april seventy-sixth thle thirty-first thle...

AMERICAN INSTITUTE OF ELECTRICALENGINEERS.

New York, April 18th, 1893.The seventy-sixth ineeting of thle Institute was held this date

at 12 West Thirty-first Street, and was called to order at 8.30P. M. by Vice-President Williain J. Haiammer,THE SECRETARY:-At thle Couacil meeting held this afternioon

the followino, associate iriembers were elected:Name. Address. Endorsed by

ADAMS, ALTON D. Electrician and Manager, Commer- Fred. DeLand.cial Electric Co., I3 South Ten- L. L. Summers,nessee St., Indianapolis, Ind. V. A. Rosenbaum.

CRANDALL, JOSEPH EDWIN, Electrician, C. & P. Telephone J. J. Carty-Co., 6I9 14th St, N. W., Wash- T. D. Lockwood.ington, D. C. F. A. Pickernell.

DEMING, EDWARD General Manager, Demirig Auto- T. C. Martin.matic Electric Safety System, 522 Jos. Wetzler.Hancock St., B3rooklyn, N. Y. Edwd. P. Thompson.

FLAGG, STANLEY G., JR., Stanley G. Flagg & Co.. J. B. Cahoon.igth St. and Penlna. Ave., Harris J. Ryan.

Philadelphia, Pa. Ralph W. Pope.GARDANIER, GEORGE W. Electrician, Western Union Tele- CG. A. Hlamilton.

graph Co., I95 Broadway, New Alfred S. Brown,York City. James IHamblet,

EGRRY, M. H., Ja. Engineer, N. W,, General Electric Chas. K. Stearns.Co., 3333 Cedar Ave., Minne- H. M. Byllesby.apolis, Minn. Geo. D. Shepardson.

HALL, EDWARD J. Vice-President and General Man- Hammond V. Hayes.ager, American 'relephone and John J. Carty,Telegraph Co., iS Cortlandt St., Wm. S. Ford,New York City,

TAYES, HARRY E. Asst. Electrician, American Tele- F. A. Pickernell,graph and Telephone Co., 153 H. V. Hayes.Cedar St.. New York City. F. W. Dunhibar.

HUMPHREYS, WM. J. Professor of Physics and Mathe- T. J. Smith.matics, Miller School, Crozet, Ralph W. Pope,Va. Geo. I1. Stockbridge,

PFUND, RICIIARD Richard Pfund, Electrical Appa- James Hamblet.ratus and Supplies, 153 Broad- Alfred S. Brown,wav, Brooklyn, N. Y. C. L. Buckingham.

PIER,CE, RICHARD H. Electrical Engineer, World's Colum- F. A. Pickernell.bian Exposition, 5434 Monroe Ralph W. Pope.Ave., Hlyde lark, 111. F. W. Dunbar.

1893.1 KWVNELLY OW IMPEDACE, 173

USINA, NI. NELIGAN Superintendent of Motive Power, R. J. Nunn, M,D.City and Suburban Railway, 78 Ralph W. Pope.Bolton St., Savannah, Ga. T. C. Martin.

WILLIAMSON, G. D:EWITT, Electrician. General Electric Co., J. H. Vail.New York City, Dobbs Ferry, Charles Hewitt.N. V. H[. W. Weller.

Total 13.

And the following associate members were transferred to fulltmembership:WILLIAMS, JAMES B., MI. D. Electrician, 44 Btoadway, New York City.SMITfH, IRANK STUART, SUpt. of Carbon Department, Westinghouse Electric

and Mfg. Co., Pittsburg, Pa.Ross, ROBERT A. Engineer in charge of Engineering Dept., Edison Gen-

eral Electric Co., Peterboro, Ont.NOLL, AUGUSTUS New York Electric Equipment Company, 59 Duane St.,,

New York City.HERING, HERMNIANN S. Associate in Electrical Engineering, Johns Hopkins,

Uniiversity, Baltimnore, Md.Total, 5.

THE CHAIRMAN [W. J. Hammer]:-The Chair wishes to an--nounee that at the meeting of the Couneil this afternoon thecertificate of membership whieh, doubtless, you have all seen inthe adjoini'ng room, was adopted with one or two slight changes.,

This certificate will be issued to full members onily. It willbe a comipliment fromn the Institute to those wlio have attained ahigh rank professionally, and whose work in their profession andfor the Institute entitles thein to receiv7e it. These certificates.will probably be ready within two or three weeks and. will beprinted upon heavy parchrnrent paper at abont cost, namely, onedollar. The Secretary has beern instrutcted to send out a notice,stating the conditions under which this certificate is givenl andother matters pertainiing thereto, as soon as they are ready fordistribution. rThe American Institute of Electrical Engineersdesires to raise its status as a scientific organization in every waypossible, and it is believed that by issuing this certificate to fullmembers only, the honor conferred will be more highly appre-ciated and it will result in a desire upon the part of many of ourassociate inembers to apply for and to secure full membershipin the Institute. While in soine of the engineering societies themajority of the members are active or full members, and thereare comiparatively few associate metm)bers, in the Institute ofElectrical ETngineers the opposite is the easy, and the issuing ofthis certificate under the cornditions as recommended by theSpecial Commnittee will prove advantageous to the interests ofthe Institute as well as to the miembers receiving the saine.

I will refer to the subject of badges as several members haveasked rae about them to-night. Some of the badges we:re de-livered to-day, and I might say that within the next week or tendays the first fifty will be ready. Five or six moulds have beenmade and a great deal of trouble has been taken to make themr,

174 KENNELLY ON IMPEDANCE. [April 18,

correct. Those who apply to the Secretary first will naturallyreceive the badges first. Tihe price is $3.00.

'There is one other point to whiclh I would like to call theattention of the institute before taking up the paper. On behalfof the Ways and Means Committee of the Institute in charge ofthe World's Fair mnatters I would like to state, as you have alreadvheard, that headquarters have been seecLred at the ColumbianExposition. The authorities there have given us two excellentrooms adjoiningo the official headquarters in the Electricity Build-inlg. They have promnised to give us excellent facilities there-lonig-distance telephone service, electric light, telegraph service,fire protection and police patrol. The Council has instructed itsSecretary to go there anid represent the Institute dcuring theneeting of the International Electrical Congress and largelyduring the season. We have extended invitations to our for-eign electrical friends to make use of our headquarters, to havetheir mail addressed there, to write their letters there and to seetheir friends there, and it is very desirable that we should maketlhose headquarters initeresting, and with that end in view, theComnmittee is endeavoring to secure a large number of exhibitsof great historical interest. We want letters, books, sin all modelsand things of that character, autographs, photographs, etc., whichwill be of interest to our friSends and to our members. We wouldlike to make ouL headquarters the most attractive spot in theElectrical Building. You hyave doubtless noticed in the otherroomn small reproductions of photographs of a great many emi-nent men. Those are largely based on a n-umber of photographsthat I lhave been collecting for many years, and there will proba-bly be four or five of those large frames of photographs sentout there. Th-e Conmrmittee has been promised some of the thingsthat) belonged to Professor Morse and to Franklin, anid lias'already received some of them. The Secretary placed in theCoi mittee's hands to-day the original list of the members whosigned the call for the organization of the American Institute ofEleetrical Engineers. That will be placed in the exhibition.'These and rmany other things which we shall haae, will mlake theInstitute headquarters very iuiteresting to all our members andour visitinog friends. I might state that one of the large pub-lishers, Van Nostrand, has promised me to place in a few days acomplete electrical library at the headqutarters, and that thislibrary, under the care of the Secretary will be at the disposal ofouir members. It will be a very coinplete and doubtless a veryinteresting exhibit. I trust that members who have interestinagthings will send them to the Secretary or to myself as Chairmanof the Committee, and if they know of some particular featurewhich would be of interest and value that they would kindlycommiunicate with the Secretary or the Commlittee.We will now have the pleasure of listeni-ng to Mr. A. E. Ken.

nelly's paper upon " Impedance."[Mr. Kennelly then read the following paper.]

A Ia,5erfresented at tke sevenly-sixll meeting oftSe American Institute of Electrical Engin-eers, New York, AHriZ iSk, I3, Vice-Presi-den Hamimer in the Chair.

IMPEDANCE.

BY A. E. KENNELLY.

The impedaniee of a conductor is its appareiut resistanice, andis expressible in ohIIms. More strictly, it has been defined asthe ratio of the efective E. 1. F. between the terminals of theCoulductor to the effective curren-t strength it carries. By vol-tage or current in the sequel, efective voltage and effectivecurrent, unless otherwise specified, will be intended,--such aswould be irndicated bv properly calibrated alternating currentvoltmeters and ammeters.With steady continuous currents, the impedance of a conduic-

tor is its simple resistance, With periodically fluctuating cur-rents, the impedanee will in general difer from the resistanee,and will be greater or less, but in common practice greater.With such voltages and currents, Ohmn's law becomes

E

where the imlpedance is represented by 1.We may first consider periodic currents and voltages of the

.imple harmonic type, following waves in time such as could betraced uponl a band of paper, moving steadily lengthwise, by thevertical shadow of the crank-pin on a fly-wheel revolving uni-formly in a vertical plane perpendicular to the band. [Fig. L.]The ratio of the velocity between wheel and paper would con--trol the spacing and steepness of the waves, but would not altertheir sinusoidal type, while the motion of the shadow wouldbe simply harmonic.

If the fly-wheel makes n complete periods or revolutions per

1,6 KENNVELLY ON I-MPEDA CE. [April 18,

secontd, aincd the distance of the crank-pin fromii the shaft axis-its crank radins-is 'unity', theni thle eircunfereilee of the circle ittraces will le 2 , and the total distance it will rurn throuigh inone second will be 2 ;- n or 6.283 n linear units, whieh we maycall its speed, anp denote by -2= 2. If tlhein the pin issshifted outwards upon the wheel until its crank-radius or dis-taance frorn the axis is I units, where I is the numilber of henrys inany particular inducetance, then the coir esponding travel of thepiin will be 2 wT I n linear u iits per second, and this speed p I wenmay call the inductance-speed for the particular frequencv andinductance I considered.

Non-ferric inductanees (if the teri be permuitted), or in-ductances without ironi may be first assumlied, leaving ferricinductances and conductors embracing ironr, for later examina-tionl.

In order to find the -impedance of any coniduietor whose resis-

P2adew, Live

FIG. 1.

tance is r olhins, and inductance I henrys, we construct the tri-angle having as base the length r, time perpendicular of p Iuntlits, and draw the hypothenuse wbhichi will have tIme lengthvI + (p ) 2 betweenl their free extremnities. [See Fig. 1.]This length will be the impedance in ohrs. The ii pedance istherefore the geometrical or vector'm sum of the resistance andinductance-speed, when these are plotted on two rectangulaoraxes. Calling tlhis itmpedance i, Ohmn's law gives

G_ ,e

7e

corresponding to the usuial formuLlas for continuous cuLrrents. In

1 The vector sumn of two lines A B and B c is the line A c, since a transfer-ence froM A to B followed by a transference from B to c is geometricallyequivalent to a transference from A to c.

1893.1] KENELLY ON IMPEDANCE. 177

Fig. 2 a resistance of 75 C having an inductance of 0.06 henrywith a consequent induLetance speed at 100 , of

6.283 x 100 x 0.06 = 37.7

Resistance r==75 ohms.

