioe at extremes of working tempera- 
tare, cubttnl expansion, chemical activity, effect of moisture and electrical 
properties. 

S4a. Taennin drTlng aad imprecnatlon is very, extensively employed 
in the application of fluid or liquid treating materials.' The mnding or 
subatance to be impregnated is first dried in a steam-hcatcd. vacuum chamber; 
then the hot insulating fluid ia admitted, the vacuum is let down, and pressure 
is applied, to the extent sometimes of 50 lb. per sq. in. In this way toe moia- 
ture la driven out and the maximum degree of impregnation is secured. 

S49. Asphalt ia a natural mineral pitch of bitumenous character em* 
ployed in the manufacture of insulating varnishes and impregnating com- 
pounda. Chemically it ia a hiixture of hydrocarbons, generally black ia 
color, hard at ordinary temperatures, becomea viscous at about 70 deg. cent, 
and melts at about 100 deg. cent. The density ia from 1.04 to 1.40. It ia 
more or leas soluble in oil ol turpentine, ether, alcohol and chloroform. The 
dielectric constant ia about 2.7 and the dielectric strength according to 
Ssrmona ia 30 volts per mil at a thickness of A >■>• 

SM. Bitumen. The term originally referred only to asphalt or mineral 
ptteht but its meaning is now extended to embrace any of a number of inflam- 
mable minera] aubataAoes consisting mainly of hydrocarbona, and including 
also the mineral tan. Coal-tar pitch is a fair Insulator, but is brittle; 
aceorifing to Symons it has a dielectric strength of about 60 volta per mil. 

tSl. Inamel (baked) inatUatlon for small mafnet wirai baa to a 
neat extent diaplaced cotton and silk, or ia used in conjunction frith them. 
The composition of the enamelling compounds used by different manu- 
facturers is guarded with much secrecy; the base of the compound, in soma 
instance^ is said to be Stearin Idtoh. Chemically stearin is glyceryl tria- 
tearate; it melts at S7 deg. cent. It ia alao known as triatearia and is a 
prominent conatituent of many animal and vegetable fats and oils. 

The wires are drawn slowly through a warm bath of the mdted compound 
and then through a baking oven, the' process being repeated to aecure as 
many coatinga aa required. One of the defects sometimes found in the coat- 
ing is the occurrence of very small holes, like pin holes, ezDOeing the conduc- 
tor; such defeets can be detected by drawing the wire through a mercury 
bath. ' The coating is usually very thin, on the order of a few tentha of a mil. 
The dielectric strength varies O'ver a range of about 300 to 1 ,200 volta (max.) 

317 

DkjitizedbyCjOOQlC 



S«C. 4-352 PROPBRTIES OP MATBRTALS 

per mil, an aTenute value being 500 to 800 volts per mil, or about four timeia 
the value for silk. The electrical resistivity at ordinary temperatures is 
very high, on the order of 10" ohm-am. Baked enamel should stand a tem- 
perature of 100 deg. cent, continuously without injury, but breaks down ele<s— 
trioally at about 300 deg. cent. It is a fairly good thermal conductor and. 
muoh superior to cotton and silk. An enameled wire should withstaimd 
bending around a mandrel four times ite own diameter without injury. 
TurpentinCj shellac, alcohol, vegetable or animal oils, and coid-tar solvents 
will attack it, but it is not injured by clean mineral oil and is moisture-proof. 
It should be carefully handled to avoid injuring the coating. 

IM. Unaeed oil is a vegetable material derived from flaxseed, having & 
density of 0.932 to 0.936 at 15 de^. cent. It has excellent insulating proper- 
ties and is extensively used in paints and varnishes. For specifications and 
general properties see "Year Book," A. S. T. M.; and Technologic Fapex- 
No. S, Bureau of Standards, 1912. Boiled linseed oil baa the property of 
oxidising under ordinary expoeure to air and the process will continue until it 
becomes viscous or even hard; the action can be hastened by drying agents 
and the application of heat. 

U9. Oiokaclte (osocerite) is a wax-like mineral, colorless or white when 
pure and eonaistingof a mixture of hydrocarbons. It is used in making cara- 
sin, candles, etc. Crude oaokerite has a resistivity on the order of 4.5 X 10>< 
ohm-om. liquid osokerite has a dielectric constant of about 2.1. CareBln 
is a yellow or white wax made by bleaching and purifying osokerite and 
is employed as a constituent of insulating compounds; its density is 0.7S: 
resistivity, over 5 X 10^* ohm-cm. at 22 deg. cent. 