FIG. 2.

is shown to possess ani impedance i of

4 (75)2 + (37.7)2 = 83.9 ohms.If two such impedances, i1 and i2, be connected in series, their

total impedance [Fig. 3] will be the vector sum A c of ?. and icorresponding to the arithmetical sum for unvarying currentseThis vector suLm is most conveniently constrtucted geometricallyby summning separately the component resistances r1, r2, A G,and then the component inductance-speeds, G c, as shown. Call-ing the vector sum 1,

..4

FiG. 3.

the voltau,e on1 I fOr a cur-rent of c amperes will be c 1 volts.* s c ec 2

i2 " ; 2;

178 KENNELLY ON JMPEDANCE. [April 18,

but I will not be the arithmetical sum of il and i2, nor will thedrop on ] be the sum of the drops of i1 and i2 unless the sepa-

rate time constants l, and 12 are equal, when A B will be in liner1 r2

_Re6istance r500 (D

\ t;

FIG. 4.

with B c; the reason being that otherwise the currents in i1 andi2 while of equal strength, are out of step.

In Fig. 3, r, represents to scale, a resistance of 30 w, r2 20 ,op'll an inductance speed of 10, p 12 30. Then

- is V 900 + 100 - 31.63 ohms,

i2 is 4/ 400 + 900 - 36.06 ohms,I V7 2500`+ 1600 _ 64.0 ohms,

whereas the arithmetical suim of il and i2 would be 67.69 ohms.A condenser of capacity k farads (millions of microfarads) has

an impedance of 1 ohms, or in other words its impedance

_p~~~~~~~~~~~~~ k

188.5=Ppl.

Resistactce r C(p31803

J Pk~~~~~~~~~-P1=129.SFIG. 5.

is the reciprocal of its capacity speed.' The current in a con-denser supplied by an E. M. F. e at n is

e = eic1Te C T- p p

1 Fleming, " The Alteriaate Current Transfol-Imer,'" Vol. II., p. 378.

1893.1 KENNELLY ON IMPEDAICE. 179

Thus, 1000 volts alternating give throtugh 5 microfarads at

1000 X 6.283 X 100 X =( 3.14 amperes.1,OOo,oOoA condenser k in series with a resistance r has a total impe-

dance

+ ( 21)_P k

which is found by taking the base r, and the capacity-speed

SMerofarags

icMrofaaZ

A oo co - c 00 D

pk,~~~~pI 'f k

.0.025 B '0.001874 1)4100086

-i: 1.:.5C0.0026 uB0- G,<A0.0025 0.001S74 A

,A~~~~~~~~~~~~~8.0028 ~~~~~'O.Oo2o36 £ ~~001 6

*2 0.000488i 3tNt: K1-112.3

FIG. 6.

1reciprocal downwards perpendicularly. In other words,

pkits impedance is the vector sum of the resistance and capacity-speed reciprocal.

Fig. 4 represents the five-microfarad-condenser above consid-

ered, whose impedance at 100 - is 318.3 ohms in cireuitpk

with a non-inductive resistance r of 500 ohms. The resulting."impedance,

1= V6o002 + 318.32-592.8 ohms,

180 KENNELL Y ON IMPEDANCE. [April 18,

so that 1000 volts alternating harmonically at that frequencywould, when connected to this series deliver

1000= 1.687 amperes through the same.

592.8

If again, inductance is inserted in series with the condenser

z

FIG. 7.

and resistance, the total imnpedance of the three, independent oftheir order, will be the vector sum of the resistance, the induc-tance-speed, and the capacity-speed-reciprocal, the second beingdrawn upwards, and the third negatively or downwards, asshown in Fig. 5, where an inductance of 390 nmillibenrys = 0.Shenry, giving at 100 an inductance-speed of

628.3 x 0.3 = 188.5,

is introduced into the same circuit of resistance and condenser.The effect is to diminish the imnpedance from 592.8 to 516.6

FiG. 8.

ohms, increasing the currenit to 1.936 amperes. If I be theresulting impedance,

eC I

and the voltage across the resistance and inductance supposingthese combined in one coil will be c A where Al is the impedance

1893.] KENNELLY ON IMPEDANCE. 181

of these two conisidered togethier, and the voltage across thecondenser will be

l

It is evidenit tlhat this latter inay be greater than e when suitablevalues are chosen so that one or both of the factors, current andcapacity-speed-reciprocal, are large. In such cases the condenservoltage exceeds the voltage of supply, and what is commonlycalled the "Ferraiiti effect," is developed.

It is also evident from the construction of the diagrams, thatthe inductance will neutralize the capacity in its series or vtce-ver8a, when the verticals above and below are equal, or when theiiductance-speed equals the capacity-speed-reciprocal, and in thiscase the impedance degrades into the sinple resistance. Thiscondition requires that

or r k1p ~kp'

FIG. 9.

With unvarying currents, the combined resistance of resis-tanices in parallel, is the reciprocal of the sum of their recipro-cals. Thus, if three resistances be connected in multiple, of 3,2, and 6 ohms respectively, their joint resistanice is

1 ~ 1.

3 2 6In the same way, the joint impedance of impedances in multiple,is the reciprocal of the vector sum of their reciprocals. Thussuppose that three impedances, ?", i2,v 0, are connected in par-allel, the first being, for example, a simple resistance; the seconda series of resistance, inductanee, anid capacity; the third a simplecondenser. These three are diagramatically represented in Fig.6 Take" the numerical reciprocals of i,, A, and i3, and lay themoff in their respective directions. Take the vector sun of these,

182 KENYNELL ON IMPEDANCE. [April 18.

which is most conveniently done by resolving the reciprocalsinto components, summing r s alone and p 1 s alone. Finallythe reciprocal of this vector sum, laid off in its direction, willbe the joint impedance of the combination, and the componentsof this impedance will represent the equivalent resistance, andthe equivalent capacity-speed-reciprocal or equivalent inductance--speed of the combination.

Thus, in Fig. 6, i1 = r1 = 400 co non-inductive: i is theseries of inductance, resistance, and capacity, taken from the lastcase represented in Fig. 5, and -i is a simple condenser of 5microfarads -or 0.000005 farads whose capacity speed will be628.3 X 0.000005 = 0.0031416, and whose impedance, the re-ciprocal -of this, is 318.3 ohms: i1, i2and i3 are represented to scale

-0.2 o- \ , j 0 '

o> i) -J

.CooTime Seconds

FIG. 10.

in their proper directions, A B = il horizontal, C E = diag-onal, and G H = i3 vertically downwards. Immediately beneatheach of these are their respective vector reciprocals,

A/ B = 0.0025, c E = 0.001936, and G' H' =0.0031416,maintaining their directions, but to an altered dimensional scalefor convenience in working. The vector sum of these recipro-cals A' B' c' E' and G' H'/ iS A' H' indicated in the quadri-lateral 1 and measures 0.005682. The most convenient way toobtain this practically is, however, shown at triangle 2, wherethe projected horizontal component of c' E/' namely C i>

0.001874 is added to A' B', and also the projected vertical comrponent D' E' 0.00048, to G' H'. The hypothenuse of the tri-

1893.] KEATNELLY 0N IMPEDANCE. 188

'1000,.003S:,3.5 _

goo00.003 3.0 4

600I,40025 r -

200 0.006 2.0 -

01,0I0G1.IV

ire41 mic pe l7 9 15JiIeisiv Amperis fl Wie.I

H.o,M.M oerCr. nIIan

onetraghtoop235ems lo3g wit 8cm. ieaxa distnce

Resistnceofironw reM7.47mcomperCm ineIand cmII 5 C

Resistancey of8 mironhwir47.4 micohmpeC iea.m ~C

X84 KENVELLY OV lMPEDANCE. [April 18,

angle, A' H', then Trieasures 0.00.5682 either arithmetically orgeometrically. The vector reciprocal of A' H' is A H, repre-sented at triangle 3, and measures 1/0.005682 or 176 ohms onthe original scale, with projected coMponents A M 135.5 t and

ciapacity-speed-reciprocal 112.3.If the voltage measured between terminals o and P is 1000

Volts,, the current in the main leads to o and P is

10060 = 5.682 amperes.176

1000 1000But the currenit in the braneh l is 2.= 400= 2.5 amperes

Also" ; 10 1000 = 1,936 "'1

2 51l6.6

And ; ;;, , 3 1000314000 "-3 318.3 3.4 "

sum, 7.578The suim of the branch currents is therefore greater in this in-stance than the current supplied lthrough the main, for the reasonthat these currents are not in step; but at any one instant thenain current and the branch currents' sum mnust be equal; it isonly in the process of averaging over the cycle that the differ-ence manifests itself.

If two conductors are connected in parallel, as for example agalvanometer and its shunt, of resistances g and s respectively,we know that if C is the univarying current supplied throughthe combination, the portion through one of them,-the gal--' ometer say-will be C + In the same way, if C

a sd are their respective impedances to a harmionic current, the

vanometer's share will be C + where, however,10 r~~~~+ v

v + S is not the arithmetical sum, but the vector sum of thetwo impedances. Either G or S may contain capacity, providedthat this is included in its impedance by the usual rule of layingoff the capacity-speed-reciprocal against the inductance-speed.

Again, the joint resistance formula for galvanometer anad shuntwith steady currents being

r-y+ S

1893. KEEYNELL Y ON IMPEDANCE. 185

51l r -- - C00 tn=SlSOO;0\l-L --- - t1 1--1- V L 3.-0Lr

oo\-T4---4TT-Xl WCt>~~~~~~~~~~~~~~~~~~~~¢;=~4-900 [t1L-fF1\--_IXX m fl O o400000405 5 fl 0Q

300 : 1 { 10 j

4v Q

3100 X :r 4 b,e4

10000 3.5 - ~ H 1700KY,171. TV~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

200 0.003 3 ____ -4

t,:

*00 r- l- IE-

100 1A1 12 T

-00.01--- - --

4, ° = O

C.o lsM 8 0 10lad 13 13 +t ° 3 0

LL. bc~QEffective alternating current amperes in No ~ ~~~~ 0Hc' M.M.F per Cm. inland Ill ~~~~~~~~~~~~~C5 sn

18B6 KENNELLY ON IMPEDANCE. [April 18,

the corresponding formula isGS

where G S is the aritlhmetical product, but G + S a vector sum.This case could also be dealt with by the rule for joint imped-ances

1

where the vector reciprocals are added vectorially.All continuous current corollaries from Ohm's law thus be-

come applicable to harmnonic currents, when the sums and differ-ences of impedances or their reciprocals are treated vectorially,and if all alternating currents were strict sinusoids, all inductancesnion-ferric, there would be almost as little difficulty in reckoningtheir quiantitative relations as inl continuous current circuits. But,RKirchoff's laws, while truie instantaneously, are only applicable toalternating current circuits, when the currents are all in step, anidthe vector sums degrade into arithmetical sums.

Algebraically,l all, and more than all the foregoing statementsconcerning impedance comnbinations are contained in the fol-lowing:Any combination of resistances, non-ferric inductances, and

capacities, carrying harmonically alternating currents, may betreated by the rules of unvarying currents, if the inductances are

considered as resistances of the formpi I -l,and the capacities

as resistances of the form - 1 1, the algebraic operationsk - h leracoeain

being then performed according to the laws controlling "complexquantities."A valuable application of the principles of impedanee is to the

determination of the limits of error in measuring apparatus suchas voltmeters-intended for both alternating and continuous cur-rent circuits.For example, a particular sample of alternating and continuous

current voltmeter, consisting of a dynamometer without iro:n, incircuit with a resistance coil, has a resistance of 2,085 ohms, andan inductance that varies with the relative position of the dynamom-eter coils, but which does not exceed 91.5 millihenrys _ 0.0915henry. At a frequency of 140 which is about the miaximum in

1893.1 KENNELLY ON IMPEDANCE. 187

ordinary use, the inductance speed of this instrument will not begreater than 0.0915 X 6.283 X 140 = 80.5. Coristructing theright-angled triangle with base 2085, and perpendicular 80.5, wefind the hypothennase to be 4/ 20852 + 80.52 - 2086.5 which isthe impedance of the instrument at this frequency, so that 50volts E. M. F. harmonically alternating would force less currentthrough the dynamometer than 50 volts continuous F. M. F. in the

ratio of 2085 and would therefore unlder-indicate by about20)86.5'

0.075 per cent.A similar instance is afforded by the Thomson wattmeter.

The armature of this instrument has a certain non-ferric induc-tance and is connected across the supply mains through a resist-ance. The equality of the meter's record for both alternatingand continuous current circuits depends upon the equality of cur-rent strength through the armature under equal alternating andcontinuous voltages, and this is again dependent on the impedaneeof the armature circuit. In a particular instrument of 1,500watts capacity (50 volts and 30 amperes) the- total resistance ofthis circuit is 455.5 ohms, and its total inductance 25 millihenrys(0.025 henry). This represents at 140 , an inductanice-speed of22, and an impedance of 456.0 ohms =4/ (455.5)2 + (22)2 so thatthe current in the armature will be about one-ninth of one percent. less, on a supply pressure of 50 volts, alternating harmoni-cally, than on 50 volts continuous. Strictly speaking the accuracyof a wattmeter depends not only upon the non-diminution ofcurrent strength through filue wire circuit in virtue of inductance,but also upoll the lag in phase that is also there established. Itis generally safe to asstume, however, that when the error due toimpedanee is very small, the error due to lag is very small also.

Ain important application of impedance principles is to con-ductors for the distribution of alternating currents. Let thecommoni case be considered of two parallel overhead wir-es run-ning from a central station to a consanuption point onle mile dis-tant, eaelh wire of copper, No. 4, A. w. G., 0.2043 in. (0.519em.) in diameter, fixed on pole insuilators, at a distance betweentheir axes of 30 inches. At a temperature of 150 C this wire ofstandard conductivity, would have a resistance of 1.285 ohms permile of 5,280 feet, and if the wire actually possessed this conductivity, the resistance of the loop would be 2.57 ohms. Anunvaryin g current of 1 0 amperes wouLld establish in this wire a

188 H~~~~~~~~~~EN-NELLYONV IMPEDANCE. [April 18,,

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-ci~~~~~i0 ttom0 cine tco0in0 cc-c cc ccc-ccccoco occ-c-c-ccc cc -ccinooo

ccco 60 0 cc~~~~~~ ~c--c cc- c-c- cnc co c-o 0 cr cc- 6 6c crcrccc6occc

6 c-i crc co0crc -cc- c-- ccc~~~Nmlto o 0 C4-t,o 00 cc cc -cc- c-- 0 cr~ ~ ~~~~~~~~~~~~~~~~cl~tcc0

c c cc Crc crc ccc cc c cc 0 cc c-c co in co0 00c- Cc-ccc C.; 0 8881 88 88 8 8 cSc 7ic

.0

S-.' c-c-o 0c-o- 0 cccrccrc' 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~c crcn00n0

0 ci m V) "C co cc\088 0 8 -c-cc ccc c-0 0 0 0 00000 8 088 0

6 6O' 6 6 64 c- cc cr cc6 6 6

0 cc cc crc-c-- c-. crc crce8

ccccc-r-ccc.cc-c cr000 0000 000 0000 00ccc cccccco0crOO 0000 0000 00L) 0 0 0 0 0 0 08 0 cccccrc-cc 0----c--c cc c 0000Cd~~~~~~~~~~~~~~~~~~~~~~-cc--- roc--

1898.] HEYNELL Y ON IMPEDANCE. 189

"' drop " of 12.85 volts on each conductor, or 25.7 volts in the cir-cuit. BAt if 10 amperes are supplied harmonically at a frequencyof 120 , the "'drop" will no longer be 12.85 volts on each wire,,but 19.27, or almost 50 per cent. m-ore, m-Aking the total " drop " inthe loop 38.54 volts. The imnpedanee of the loop is one and one-half times its resistance, or the impedance factor is in this case1.5. The additional drop in the wires is owing to the inductance,of the loop. The magnetic flux fromn the current moves backand forth through this loop at each pulse of the current, and es-tablishes a back pressure or counter E. M. F. that com-pounds withthe ordinary c r drop, rectangularly. No attention is here paid

40-

Curve-Plate= I.

-_ f _ _ 1=~~~~~~I0.9)* / - . _ d-~~~~~~~~~~~d 0.8,/ / . ~~~~~~~~~~~~~~d =0.7'

; - =~~~~~~~~~~~~~~~~~~~~~~~~~0.5,

to the static capacity of the line, which Sis indeed of mninor in-~portauce in overhead wires of only a feew miles inl lengthl, bultwhose influence on the imnpedance factor increases with the:capacity of the line, the frequency, and the E. M. F.

In order to reduce the impedance of our pair of overhead wires.as far as possible, we must bring them close together, so that theloop may hold le s flux, and the counlter F. M. F. fromn the oscilla-tion of this, will be correspondingly lessened. A safe practicaldistance might be ten inches (25.4 ems.) apart. -By bringingthem to this distance thleir impedance wronld be redncedPto 34.7ohmns for the whole loop, and the imnpedance factor from 1.5 to

-190 KiENNELLY ON IMPEDANVCE. [April 18,-

o4-t. 00LO0cc--"d 0 fom0 NO OOCq -4C-0 1-10cc ccNo 00000NVI 0000

o (I

OcNO 4-4 000''-00 incc Oc0 0 c 0cc O O'4-0 N00 -- 80,0 c-N 0c.occc00c.. OcO .04- 00 NO~Co inccc- 04- 0~n0 inc icn in4-0 0 N

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o Mo k U- m 0004100 Oc) 0 ln000 U000000 0 0ch0 cc 00 t- Occcc 00 000C.0ifc.c c c-.1- ic ct-0ol00 ci Ccc 1coc c-ccI r 111~ R11 H0Occ .00bt'. 0 0 cin ~-;9 9 9 ~ 9 0 00 0 i0000 000 '- '4-44 cOOO.0 .00CRI

cc

1o ~ ~ ~~ ~~ 000N 00004-0 00-0~~~

r, 0

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0coc ccoe ,Ccco 0000.. 04-c--0 0.0 0C;0C; 0 '404-0cc '4-OccoocO .0 000c0 00000ON c 0- t-0c 0 0.000 00t-

~~~~~~~~~~ cc ~ ~~ ~ ~ ~ ~~~~~~~~~~~~~~~Nc mm 0~ o~

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t, 0 ,d- t, c0 0.00 -00000in

~~, ccc ~o.coo cc.0c..-ci-cc 00000.0cc~~ cc cc c-c cc 04000 0000 .n ~ UL

occ occcccio kCN U qoo 00co 0 Co tI IDOOCI,%OI00 00 00. t0 00000~

.0Cd 0 0 0~00 00cO 4- N '0 0 00 0 08 c c3

cc cc 00000 00000 00000000000000Hcn 0n 00000 0 0 0

to I 0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~m*0 hNt n

cc~~~~~~~ ~ 0 0.00 0 occcc4-cO o)ci in t0c c0o4-0nc. ~0t- 0-C 0 ~C

00 ccccoocc0000cc~i Occncccoccoin040.0c cN

cc c~~~~.o ~~~00000 00000 00000 ~~~~~~~~cccc.0-4-t '4- ccMt,cc-0 00inN-to0 inOOc

~~~~~ .0cc cc cc~~~~~~~~~~~~~~~~~~~~mHNN im~nt,0 i t

- c-. 40 00(4~~~~~~t0~0,C0, r "MM MO00O ccV~t,0NO coo~N 000n MO 0cc 00~~~~N M I -1D t10 )HN 0t,0 00000oot 0.0 0c0N0 0 cc-oN

00

0 000 0 0 .0i-'4-cc l.0 0co cc006 NO 0 O.-c0 N.00- oc oc .~~ 00000 00000 00000000~~~~~N o00 01 0%000 occccc --'400

od .oo 00 0

4 o0 00.000 4-0 COo co in 00 00 Mo00cc000

088 . N e0

n00 C0 000000,0c --ct00

0U-'6 6.~ o4 cc6 0 ccc c c 06 6

10

C:PI~~ ~ ~ ~c 0 0 4 N00

.0 0 0 00 4- 0000 00 0~~~~~~~c 4- 00 00 m0 . t000 in i0 N

N 8 8 80 8 0 0 0 0 0 0 0 .0 c08 0 0 0 0 0 0 0 0 0

0.0 00 00 00

O 0.~~~~~~665 0 n0 ccN 00 .0_ 00 N . 0 00- to0

,C) m 0~~001 00

6j~~~~~8 0 0 0 0 0 0000

~~~ ~~~-6~~~~0,0 0 00 0cc0

~~ .8 66 6 66 . c~~ 4 Rc~~ ccc 6 6

[0.0.00000 00000~~~000%00 0 n08%3 0

1893.] KENNELL Y O IMPEDANCE. 191

1.35. At this distance of ten inches between wire axes, the iui-pedance of the circuit of No. 4 A. W. G. will oe a little less thaniwith No. 3, A. w. G., at 30 in,, although No. 3 has 26 pe:r cent.more weight and cross-section. The energy expended thermallyin the wires as e2 r, is of coiurse strictly in proportion -to the ohmicresistance, so that in respect to loss of energy, No. 3 would havethe full advantage of its weight, but as far as regards drop in-voltage, with its attendant influence upon the pressure regulatioTn,over the system, No. 3 at 30 in. is almost the exact equlivalent of"No. 4 at 10 in.

60 \ 2-5 Curve-Ple 11.

b.~~~~~~~~~~~~~~~~~~~~~~~~~~~.

Distance between Axes Cms.

Curve-Plat 11.

If the frequency had been 140 - in place of 120 the impe-dance factors of 1.5 and 1.35 would have become 1.9 and 1.45respectively, and the Nos. 4 wires at 10 in. would have had 4 percent. less impedance and drop, than Nos. 3 at 2 ft. 6 in. apart.

It is evident that for alternating current supply eircuits whichcommonly consist of pairs of overhead line wires, the influeenceof their proximity is of practical importance, and grows with thesize of wire. They shouild clearly be placed for lowest impe-dance at the minimum intervening distance consistent with

192 ~~~~~~~~~~KE,NELL Y ON IMPEDANCE. [April 18,

0o- , 000000~o0 0HC0000 0000-000m CY,HOk imo0000000000000 0 004 -00Q4r 00000000i-00l c \00In'-' 0OcO 000(00co 0 000)~- - 0 m000N000 0 0000

CO22TL0 ,, - 00o0 0o00oo00" 00C4~c0000cd~~~~~~~~000 0000C 0--0 000 0 0)0000

0 6686~~~~~~t,0'ri 6666O 8 0

.0 00 c00 00k-mIn C 0 0 o C q N0r o m~ f l" 0LoS 00000000..~~~~~~~m 000'-0o 000 00 oa r t L)t,0Nc

0~~~~~~~~~~~~1C)~ ~ ~ C0000 00 00 0000 0C00 00 0o-00 CO 'oCOOO 0 0000

~~ o ~~~~ 000000 00000000 0000000~~~~~~~~~~~~M t~0000mo 0to-00000'000n0 L)0000000000 00000-00 00000000 0000000 0000000000~~~~~~~~~~0000000 00000E