SM. PanUAn is a colorless or white waxy substance, consisting of a com- 
plex mixture of hydrocarbons, obtained by the distillation of wood, coal or 
oil. ^ Chemically it is inert, being unaffected by most strong reagents. Ac- 
cording to composition, it melts at from 45 to 80 deg. cent, and has a density 
of 0.87 to 0.94; resistivity, 10" to 10<> ohm-cm.; dielectric constant, 1.9 to 
2.3; dielectric strength, about 300 volts per mil; poweMactor at 920 cyclea, 
0.00O3. 

tU. BMin is defined as any of various solid or semi-solid organic sub- 
stances, chiefly of vegetable origin, usually yellowish to brown in color, trana- 
parent or translucent, and soluble in ether, alcohol, etc., but not in water. 
They soften and melt on heating. Chemically they differ widely, but all are 
rich in carbon and hydrogen and contain also some oxygen. Among the com- 
mercial resins are amber, copal, dammar, guaiacum, Tac, mastic, rosin and 
sandarac. Lac is the raw material used in making aheUac, wnich has a 
resistivity on the order of lO'* to 10'* ohm-cm. and a dielectric constant of 
about 2.7 to 3.8. 

SM. Wax is defined as any of a class of natural subetancee oomposed of 
carbon, hydrogen and oxygen and consisting chiefly of esters other than those 
of ^ycerin or of free fatty acids. In this class are included beeswax, sperma- 
ceti. Chinese wax, carnauba wax, etc. Beeswax is a dull yellow solid, of 
density 0.96 to 0.97 at 16 deg. cent, and melting at 62 to 64 deg. cent.; 
resistivity, 10i< to 10" ohm-cm.; dielectric strength, about 290 volts per mil. 

UT. Weatherproof compound! for saturating the cotton braids on 
weatherproof wire usually contain an asphaltum base, with an admixture of 
wax so that the surface of the braid may be given a dull polish. 

ursvLATno <HI.8 

tn. Oil is emp>oyed as an insulating medium in many ways. It is em- 
ployed by itself to insulate transformers and switches by immersion; it is 
used for saturating fibrous and other materials, as in cable work; drying oils 
Oinseed) are used for coating papers and cloths in sheet insulation; various 
kinds of oil are employed in mixing insulating iiaints and varnishes. Oils 
of practically every variety are poswssed of very high reeistivity and dielec- 
tric strength. Chemically oil is composed of hydrocarbons having the gen- 
eral formulas CnHtn^i and C.Hin. The desired characteristies of an insulat- 
ion oil are high resistivity and dielectric stren^h. low viscosity, high flash 
point, chemical neutrality toward metals and insiilating matenaJs, freedom 
from moisture, sediment and impurities, and chemical stability under local 
high temperaturaa, 

318 

Digitized byCjOOQlC 



PBOPBRTIBS OF UATBRtALS 



Sec. 4-369 



roil. The ideal eooliss and inanlstiiu; fluid for • tran*' 

■bould have the characteristic* named in Bee. 8, Par. M. The oil 

Iwcrly used is a mineral oil obtained from crude petroleum by fnietioaal 

CaBlatioD, having the following charaeteriatie*. 





Medium 


Light 


Db^ point, di^ ceot 


180 to 190 

206 to 215 

-10 to -15 

0.885 to 0.870 

100 to 110 sec. 

None 


130 to 140 

140 to ISO 

-15 to -20 

0.845 to 0.860 

40 to 50 see. 

None 




QAi tot' 


OeoHty at 13.5 des. cent 


TiH»>t)r at 40 deg.~oeot. (Saybolt test). 
iaid. alkali, sulphur, moisture 



.J free from moiattire the dielectric strength, between 0,&-in. discs 0.2 
in. apArt, with sine-wave e.m.f., should be from 45,000 to 50,000 volts; or 
i i X m iXM 0.5-in. braae spheres 0.15 in. apart the average dry oil should not 
knak down at Ion than 30,000 volts. The medium ^ade of oil is usually 
eaqdoyed in self-cooled apparatus and the light grade m water-cooled appa- 
nCas, bat the dielectric strenf^hs ars the same. The dielectric strength 
hsla<wi and 100 deg. cent, increases about 0.4 to 0.5 per cent, per wz- 
TW reastivity of dry oil is on the order of 10" ohm-cm. and decreases with 
fise of temperature. The effect of moisture is very harmful (Par. MS) 
•ad it is of the greatest importance to keep oil abeoluteljr dry or as nearly so 
is pnswMe. One of the principal advantages of oil as an insulator isits prop- 
«ty of adf-rcBtoration after dielectric discharge or puncture; this property is 
Bst independent, however, of the energy of <Cacharge. and excessive energy 
nay overheat the oil and cause exploeion or fire. The specific heat of 
Inasformer oil is about 0.30 to 0.51 and the thermal conductivity ranges 
iroBO.00033 to 0.00043 gram-calorie per em-cube per deg. cent, per see. The 
folowiag r«ferenees showd be consulted for further information. 