~~~~~-o66 ~ ~~~0( 000 1Dr C,-) co -C 0 0000d,cq0 00000,I 0 000o~ o0000 001000000"0000000- 00 m00-0 )C, 0 ,00t t ,r O 0N

~~~ 00000~~~~~~~ 00'00-' ,68o..6-8 6666o ,oo oo 6o 666 666\o0

C14

0 00 0000000 '0-00,.6oc688 00000

.~~~ 60~~~~00000 00000 00000~~~~~~~~~~~~~N t\000 0 0000 00000c 000.0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~N 0

10 %c000- o0 0000000l) 00t,00 'C14 C 00 ,t 0 1-0o 0Mmi ,t000000.c) n000 t-0 000 4 IQ ~,t0000-000 868N f) 0Co664 d 1000 0000olt-

C0 t-,

00i000000-00 n'0- oi' 0000 to000 000U- )00i)0000 00000008 000--0 0-0- 0000 00000000 00000000~~~~~~~ccq m00000 000t-0-0'000 0000000o I-00000

00 0 0000000-,0-0000- 000000000 00000)-00000 OOooO 00~~~~~~~~~c,00i 0 0000 oOO 00

0 000n80 000 00 0- 0000", 'ot,t-t,

o ~ ~ ~ ~ ~ ~ 0 0-00 0000 0 0 0 . 0

00 '0 0 000 0 00n-00 00000

00 0 00c00 00 0 000000 --0000 00000006~~. 60"- 0000000000 00000 00000 oOOOO00~~~~~~~~~~~~~~~~~~~~~~14 B000N m

0,4 8 00 0 i00 D0-00 0 )000 N 0000 0 0 00 00 00 0000 000 000 0- 0 00 0 00 -0 ')C0 000 )0000-0000n0o0-00 0 00000 0 No0000.00 00t-

~~. 6~~ ~~0000000000000000000000-~6 I; O' 00in 0 0000000 0

0-0000 0 00 -0-0~~~~~~~~~~~~~~~~~~~~~~~~~~~~1 -I0 C- 0

-I0 C f o 0No n t0 00 00000000066606 )O mcq 0 tm MO mt,000 00oOCmc00"0- 0to 000-00000000-r)" to 00 *l 666~ 6666,

o 0~~ ~~ ~~~~~~~~~~00 0-00 0 0 0 0 00 0 0 00 0 00 00 00 000-

oo ~~~ 8 8 8 8 8 0 0 0 000~~~~iC 0 80 0)00C)

00 000000 0 .~~~~~~~~~~~~~~~~~~~~~~~i I\ 0

~~~o ~~~~~~ 0 000 0 0 0 0 0 0 0 0 0 0 0 00 0~~~~~~~~~~~~~~~~~~~~~~~~~~~N m000oo

8.5*. 00000~~~~~~I 00t 00 C-%O c 0

o1(oo' 0 0 0-, 00 00 0000co 0000

80 0 0 0 CO~~~~~~~1 00 0-00 00 0 0 00 0- 0 0 0 0 00

0 0 00 0 CO~~~~~~~~~~~~~~~~~~~~-, 0~~~~~~~~~~~c 0006co6t

- . 00~~~~~~~~~~~~~H NK 000 0) 00 C000~~~~~ 0 008~~~~~~~~~~~~~~~~~~~0N c

cq 0 ~ ~~ ~ ~ ~ ~ ~ ~~~~ 000

0100 00~~~~~~i 6 '

00- in00-000, 800 00

0 0 0 0 0 00 0 0~~~~~~~~~~~~~~~~~~~~~~~~0 00

1893j KENNELL Y ON IMPEDANCE. 193

safety; on adjacent pins at the samne side of the pole, rather thanon opposite sides. Not only is their impedance thus reduced, buttheir inductive disturbing inlunenice upon parallel telegraph ortelephone circuits is reduced also. A still better means of reduc-ing the impedance is to subdivide the lines, anld employ severalloops of sinall wire rather than one loop of large wire.

Curve sheets I to VIII, corresponding to Tables I to VIII

d 0.u

v = 0.

2.0

.___ ==________ ____ .__ d-0.7

G__.___ _a____ 0.6

E

Distance between Axes Oms.

Curve-Plate III.

are arranged to indicate by direct inspectioin the impedance fac-tors. of such pairs of overhead copper wires. The covering of thewire, if free from iron, of course plays ino part, or at least no

practically appreciable part, in this matter. The tables are basedupon. Matthiessein's standard couductivity, and a temperature of'15Q C. (59Q F.), represe-nting, perhaps the mean annual tempera--ture of wires in the temperate zone of climate. The factors are,

194 KENNELLY O1 'IMPEDANCE. [April 18,

0o0000u0.00*t'InI 00t 100 0000 L000 in000 200000-'4-00,a, ooooo t-.00i

C4Cn4U~,s 06 20006 CC0 0 000 0 000000 000 QQOoo o000 in- r00.100 in 0d00n

C.o- 000.00 ino 000~ tn. Co 000000t00t0 '0-0o 0m0 00000000I 00t

0000 0-0 "0 200

z no 00 L0 00--.00~0N000-00'C 0010-0.00o CON Moo 000 0-0.0000tQ10 22o12 20(200.-t-n qI

0000 2000001 O

00000 ~00

-.0o o-4 .o6 lNN i4466 4 6 64666 6666

00~~0-o .4-0-. 00-00 0-00-0-0-0 0000 -~~~~o o-.iooo 00- 00.00 m0oo 04 M oo

-00d 0-0-,cr q-.-0000 0-C000 00000-C2 00 10.0020. 0000002i 00 0 002UQ 2 t-0-000 0000 '0-C-) -00 000000 % -0 - N~0000 20000\0V)o4 '000.00

0~~~~~~0 0~~0C 000000- D 0 C000 0 0 0 000 08 0 00000-20 0020000C~ 0 0-0000 000000 0

0000o0.20- 1-0-00 00'\0 co00 '0-q0000'O1D ,c20000000 0020 (-0 0000.Coo 0004*00U ('00002)bl=H,- 00-0000 000000200O0-00000000200000NI, N0 OO 40000000Ut 000 00 00020220000 d V k0400000-0- 00000000 < 00000 0.0 0.000

0) ~~~~~~0 020020000 0- 0000 00~~~~N l)tot, r- --o H m 0~.6CC 00 00002 000000-00 0.000004 6o;o666 66666~~~~~~~N NN cnm i6666 66I600000. 0 0 '1 0 N0 00122 00-o000co0I2D0-0.00t000ID2llt 00022ino

Oo2 00-0

0 0CT,0000-0. .00-4D000 0000 2200000000)0020002020 00-00000 000020 000000 000000000 0 0 0002 000000000 00000 00220~~~~14C 2002 00200000I- t 0000000- 0-0-0000

0 00~ ~~~ ~~~~~~co 000r,0 -0 O , *N0 0 c)ot ,,o I nt,0 r) H M-0) 0~~~~~~~ 0~~00- 0 00 00 0 0 00000)mmr)I- t

00

--C 2000 0 00020000o4- ~0 t,0L00200i0000)0000- 20.m0 2 0-)0 000 0 000000

00 2-0000~~~~~88 0 0 0-2 d n 10 ,0 ,0 HHNNm ,0 ,NI-I

Cd 0 0-0 . 00 00i 1~ 0002i'C 0. 0- 6o0 2 0- 000000000'$4 UU 0-o 8888 0 0~~~~~~~~~~~~~~~~~H1- 0 0o 00 N 00- 0- 00 0 0 00000

02 0000 0---- - 0~~~~~~~~~~~~~~ 0 0 0 0 0~~~~~~N Id10 00 0 000

.0

o % 00000 000 00

CO~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_3 66 0 02' oi6 66 6 66O 666'O'OCO . .~~~~~~~~ 2 00 2000. 2 0 0.~~~~~~~~~~~~~~~~~~~C 0. f r,2i

CO0 8 0 H 8 -0- 00 0. 00 000000000.001o,.~~~~ U~~~~ 0 0 0 0 0 2202222.

ci 0 0 0 0~~~~~00 0 0 0 0 0

m ol ~~000 0000

00 0- 108 0. 00 00I- 0 0 0 0 00~~~~~~~~~~ UU g~~~~~~~~~~~~~~~~~~~~8 88 8 8

2 00 00 0 0

200 -0000 00 0000IN 0000000 000002 00000200 0 0-00C00 00 M00002 8 8 88o8 0000 0 6o0220000-m 00000.000o 0000 20.

22000-4OA

1893] KENNELL Y ON IMPEDANCE. 195

strictly speaking only correct at this temperature, but if appliedto the resistance of a wire at its actual temperature, the error isusually sinall. Thus the impedaiice factor for a No. 5 A. W. G.wire at 9.1 in. (23.1 crn) inteiaxial distance, is seen to be 1.311

I0

<N=______ ___ ___== _=

'z3,5 ___ ___.______ / ____ ____ _ __ ____

~d 0.0

_______ _____ _/A____ ________ __ 0.05tf _ H _ __ ~~~~~~~~~~~~~~~~~d- 0.6+- 20 X--F--- --~~~~~~~~~~~~~~~= 0.3--1.5c of 0 a s d= 1.5

1h z_ - - - t- -~~~~~~~~~~~~~~r =.0,2

-I~~~~e tfoot. Bt ifth wire weea

freezing point of water- their resistance per foot at thattn-g.

L w .1 1 1 . .I I . I . X~~~~~~~~~~~~~~0.

050 lOV 150 200 .250

Distance between.Axes Cms.

CDurve-Plate IV.

,at 140 -so that its resistance at sta-ndard conductivity and 15QCD of 0.0)00306.9 olims per foot becomnes a-n imnpeda-nce u-nder these.Conditions of 0.0004024 ohm;s per foot. B3-1t if the -wires were at-the freezin-g poiint of water, their resistance per foot at that teim-

198 KEYVNELLY ON IMAPEDANCE. [April 18,

'IO IC0 -,d000 0000000o 00V)to100000 L 00000.1000c 00 t0.o0000 1 0- I-0 0000o H0000000in0r 01 00101004..HC,N0 0CC OC0,00 410 000oM .00mm'Cto mL'0

00's0

006 66 66 6 66 6666 6 6660800000000 CC

i ,0if n0V 66in 0008 080

~~4 00 00o-~~~~~00 ~ 0, 0000 0 00.00 00 00000 000Irc' 0 10inCC00CC0 000010o.10 00-00000~~~00 \0000000 ,0- 0-00011r0 010000000 C000..t .0 0000-441-41-0t 00 El, .00-

o o 0 000000.. 0o C00 0 000 -00al 0

Q 0001-.000 00 000-41-~~~~~~~~~~~~~~~~~~N t-O :7c~00o0 00000HQ0 in 4 000n 10400000C.)0000000000 00000041- 0010 00-. 0-.0-.oocooo 000000 00041m> moo cli t t-

* 0000 .0 00000 00~~~~~~~~~oe m0~00 c Nt

00000 0000

MID00 0000o t0 000

00 ~~~ ~ ~ ~ ~ ~ ~ ~ ~ 00~ 88

~0 c\0 0 0 -100 0100 8-0 .800 0 0000000,

CO 0.000 000000000 0.0000-0- 00000000.~~~~~~~~~~~000000'o000C 00000100 0 0 000.000 0 0000 00000 00000 00000 00000 00000~~~~~~~~~~~~~~~~NNm 1110000 0 000

- 0.0000.000000400 0000 00~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~N \00

"oo"0-d t Nint,in~0t00 000100.000"o i 0.00c0 I0000000 0 100 00w~~~~~~~~~~~~I mI -a t 00- 0 0 00Ito 040 0000000- 00 000

~~ 0000 0.1 01.~~t~0 ' 4410000n"C00 01 0 0 0,4 00 0 00 0

Q 000000000~~~~~~~~~ ~~00 0000~t 0064c n66V ,O lOO O0~

4.)00~~~~~~~8HN 1-t U)E 0 )0001 E 000000000 0 0000000. 0000 6,- 566C

0 0 000u 00 0 00 00 0 00 00

0000~~~~~~~1 .11 I?

-.4 ooooo IN ; 4 in ~o64..in 4ooi.6A6o,66 1A-)C'M 6o 6 6 66 6

CO ~~~~~ 0 00 000 00 00 00 00 00 00 ~~~~~~~~~~~~~~~~~~~~~~0 00 00 0 00 0 00 0

o 06.~~~ ~~~~C 0~~~~~0000

O Coo 00 0 00 000;0 00 0 0 0 0~~~888000000 0 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~c0000000

000008 00 0 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~o004-~~~~~~~~~~ 00~~~~~~~~~~~~~0 - . --~~~~ ~~~~~~~~~~~~~~~~~~C C

t 008

4~ ~ ~ 0 00

0 0 0 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C

0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r

~~~~~~~ C 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 60...~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

00rnMoo0cC0 000n 00 00000000888 0 080 0 000 0 00 0c 000000 0000000 0080 8000 0.0C-4MI-M~ 0000000In0 000000


perature wouild be 0.000289'7 ohms, an impedance with the samefactor of 0.0003798, while the correct value for temperature 0, C

}_ 1.0 cm

_.5

d =0.8 cm

d 0 Sc.7

~~~d .6

-= 0_._

- .d70.3cm.

...-Lf d 09m.2

B.6~~_ _ ___/_ __ / _ ____ = cm

E

Distance between Axes, Cms. Ba Poatee, sm N.Y.

Curve-Plate F.

would be 0.000389 and the corrected factor 1.344, a discrepancyof about 2.5 per cent. for a ch-ange of temperature amounting to

198 KENNELLL ON IMPEDANCE. [ApriI 18,

00 oo inCotnO C0in 0

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00-4t

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0) .0~~~~~0

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t, 0 -d- t" 00 in N ,O0toO0 IC NI~~~~~~~~~~~~~~~~~~~~~~~eOCoCO COO-t i 0'C

~~~~ 0~~~~~~~0lI :,M0 COCO, i',-OC C- CoM 004'~h0 0~ q0 M t,"O o CO r'i-Co I

~~~ 88o8~~~~~~~ 88ooo 00000M'I I t ~ ~0 0" O "-0 O,OC

~~o CO~~t-~~ Ci 080 000 00 0 00 0 0 000 0 000 000 000 00

0)~~~~~~'0 '-~C;h0''oCo "iOC Co'Li r;6 4

6~COoC t-ococoC6 6cA46 6 66666O'O ...

0 0 000 0 0 0 0 0 00 00 0 00 0 00000

~~o 6~~~o-~~~00000 00000 00000~~~~~N i00 0 00Intl000I ni00000 i 0000o .0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~NNM nt. Nt

0) 0 ~~~ ~~~~~~~Co Co Co

- -0

to I~~~~~~~6 6 - ~ 1) L ~c1 0'0' Co Co~~~~~~~~~~~~~ 0 t

~~~~ ~~~~~~8 0 0Co~~~~~~~~~~~~~~q+~ 8

Ct0

~~ Co Co ~~~~~~~0 O'0 'OCOCO 6 6 66. .66.~~~~~~~~~~~~~~~~~- )

0 0 "I'll.~~000-0C 0 0

~~~ ~ ~ ~ ~~~~ 8 8 8 8 8 3 oootC~~~~~~~~~~~~~~~~~~~~~~~~~I

0)~~~~~~

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0O- O O

60~~~~~~~~~~~~~~~~~~~~~~~~~

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00888M '01

1893.J KENNELLY ON IMPEDANCE.

.___1140-

45.0

=..._ ___ ____ / _ .-__._

___.5 __- ___ ___ __ ___ii-- -_ /-.___iX-~~~~~~~~~~~~__X__

__ f ~~~~~~~~~~~~~~~J (,,/_.13 _ _

1.. , /_ (. ._... .

_IW-/ __-_H.2.5 -/ ---__ -1------ ----- --- 1 --

Ce

2.0~~~~~~~~0 1; 2-_ a C

Bradley PbaWe,Perpendilcular distance between Axes BngavrsA.

Curve-Plate:V.

200 KENNELL ON IMPEDANCE. [April 18,

15Q C. A correction formula, for a greater degree of accuracy,is, however, given in Appendix I.

Tables anid curves I to VI inclusive are of general applicatiorn,dealing with wires from 1 mm. up to I cm. in diameter, and alsoall interaxial distances up to 250 ems., for the successive frequen-cies of 40, 60, 80, 100, 120 and 140 -. Tables and curves VIIand VIII apply more particularly to American practice, dealinrgwith all sizes of A. w. G. wires from No. 000 to No. 11 inclu-sive, and all interaxial distances up to 100 inches for the two fre-queneies 120 and 140 '.Factors for intermediate sizes or fre-quencies can readily be found by interpolation. For instance,suppose that the impedance factor is required for a pair ofNo. 6 A. W. G. wires suspended at an interaxial distance of 40inches at 15" C, and at a simply harmonic frequency of 130Curves VII and VIII give

No. 6 at 140 , 1.34 at 40 ill." " 120 = - 1.26 " "

Taking the miean value for the midwav frequency, we hav-eNo. 6 at 130 - 1.30. Direct calculationi yields in fact 1.300as the factor at 130 .The evidence upon which these tables and curves are based is

nlot merely theoretical. Observations made upon voltage dropson overhead wires in actual alternating current systems have cor-roborated the results. A particular set of observations is alsoadded in Appendix I, together with a simple development of theformula from which the tables have been computed to the fourthsignificant digit.The same tables and carves will of course apply to secondary

circuits or interior wiring, and even if the pairs of wires airetwisted together into double cords, without serious error, the onlvexception being to wires laid in, or close to iron pipes.

Single copper wires suspended overhead at a mean elevation A,with ground return, have an impedance as though that groundreturn were replaced by an insulated copper wire of equal sizeverticallv beneath, and at a distance A below the surface. Antelevation h, thus represents a loop interaxial distance of 2h, andthe imaginary wire below ground is the "image " of the sus-pended wire, so called from the optical analogy with respect tothe surface midway between. Heaviside has pointed out' thatthis resnlt is based upon the assumption that the return current

1. "Reprint of Electrical Papers," vol. i. p. 101.


through the ground spreads unifornmly througih a thini filmn overthe sulrface, and does not penetrate the soiL. As a fact, the cur-rent cannot be confined to this 'superficial layer, and the realequivalenit loop muist be considerably wider than the hypotheticalimage requires. However as the real limits can scarcely be as-signed the image impedance factors may be justly regarded asminiima, while the increase in the factor is usually very slow withmoderate elevations, even for large changes in the interaxial distance, so that the error is nlot so great as might be deemed on firstapprehension. The miiinimum impedance factor for a wire say20 feet above ground, is therefore, its loop impedanace factor at40 feet between axes. The curves indeed could not convenientlybe extended, at their existing scale of construction, to ineludeoverhead wires, but the tables have probably sufficient range forpractical purposes in this respect.We may next examine how far these tabulated impedance fac-

tors are liable to be affected by waiving the restrictions hithertomaintained concerninig thle type of current waves, and the non-ferric nature of the inductances.

Impedalee factors for conductors remote from iron, while in-,lependent of the current strength, depend immediately upon theicurrent wave character. In practice, alternating current circuits"contain motors or transformers, in whiclh iron plays a prominentpart; and owing to the hysteresis in this iron, the current wavesdeviate from sinmple sinusoids, particularly at light loads, even whenthe E. M. F. supplied by the generator is simply harmonic. Ofa11 possible current wave types. however, the simply harmonic orsinusoidal has the lowest impedance factor, and the entries in the-tables are consequenitly minimum values; but there appears to beno limit to the possible augmentation of these factors underappropriate conditions, as, an example will indicate.

Let the current waves be of the saw-tooth type [Fig. 7], therising and falling lines intersecting the zero line z o at equalanigles but in opposite directions. Here the time ocecupied inascent from, or descent to, the zero line, is just one quarterperiod. The impedance factor for such currents is

+ 18 n%

where n is the frequency and the ratio of inductance to resis-r

202 KEN.NELLY1 ON IMPEDAIVCE. [April 18,

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1893.] KENNELL Y ON IMPEDANOEl

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D:istance between Axes, I nohes. &radley 1%Pateo, EZ,g2avre,e N. Y.

Curve-Plate ViI.


tance in any length of conductor, or in other words its timeconstant. The tabulated factors for simple harmonic currentswe know to be

v/ 1- p212,Ift2'

or 1 + 39.48

so that the saw-tooth factors are the greater. If we file downthe points of the teeth as shown in Fig. 8, the current will risefrom zero to a maximum, along the straight line o A in less thanpperiod, and the factor diminishes, until this time of ascent is

reduced to 3 of a period [indicated in Fig. 8], when the factorhlas its miniimum valne for this character of wave, viz.:

I + 43.2

After this, as we shorteni the period of ascent, the factor rises.Neither wave amplitude nor strength of current can of courseaffect this co-nsideration.

When asc. and des. each occ. I period, factor V + 48 n2

"; '' "; "; ;; {;" " = "/ I + 54.5 ;4 1 i c;= \/1 + 62- l+ 411-

avid finally, whein the ascending time is reduced to zero, so thatthe rise is absolutely perpendicular, as shown in Fig. 9, the fac-toi' becoines indefinitely great, and the drop on such a wirewould no longer be finite with a finite current, which is equiva-lent to the statemenit that it is practically impossible to createcurrents of this strictly rectangular type.