SUnner, C. E. "Transformer Oil." Electric Journal, May, 1004. 

Kintacr. 8. M. "The Testing of Transformer Oil." £<«c(rte/<ninia{, Cot., 
MOB. 

TobCT, H. W. ;;_Dielectric Strength of Oil," Tronj. A. I. E. E., 1910, 



JVaS^'l. B. 



X pp. llSO^to 1232. 



The Dielectric Strength of Thin Insulatinc Material*,' 
1913. Vol. XXXII. pp. 2097 to 2131. 



MO. Baetrical propertiM of oU 
(Circular No. 36, V. 8. Bureau of Standards, p. 24) 



Oil 


Deniuty 
at 20 
deg. 
cent. 


Resistivity 
(ohm-cm.) 


Phase difference 


Dielectric 
constant 


100 
cycles 


1,200 
cycles 


PiMts astral (kero- 
rl^i 


0.78S2 

0.8710 
8795 
0.8882 


470X10" 

1,100X10" 
49X10" 
3.1 XIO" 


0»2'H" 

0V36" 
1* 6'0" 
0»30'0" 


0°0'25" 

OW 6" 
0«6'10" 
0»8'30" 


2.34 

2.41 
2.51 
2.47 


TiaasformeroUCA).. 
nsarformer oil (B).. 



tU. Dislttctric streiiftli of chI with a l-mm. gap (39.4 mils), expreaaed in 
Tilti per mm^ ia ^ven in the table balow for numerous Tarieties of oil. 





13,000 
7.000 


Nestsfoot 


9.000 
7.500 

16,000 
8.500 
9,000 

11.000 




Olive 


Isrd. 


4.000 
9.000 
8,000 
5.000 


Paraffin 

Sperm, mineral 


'iiiiLJ. till 


lumia twilral 


L«iiri<4«ing 


Turpentine 



319 



jilizedbyV^iOOyiL' 



Sm. 4-362 



PROPBRTIBS OF MATERIALS 



Ml. IHaleotrie eonftant* of various Idndi of oil* are (iv«n in the ac- 
companying table. The values probably change very appreciably with tli« 
temperature. 



Arachid. . . 

Caator 

Colaa 

Lemon. . . . 
Neatafoot . 
Olive 



3.17 
4.6to4.8 

3.07 to 3. U 
2.2S 
3.07 

3.08 to 3. 16 



Petroleum.. 
Rape seed. . 

Sesame 

Sperm 

Turpentine. 
Vaseline 



2.02 to2.19 
2.2 to 3.0 

3.17 
3.02 to 3.09 
2.ISto2.28 

2.17 



) 






lU. IBaetf of moistura and dust on iniulatlnf propertiai of oil. 

The presence of moisture in transformer oil has a very serious effect on the 
dielectric strength, as shown by Fig. 36. In order to obtain a dielectric 
strength of 40,000 volts (0.2-in. gap between 0.6-in. discs), the water prea- 
ent as distributed moisture in the oil mua^ 
not exceed 0.001 per cent. Fine dust is also 
very injurious to the dielectric strength. 
For these roasons, various manufacturers 
have developed oil dryers and purifiers, which 
operate on the principle of a niter press. 

IM. Formation of dapoiiU in oll- 
oooled tranaformara. The foregoing suh- 

• " I I mi U I I I I I I M I [ I N '•** formed the title of a paper by Dr. A. 

I 10 "! = = "::Tr::: C. Miohie before the I. E. E. in April, 1913. 

4 qI 1 1 M 1 1 M I M I M M I I □ The author stated that all oils oxidise in 

H • ' • ' • ?„i.Li,L. time, but the formation of deposiU can be 

»««.,«« 1.10.000 b, to™ prevented or minimised by avoiding th^ 

following conditions; (1) Overheating; (2) 

Fia. 36.— Effect of water on undue acoeaa of air to the oil; ^3) conStiona 

didectric strength of oil. likely to give rise to the formation of osone: 

(4) contact of the oil with clean surfaces of 

copper, lead and iron. 