Since theory assignls no limits, we are compelled to accept theterms that existing practice may impose. Fig. 10 shows a waveform taken from Professor Ryan's paper on Transformers' readbefore this Institute in January, 1890. It was the wave of pri-mnary current suLpplied to an idle transformer by an alternator

1. TRANSACTIONS, VOl. Vii, P. 1.

1893.] KENAELLY ON IMPEDANCE. 205

whose E. M. F was nlearly sinusoidal. This wave has been ana-lyzed into its harmo-nic components, given in Appendix II. Weknow from Fourier's beautiful theorem, that any periodic, n0on-re-entrant wave, however complex in outline, can be compounndedby, or analyzed inlto, simple sine waves whose frequencies are allsome miultiple (integral and not fractional) of the resultant orcomplex wave frequency. It is evident that any wave, howeverirregular in form, can be constructed out of a sinie wave of thesamne length, with sine ripples of sufficient nuLmber and diminu-tiveness added to or subtracted from this fundanmental sinusoid atsuitable points, but it is wonderful that the process can alwaysbecompleted with sine ripples, each belonging to an endless succes-sion of its own type, and each ripple-chain having a wave lengthsome submultiple of the fundamental. The impedance factor forany com-plex harmonic currenit wave is always determinable fromthe formula of Appendix II, wheni its dissection into componentripples, that is to say its harmnonic analysis, has been determined.In this ilnstance the harmoniies and fundamnental waye that ap-proximately compound into the current wave considered, are indi-cated by the dotted lines of Fig. 10, and the impedance factor is

V 1+ 1.605 2P or .\/ f 5r2

so that a pair of No. 2 A. W. G. wires interaxially distant 30 in.would offer an im pedance factor to this current wave at 140 - of2.708, ani increase of nearly 22 per cent, above the tabular value forsimple sinusoids. It is evident that the drop in voltage oversuch wires, or over any suitable coil of known resistance and non-ferric inductance, would furnish evidence as to whether the cur-rent wave type differs sensibly from the siiiply harmonic. Tllesensitiveness of the test increases with the frequency, and withthe timie constant of the coil. Thus the wave in Fig. 10 whichadds 22 per cent to a normal factor of 2.22, adds only 8 per cent. toa nornal factor of 1.18 at 140 , such as would be furnished bytwo No. 8 A. w. G. wires 66 in. apart.

Professor Ryan's paper shows, however, that this distortion inthe current wave through the primary circuit of the transformer,gradually disappeared as the load was added to the secondarycircuit, and in fact at full load, the current wave was nearly sinu-soidal, with ani impedance factor close to the normal or tabular

206 KENELL Y ONiIMPEDANCE. [April 18,

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1898.] KENNELLY ON IMPEDANCE.5 S_=_ _v_ --- - A.W.G.

5.7=__ _ iic __

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CE 1 A.W .G

<> o o E x, c o o o mO~C>C

Distance between Axes, Inches Bnradley Poateq,

Curve-Plate VIII.

208 KENIVELL Y ON IMPEDANCE. [April 18,

value. This condition is the more fortunate, since in arranginigsupply circuits, it is onlv the full load drop that is usually of con-sequence, and for this it would seei that the tabular impedancefactors are closely applicable, provided that the wave of E. M. F.generated by the alternator can be regarded as sinusoidal.The impedanee factor for an overhead line wire of copper is

the same, whether the current it carries is returned through oneor through many similar wires, provided that in the latter casethe return wires are all equally distant from it. In other words,if with any single outgoing wire as axis, we trace a cylinder inspace, the imlpedance factor of that wire will be the same whetherits return circuit be completed throuigh one or many wires of itsowin size, provided that all such return wires have their axeslocated on the cylindrical surface, and independent of the propor-tions of return currenit that these may individually carry. In theextrer me case the return wires will all be in contact side by side,,and form a continuous shell or cylinder round the outgoinig con-ductor at the centre, whose inductance and consequent im-pedanceremains the same as when all the returns are remnoved save one.It follows, therefore, that the inductance of an insulated copperwire of radius r, concentrically surrounded, (or even, it happens,eccentrically), by a very thin conducting cylindrical sheath of radiusR has the impedance factor of the same wire when forming oneside of a looped pair at interaxial distanceR. The inductanees andimpedance factors of the return conductors in these cases whenseparated or dispersed, are always much reduced, and in thislast example, the inductanice of the exterior colnducting shelldiminishes indefinitely with the thinness of the cylinder, its im-pedanice factor tending coincidently to the limit unity.For the same reasons the tables and curves also apply to three

parallel copper wires carrying triphase sine cuirrents of equaleffective strength, provided that the three wires are equidistant.The distance between any one of the three pairs will then cor-respond to the ordinary loop distance.

All the results thus far considered and tabulated have beenbased upon the assumption that the current density in the con-ductors remains uniform. It is well known that with alternatingcurrents, as the size of the wire and the frequeney increase, thecurrent waves cease to penetrate with full amplitude to the axis,but te-nd to desert the interior for the more superficial layers, thusincreasing the apparent resistance of the wire while diminishing

1893.] KENNELLY ONIMPEDANCE. 209

its inductance. The basis of this phenomenon of incompletepenetration involves the theory of the transmission of electricenergy through space, as well as the relative share of the conductorand its environing dielectiic in this activity; but without ex-ploring fundamental causes, the facts are readily explained bycauses more proximnate and familiar. If we cause miagnetic fluxto oscillate rounrld a straight conductor, an induced alternating E.M. F. will be set up along that conduietor, as in any alternatingtransformer. But an alternating current sent through the wirewould itself set up an oscillating field of this nature about thewire's axis, and the cuLrrent would be opposed by the inducedE. M. F. it thus establishes in the suibstanace of the coinductor.This E. M. F. would be greatest at the axis, for at the surfaceonly the fux sweeping round the wire externally, generates volt-age, while as we descend towards the centre, the flux within thewire adds to the effect, particularly if the wire is of ironi or nickel.At the axis, all the flux in anid beyond the wire unites to generateE. Mi. F.. in oscillation. UTnTder the resultant influence of this,and the impressed voltage at the terminials of the wire, the cur-rent will be strongest where the induced counter E. M. F. isweakest, namely at the exterior surface, and its distribution mustbe such that the " drop " will just sustain a balance between thisinduced and the impressed E. M. F'S. at every point and instant.

This extra virtual resistanee by imperfect penetration is gener-ally negligible in ordinary sizes of copper wires at the frequen-cies employed in practice. Thus with No. 000 A. W. G., the larg-est wire in the tables, this extra resistance is 1.6 per cent. at 140 ,1.2 per cenit. at 120 -, and 0.8 per cent at 100 -; while theimpedance factors, comlbining this with the inductance are af-fected in a still lesser degree. Againi for No. 00 A. W. G., theextra resistance is 1.0 per cent. at 140 , 0.75 per cent. at 120 ,

and 0.5 per cent. at 100 -, so that for nearly all purposes wemay neglect this influence and accept the results embodied in thecurves and tables, wherein perfect penetratioil is assumed.But in iroin wires this virtual extra resistance is known to at-

tain large proportions within practical limnits of size and fre-quency. Figs. 11 and 12 represent a series of observations uponiron wires carrying current waves approximately sinusoidal,'

1. The analysis of the wave of E. M. F,, generated by the alternator in theseand other experiments described, was made by a wiping contact and staticvoltmeter, over 100 subdivisions of the cycle, and the plotted observationsnowhere differed fromi a sinusoid by more than 3%.


at 140 These iron wires were stretched in a long loopupon the testing room floor, the interaxial loop distance being 10ems. The imnpedance factors of the wiires in copper under theseIircimstances would have been 1.42 for No. 5 B. W. G. anid 1.1for No. 9 B. W. G. The impedance factors commnie eed at valuesniot far above these, but increased with the current to a maximumabout ten am-peres for the larger wire, and T.5 amperes with thesmualler, while beyond those currents the factors dimninished.These impedances were comnpared with that of a stout germnansilver wire in the form of a long loop, and with the aid of a differen-tial dynamometer,' each of the two separate dynamometers inthe complete differential instruimxent beinTg conniected by "pressurevires" with either the standard loop of german silver or themeasured loop of iron wire, the connections being occasionallyinterchanged as a check. As the current in the loops varied, theelectrodes on the iron wire loop had to be slhifted, in order to re-store the diferential balance. In this way reliable results could beobtained with 55 metres of stout iron wire, and so long as thetemperature of the iron is not sensibly elevated, the results aredefinite, and retain, within the limits of observation, the samevalues in ascending or descending series of current strengtls.By welding short lengths of the two samaples of wire into circu-lar loops, and wrapping these with wire, their permneability andreluctivity were determined. by ballistic galvanometer accordingto the curves slhown.A similar impedance test of a loop of No. 14 A. W. G. iron

wire (diameter 0.16 cm.) showed that the impedanee did not sen-sibly alter between current strengths of 0.2 anld 2.0 amperes, thelatter being the limit imposed by elevation of temperature. Inthis case with an interaxial distance of 19 cms. and 140 , theobserved factor was 1.03.The influence of imnperfect penetration on the impedance of

iron wires has been calculated by Raleigh and Heaviside on thebasis of a uniform permeability through the wire. In reality theresuilts are still more complex, owing to the variation of the per-meability at different distances from the centre.A number of mneasurements upon impedance in iron wires of

the quality in ordinary use for telegraphic and telephonic use,seem to show that with comparatively feeble currents, the meanpermeability of the iron is about 150. This means that the in-

1. This instrument has been lately fully described in the Electricat ngtneer.

1893.] KENNELL Y ON IMPEDANCE. 211

ductance of an iron wire is 12 millihenrys per mile greater thanthe inductance would be if the wire were of copper. On page10 of Vol. VIII. of the TRANSACTIONS of this Institute, a tableis given of the inductance of suspended single wires of copperwith ground return. The average value is abo-ut 3 millihenrysper inile. If these are increased by 12 mnillihenlrys, the entriesshould correspond to the average indnctances of iron wires undersimilar conditions ('i.e., about 15 m-illihenrys per mnile)> exceptthat for wires of more than 1 mm. radin-s or 2 mms. diameter-say No. 12 A. w. G.-the influence of imperfect penetration com-mences to be seriouis, and impedances calculated from theseindnctances are only reliable for iron wires of No. 12 A. W. G.or smaller.

ContinuLing, Mr. IKennelly added orally:In concltusion, to sum up briefly in inverted order :-First the

inductance of a telephone iron wire is about five times as greatas the inductance of that wire if it were copper. From thatinduietance, the impedance of the wire for varibous telephonicfrequencies can be determnined.

Secondly, the impedance of a larger iron wire, wherein im-perfect current penetration plays a considerable part, is suchthat it inereases to a rnaximum with a certain current, and thendiminishes as that current is increased.

Thirdly, the impedance of copper wires such as are used inthe distribution of electric light and power on alternating cur-rent systems can be determined, if the current waves are knownto be practically sintisoidal, when the distance of these wiresapart, and their sizes are known. Take the drop that would be es-tablished by the current if continuLous, and multiply by the fac-tor as shown in these tables and curves.

And, fourthly, and with most empphasis of all, the paper hasbeen written with the endeavor to point out that the difficultieswhich at present enshro-ud the use and the working theoryof alternating currents are largely fictitious. An alternatingcurrent circuit is certainly a very complex thing; but so isa dynamo, and we can predeterinine dynamios with a degree ofaccuracv sufficient for all practical purposes. We know when amachine is desigyned, within reasonable limits, what the voltagewill be at its terminals when driven at a certain speed with acertain excitation and load, although the exact calculation wouldtranscend all the capabilities we possess at this day. Similarly,

212 KENNELLY ON iMPEDANCE. [April 18,

working theories which are sufficiently good for most practicalpuirposes run tlhrough all the kindred sciences, whereas the exacttheories are beyond present human capabilities; and althoughalternating currents are so difficult when studied accurately andabsolutely, thl:e working theory of alternating cuirrents can bemade as simiple as the workinig theory of continuous currents.I am firmly imnpressed with the belief-a belief which I trust Imay be able to communicate-that the most convincing way ofproving that this difficulty which has hitherto suirrounded tl:ealternating current and its distribution, can be eliminated and re-moved is, by the development of the notion of impedance.

1893.] APPENDIX. 213

APPENDIX I.Determinationi of the inductance of a loop formed by two in-

definitely lonlg parallel copper wires eaclh of radius r ems. fixedat an interaxial distance d in a medium of inductivity p. Letthe substance of the wires have a resistivity p and ind-uetivity 1%.Let the two wires be denoted by the symbols A and D.The inductance L (emli.) of a given length I (ems.) in either of

these wires, say A, will be the total flux through the loop linkedwith uniit currenit (r 1) flowing through that length. Thisflux is partly externial to the wire A and partly within its sub-stance.

Conisidering first the externa] flux, the intensity B at any point

PisB_ 2Tpp

due to uniform current of r units in A where p is the radial dis-tance OP. from the axis 0 of A. In a rectanigle of length I andbreadtb d p drawn in the plane througlh the wire axis, the totalflux will be

F= Bl/dp=2lryI..t0The total flux through the loop from the surface of A to thecentre of D, so far as depends oln A's current is the integralof this expression between the limits p = r and p = d or

F= 2l;,uloge d

and all of this flux encircles and is linked with the current r-mnaking the current flux

2 pIl ' log ed

Within the substance of A, and at radius p, the intensity willbe

B o 2 2_r_wrpS2 p rpIn a similar rectangle of lengtlh I and breadth dop the penetra-ting flux is

and this flux is not linked with al1 the current r, but with thatportion only which is within a cylinder of radius p namely with

7rf2 p2

so that the current flux linkage is2 7 ePo pdop


for the elementary rectangle. The total flux linkage within thewire will be the integral of this expression from

2p = oto p r or 1T2

The total current flux linkage for the wire A is

r1(u0+ 2 ,5 log r).This is the inductance I of the length of I when r = 1 so that

l =zQ(y2±+ 2,p log X-)and the inductance per cm.

i = -n= 10° + 2 fl log 6 ,1 2

iBy symmetry it will be the same for either A or D.For wires in air u is practically unity

and i-o + 2 log d

For iron wire in air ,"0 is practically about 150 for currents ofa few mnilliamperes from a number of mleasurements, so that

F,e _ 5 + 2 log s 1) centimetres.

For copper wire t,u = 1 practically, and

iiCg = (4 + 2 log di{) centitnetres.

The harmonic impedance factor for copper wires isf V + -2

where 22r = the resistance of the wire per linear crn.- P

v +r

This is the formula from whicll the Tables I. to VIII. havebeen computed, p being takeni for 150 C as 1688.6 unit,, c. G. s.

For any simall change d p in p, such as might be due to achange in assumed temperature or condtictivity, the correspond-ing discrepancy introduced into the tubular value of the factorf is

df d(/iz 1)

1893 1 APPENDIX. 215

and the fractional errordf- do /f2-1\7 f

The coefficient

f fL(1-f2)is the coefficient of reduction from a small pereentage variationin the resistance to the corresponlding'percentage variation pro-duced in the impedance factor.Thus for

f 2, 1

and a chanige of 4:% additional resistivity in p will reduce theimpedance factor by 4 X ; or 3%.

PARTICULARS OF THE MEASURED VALUES OF IMPEDANCE FACTORON THREE PARALLEL OVERHEAD COPPER WIRES.

These parallel copper wires each 4,000 feet lonig and No. 6 B.W. G. 0.203" (0.516 cm.) in diameter, suspended on poles at anelevationi of about 18 feet. The mean distance of tlhese wiresfrorn one another is approximately one foot (30 5 ems.)The mean resistance of each wire was 1.03 to and the mean

inductance of each wire when tested in looped pairs 1.264 milli-henrys, the temperature of the air in the shade being 290 C.Insulation of eaeh wire approximately 30,000 Xo to ground.A 1,000-volt alternator of 141.6 whose F. M. F. is prac-tically

sinusoidal, was connected to a transformer reducing to 50 voltsand this secondary pressure through volt and ammeters to succes-sive looped pairs of tlhese overhead wires. The mean impedanceof each wire by volt ampere reading was 1.5513 wo. Reproducingwith the samne instruments the same readinLgs of current andvoltage from a continuous current dynamo, the mean resistancewas 1.029 wo per wire, making the observed impedanlce factorT.47. With the mean ineasured inductance of 1.264 millihenrys

the calculated impedance factor is 1.48 by the formula

V p212

For No. 6 B. W. G. wires, the factor for an interaxial dista-nceof 12 inches is in fact 1.485 b-y interpolation from the curvesand tables.


APPENDIX II.If the periodic current of c amperes (effective) flowing through

a wire at n be analyzed into harmonlic components:-0= C sin_pt+D sin(2pt+02)+Esin(3pt+03)+Fsin(4pt+04)+=C sinpt+ a sin(2pt+%02)+ sin(8 Pt+03)+ r sin(42t+04)+

The impedance factor for the wire -will be

I= (w±i?4i) -V7 J2 1+ ~ 22±P2[2r

or if S = -Jr2

=/}(+J) &2 (t+ 4$)32(j+ 9 J) -+ ( + 1(i J) +~I ± 2 + d2 + r2 +

The primary c-urrent wave observed by Messrs. Ryan andMerritt as supplied to an unloaded tranisformner is approximatelycompounded as follows. See also p. 454 Fleming's "Trans-former," vol. ii.

i = 0.1963 sin (pt - 49°. 20') + 0.04827 sin (3 pt - 760 50')+ 0.01,627 sin (5 pt- 90Q).

Here = 0.04827 _ 0.2463, and 8 = 0.01627 - 0.08156.0.1963 - '0.1963

/ (i+-j)-+0.06066(1+-j12) +0.006652 (1+25-Pi)1 + 0.06066 + 0.006652

=Vl +1t605nPo2

=Vli + 63.352

1893.] DISCUSSION. 217

DISCUSSION.THE CHAIRMAN:-I think every one here will agree with me

that the Institute is to be congratulated upon this magnificenitpaper of Mr. Kennelly's. It is indicative of a very large amountof painstaking care. There are quite a large number of gentle-men here in the meeting to-night who have made considerablestudy of this subject, and the Institute will be very glad to hearfrom them. Betore, however, asking for remarks, the Chairwould like to refer to one point in Mr. Keinnelly's paper that hemade inquiry about in Londou during the last year. Mr. Ken-nelly referred to the "well-known Ferranti effect." As I under-stand, shortly after the station started-the sub-station, I think itis in Grosvenor Gallery, some miles dist ant fromn the main station,was supplied with electricity from the main station, and whentests were made, it was found, to the surprise of a great manypeople, that the potential, instead of being lower at that point,was higher than it was at the original source.

Last year while in London, I visited the Ferranti station atDeptford a number of times and inquired particularly of Mr.d'Alton, the mnanager and electrician of the company, whetherthis so-called Ferranti effect existed upon the Ferranti mains,and whether it was due to an electrostatic effect or not. He in-formed me that it did -not exist, and that many prominenat scien-tific men had rushed into print to explain tlheoretically the causesof this effect; that a number of papers had been written aboutit, but that it was :found afterwards to be an effect whieh did notexist. I asked if lie could slhow me the difference of potentialbetween the generating station and the sub-station, and he tookme to the switchboar(d and stated that the difference of potentialwas several volts lower at the sub-station than at the generatingstation. Periodically a signal was sent from the latter to theformer, indicating that the potential had fallen below normal." If you will stand by the instrument," he said, "you will seethat the difference of potential is exactly what the drop is calcu-lated to be between the sub-station and the main-station, and it ishigher at the original generating source thani at the other. Ac-companying me at the time was Mlr. C. H. W. 1i3iggs, the editorof the Electrical Enqineer of London. Mr. Biggs and anothereditor of a paper in London stated to me that this Ferranti effectdid not exist, and that a great deal had been written about it thatAShould not have been written. Mr. IBiggs said that at the tinmethis appeared, hie stated editorially that it was based upon wrongpremises. This is all that I can say personally about it, but Idoubt not that Mr. Keinnelly can give further information onthe subject and I should be pleased to hear from hi'm upoII the'subject.MR. DOUGLASs BURNETT:-Mr. Chairman, let us for a moment

,consider a little more carefully two of Mr. Kennelly's equations.

218 KENVELLY ON IMPEDANCE. [April 18.

First, the on,e on p. 178. Let us put it equal to G; i.e.,eC =ee_p k-w2 keD(k )

and regard G and it as the variables. It is evident that the curvegis a straight line passing tllrough the origin. In other words,,for zero frequency, we get zero cuirrent through the condenser,and thereafter current is directly proportional to frequency.For infinite frequency, infinite curre-nt passes, at any finite vol-tage e.

Second, observe the formula of p. 179, for impedance. Wemay put it equal to I, and hence

(1)2 Vr- +(2--T)2 * (II)

This may be transform-ed into

n~~~~~VeT+/,/2s (III.)27 k+_

We see directly that:(a) For the same frequency, current is directly proportional to

E. M. iFx, which was to be expected; that(b) For the same m.M. F., resistance, and capacity, current is a

complicated funetion of frequency; and that(e) For the same current, necessary capacity is inversely pro-

portional to frequency. Substituiting, as in the paper,1= 000; r -500; k= S X O-6;

in either II. or III., we get the curve of frequencies and cur-rents. [See Fig. 13, p. 232.] For direct currenits,

e_1000nA 0 & co. For =rn =z e 2.

r .500For frequencies above 200, e lies betweeni 1.906 and 2.0. Thislast result is the same as if the condenser were quite short-cir-cuited, and onlv the resistance existed in circuit.

Equations II. and TII. probably apply to (1) the leakage cur-rent of a condenser, and to (2) an electrolytic cell used as a con-denser, especially when current-density on electrodes is smallerthan that value at which decomposition takes place.

If we consider as the best in practice, a diacritical point on thefrequency-current curve (see Fig. 13), as with H - B cuirves, atwhich the tangent to the curve makes equial angles with bothaxes, we should have (from III.)

don (IV.)

189~.l DISC USSIONY. 219

Fromn whieh we find that= 22wk(S- r2r2). (YV)

is the best conidition. That is, in designing apparatus for a cir-cutit consisting of condenser and resistance in series, such a fre-quency shouild be chosen as makes the different quantities lhavethe relation given by V.

It is to be noticed that the laws given by Mr. Kennelly arestrictly applicable to Wlheatstone's Bridge.While on the relations between frequency and other quantities,

one effect may be worth mentioning. We consider, with Flem-ing,' a circuit of resistance R and induLetance it, carrying currentw, in parallel witlh a simnilar one of resistance S and inductanceN, carrying currenit y; then when S IL > PR 1, the current yleads alhead of the main current by an anigle so, determined by

tan~-(IS-R A)pRe(-R+ S)±LI,(L , +N)2

ilere for botlh p () anid p =- c, Sc becomes 0. That is, forcontinuous and for inifinitely rapid currents, tlhere is no lead.UJsing the ordiniary rule of calculus for determining the maxi-mum, we finid that for

n= 1 /pR) (VI.)2 i- l/ L (:L + X)

the function is a maxiinum. Or,

tan _ S - RNN (VII)2 4/RI (P+S)(L%+ )

Therefore, for a certain determinable frequency, dependent onthe resistances and inductances, the lead is a maximuin.