SM. V. S. OoTemmont apocifloatlon for tranaformar oU calls for a 
pure mineral oil obtained by the fractional distillation of petroleum, unmixed 
with any other subsfanoe. It shall be prepared and refined espedally for the 
purpose; shall be free from moisture, acid and alkali, and shall contain a 
mimmum of aulphur compounds. The flash-point determined in a closed cup 
shall be not leas than 170 deg. cent. ; on cold test it shall not begin to solidify 
and no wax shall form in the oil above deg. cent. It shall stand a break- 
down test of 30,000 volte between spherea of O.S cm. radius, 0.40 cm. apart. 
See Circular No. 22, Bureau of SUndiards, 1911. 

aAsn 

tM. The iniulatinf propartiat of gasaa depend upon, and vary with, 
the pressure and the temperature, and are affected also by the humidity. 
The only gaseous dielectnc in extensive use is atmoepherie air, wheaa prop- 
erties have been the subjet^ of extended research. 

SiT. Air. The dielectric properties of air, and particularly its disruptive 
strength, have been the subject of more investigation than any other dieleo- 
tric in use. Extended investigations and researches have been - made by 
Ryan, Mershon, Fisher, Peek, Whitehead, FaccioU, Harding, Bennett, For- 
tescue and Farnsworth, whose results have been published during the past 
10 vears in the Tram. A. I. E. E., and by Russell (jseeJour. I. E. ET). 

Air in the free state has electrical conductivity. The results obtained (soe 
Whitehead, Proc. A. I. E. E., May, 191S, p. 846) indicate that in the open the 
current passing between two parall^ platea 10 cm. apart and each 100 era. 
square, assuming perfect insulation, would be of the order of magnitude 3 X 
10' >* amp. This is the maximum current which may be obtained and doee 
not increase with increase of voltage; it diminishes greatly if the air is con- 
fined in a doaed vessel. The conductivity may be greatly increased by 
expoaing the air to Rdntgen ravs, ultra-violet light, etc.ibut the magnitude of 
current still remidns very small. 

The dielectric constant of air is usually taken as unity, and air is almost 
universally the medium of reference in all measurements of this constant. 



no 



jbyv^iuuynj 



PSOPBBTIBS OF MATSRIAIS 



Sec. 4-368 



The ili i Mpt iTB atmisth of ab in a nnifann, elettroaUtia Held, undsr moit 
tftTOrable oonditioiw, »t ordiiutfT temperature and preeeure, ia of the order of 
38 k-r. per em. or 87 volte per mil fmaiiimim inateed of r.m.*. value) ; White- 
head found a value of 32 kv. (max.) and Peek found a value of 30 kv. (max.). 
Under unfavorable eonditioiu, the strength ia below 30 kv. max (21 kv., 
r.m.s.), aa ahown by inveeticatioiia of corona on o^ndrieal wires (see See. 11). 
Tlw (Uamptive strength is direetl^ proportional to the air density .over a con- 
■derable range. If the air density at 76 cm. barometer and 25 deg. cent, is 
taken as nnity, the relative density at any other pressure and tamperatun is 

I— M?» (201 

• 273 + « ''^' 

where 6 is the barometer in em. and ( is the temperature in dec. cent. Appar- 
eniljr the degree of humidity has very often little, if any, eneet on the dis- 
ruptive strength. 

Advantage is taken of tlie low disruptive strength of air at low jireasuree 
(small fraetion of one atmosphere) in so-eaDed vacuum-type lightning arres- 
tots, reeently developed for low>-voltage, low-power eirouits, such ss tele- 
plMHW, telegraph and signal linea. 

Sparking distanees in air, using needle gaps and sphere gaps, are given in 
the A. I. E. E. Studardisation Rules, See. 24, Par. Mi to 1717 
MS. BelatlTS diwnptiv* Btrengtha of hydrocen, oiytHi, earben 
dlindda and nitrogan 

(Wolf) 



Pressure 

in 


ReUtive strength (air - 1) | 


Hydrogen 


Oxygen 


Air 


Carbon dioxide 


Nitrogen 


I 
2 
3 
4 
5 


0.87 
0.76 
0.72 
0.60 
0.68 


0.05 
0.03 
0.92 
0.92 
0.90 


1.00 
1.00 
1.10 
1.00 
1.00 


1.20 

i!os 

1.03 
1.02 


1.16 
1.15 
1.15 
1.14 
1.14 



I OOHOUUTIVITUS 

•. Thermal eondaetMtts* of Tartvos inantotfiic m