These points are mentioned as showing the importance of re-membering that in discussions like Mr. Kennelly's, we are dealingwith a factor, oftenl subordinated, but which sometimes exertsgreat influence-namely, frequency.MR. T. D. LoCKWOOD :--I presuime tlat each memtiber present

had been profoundly inter sted in Mr. Keninelly's paper, and thateaclh one of us catn also say, and say it sincerely, that this eveningwe have added soniething to our stock of knowledge-not somuch, perhaps, that we can all assimilate at once everything wehave iheard, because tlle paper, tlhough beautifully plain, anidmade still more plain by the admirable extemporaneous exposi-tion whichl accompaniied it, is still far too copious anid exhaustiveto be readily digested at one sitting; and this f conceive, Mr.-Chairmran, is the real value of the paper, that we have had a.store

1. Fleming; "Alternate Current Transformer," vol. i, p. 133.

220 KEYNELL Y 0N IMPEDANCE. [April 18,

of knowledge, as it were, brought right to us, and so placed that itcan be embodied in our proceedings in order that at any time wemay refresh our nmemory and replenish our mnitnds by going to it,as we now go to a text-book or an encyclopedia.

It is now, I think, three years since at the Boston meeting ofthis Institute,' I pointed out that impedances were capable of, andhad already -been employed in mnany useful applications to elee-tric work, although we did not at that time ofteni make use of theword "' impedalee." It seemns to me that one of the great beau-ties of practical electrical work is that functions Matgnitudes, andapparently disadvantageous phenomena, which seem at first to beprejudicial to good work, can often be utilized anid made subser-vient to good work in other directions. I may inistance thepolarization, which to the early battery inventors and construietorswas such an obstacle, frequently opposingr their best attenmpts atsuccess; yet at the present time the phetnomena of polarizationhaving been more fully worked out, we find that it can be mnadereally advantageous, and that by prosecuting researches in suclhplhenomena, the storage battery has been reaclhed; so, taking tyown special line of work, it was found in the yery early years oftelephony that an electro-magnet in a telephonic circuit was avery strong bar to the passage of the telephonic impulses; somuch so that one of our members, Mr. F. W. Jones, in devisinga remedy for it, said that electro-magnets were opaque to rhyth-mical or rapidly alternating currents B3ut with the greater ad-va-nce of the science in its many induistrial applications, and ourown imiproved knowledge and experience, it is found that impe-dances cani actually be made useful, in that two wires can be madeuse of to transmit three rnessages at the same time, using the twowires as the direct and return wires of the metallic telephone cir-cuit; while on the Van Rysselberghe plan, each one of the twowires composinDg that circuit may be severally used for the trans-mission ot telegraphic messages; and this simply by placing im-pedances, made by properly winiding covered wire around theiron, anid interposing them between the telephonic cir'cuit and thetelegraph circuit proper. Such contrivances are much older how-ever in telegraphy. I believe Mr. Cromwell Fleetwood Varley(now gone from uls but whom England and America delighted tohonor,) used imnpedances in 1870-he called them echocyimles-fora similar purpose, that is for workirng Morse telegraphy and har-monie telegraphy on one and the same wire. In the matter ofelectric lighting we find that Professor John Hopkinson devisedimpedances by winding wires, the amount of which could bemade adjustable, on closed magnetic circuit laminated iron cores,in order that arc lights might be regulated in multiple arc; and Ineed scarcely call the attention of any one here to the wonderfulapplication in the autoinatic regulation of lighting by transform-

1. " The Industrial Utilization of the Counter Electromotive Force of Self-Induction-` TIRANSACTIONS, vol. vii., p. 226.

1893.] DISCUSSION. 221

ers, as suggested, I believe, by Mr. Kennedy, but worked out byhis successors, Messrs. Ziperniowski, Deri and Bl3athy.

I have mentioned that "'impedance" is an extremnely modernterm, it having beeni devised and given to us by Mr. OlivTerHeaviside, within the last seven years; it is, however, a verygraphic and highly suitable term, and I for one am mnuch obligedto Mr. Oliver Heaviside for this favor, and others of the samiekind.

Mr. Chairman, I have heard or read, I cannot tell which, at thepresent time, that the late Lord Derby in one of his addresses tostudents, defined knowledge as that whicll a man has so securedthat lie can produce it at any mnoment from his own head. Re-ferring once more to the remarks I first made, I would like to saythat 1 agree with Mr. John T. Sprague entirely, in his view thatwhile that definition is no doubt a first class definition whencramming for an examination, it is not such a good definition whenapplied to the man of science who inust nse his science to earnhis daily bread; and that real knowledge, the knowledge whichthe practical man carries in hiis head, is not perhaps the most val-uable part of his knowledge. Wlhat really constitutes the bestpart of his outfit, is the knowing where to find what he wants.when he wants it; and it seemns to me that the paper we havehad this evening will be a great aid to many of us in that kind ofknowledge. Hereafter when we want to know anything aboutimpedance, so far at least as it has up to the present time been in-vestigated, we shall come to Mr. Kennelly's Paper.The knowledge whieh we can carry in our heads is, it seems to

mie, very muclh like money we carry in our poekets-very usefulfor making small change at the moment; but not so useful tocarry on business with. But the knowledge which we can gethold of when we need it, when we are asked a question about it,or when a question comes up in1 our business-the kniowledgethat we can have recourse to, and find out what we want-suchknowledge is more like money that we have irn our bank accounts,that is to say, if we have bank accounts, and any money in themn.DR. PUPIN:-Mr. Chairman, I intended to make several remarks

on the paper, but since it is so late I feel that I must cut themdown and be very brief.

In the first place, it strikes mie that Mr. Ken nelly has done verygood service to practical electrical engineers in making tables towhich the electrical engineer can always refer, just as he refersto tables for his resistances, and finds out w:hat will be the impe-dance of such and such a circuit. It is a very useful thing and itis done in the way in which only Mr. Kennelly can do it. He iswell knowin for his neatness, and for his patience in working outsuch problems, so that any eulogistic remarks from me would besuperfluous.The other point which struck me as a very good point indeed,

is Mr. Kennelly's remark regarding the simplicity of the alterna-

222 KENNELLY ON IMPEDAJNCE. [April 18,

ting current theory. I pointed out in a paper read three yearsa,o at the Boston mneeting of this Institute,' that the alternatingcurrent theorv is just as simple as the continuious current theory ,it is based on one single law, nam-ely, Ohm's law. But, of course;we h-ave to limit ourselves to instantaneous values of things, andjtist as we say in a continuous current circuit, that the imipressedelectromotive force plus the total drop is equal to zero, so we cansay in the alternating current circuit that the sum of all the elec-tromotive forces taken with their proper sign plus the total dropis equial to zero. We have therefore one and the same law forboth kinds of current. That gives us our fundamental equationor fundamental relation between the quantities wllich are involved.But since that relation is true for infinitely short intervals of time,its symbolical expression gives us what is called in mathematicsa differential equation. The integral relations which will holdtrue for any interval of time are obtained by the process ofintegration. Now in finding the integral relation between thecurrent and the other quantities which define the circuit, likeself-indtuction, capacity, resistanice, etc., we find that if we wantto obtaini the current, we have to divide the impressed E. M. F.,not by the resistance alone, but by the resistance plus somethingelse, and that something else is comnposed with the resistance, justthe same way as two forces, niamely by the parallelogramn of for-ces-two forces wich are at rigllt angles to each other. We havetherefore the simple rule that the resistance can be composedwith the inductance speed, as Mr. Kennelly calls it, justthe same as one force can be composed with anotlher whichis at right angles to it. In other words the parallelogram offorces is applicable to this case. If there is a condenser, thereis capacity in the circuit, and in finding the integral rela-tion between the current and the time, we find that thebehavior of the condenser can be represented graphically in avery simple way by introducing inlto the parallelogram of forcesjust mentioned, a third component equal to the capacity speed,this third component to be always subtracted from the compo-nent representing inductance speed.

I call this graphic method of representing impedance the appli-cation of the parallelogram of forces to the alternating current cir-cuits. Mr. Kennelly prefers to speak of vector quantities andtlhe addition of vectors. But, of couirse, these graphical methodsare incidental results of considerable practical importance. Theprimary law is Ohm's law in its generalized formn, and its applica-bility to variable currents, variable but stationary. If the flow isnot stationary, then Ohm's law even in this generalized formn willbe applicable to infinitely short lengths only of linear conductorsas, for instance, in the case of very long wires and high fre-quency.

1 4"Practical Aspects of the Alternating Current Theory TRANSACTIONSOvol. vi. p. 204, 1890.

1893.] DIS,CUSSION. 223

The next point whichl I wish to discuss very briefly is the soailed Ferranti effect. I am, however, somewlhat timid abouit it

after the remarks of our Chairmian, saying, that a great manypeople lhad rushed into print abouit this Ferranti effect.THE CHAIRMAN:-It was inerely the statemnent that was given

to me.Dn. PUPIN:-Well, the statemnent then that was given to our

Chairman makes me hesitate. I also ruished into print aboutsomething like the Ferranti effect. I published a paper in theAmerican Journal of Sciencel and thie next paper is now in prinitabout this very thing. The Ferranti effect is a real, existing ef-fect and can be made very strong indeed. Most people have noidea how stronig this effect can be mnade. It is very simple. TheFerranti effect is only a special case of the more general effectwhich I call the resonance. It couald have been foreseen twenty-five years aguo from Maxwell's equiationis deduced at aboutthat period. Maxwell, I think, was the i'rst to show the effectof introducinig a condeniser capacity into an alternating current,ircuit, and it is very interesting to observe this circumstance.Maxwell was spendinig an evening with Sir William Grove whowas then engaged in experiments on vacuum tube discharges. Heused an induction coil for this purpose, and found that if heput a condenser in parallel with the primnary circulit of his induc-tion coil, that he could get very much larger sparks, which meant,of course, that he got a very n uch larger current through his pri-mary coil, an alternating current genierator being used to feed theprimary. He could not see why. Maxwell, at that time, was ayoung man. That was about 1865, if I do not err. Grove knewthat Maxwell was a splendid mathematician, and that hle also hadmastered the science of electricity as very few men had, espec-ially the theoretical part of it, and so he thought he would askthis young man how it was possible to obtain such powerful cur-rents in the primary circuiit by adding a condenser. Maxwellwho had not had very much experience in experimental electric-ity at that time, was at a loss. But he spent that night in work-ing over his -problem, and the next morning he wrote a letter toSir William Grove explaining the whole theory of the condenserin multiple connlection with a coil, It is wonderful what a gen-ius can do in one night! IHe pointed out the exact relations be-tween the coildenser, the self-induction and the frequency whichwould give the largest current, and lie was the first to do this, sofar as I know.We must always remember that as soon as we add capacity to

a circuit we are giving it elasticity. Without capacity the circuithas no elasticity. Take a stiff wire and suspend a weight, say acylindrical bar, by it. Suppose that this wire has no elasticity.In order to twist this weight, in order to deflect it from its posi-

1 April, 1893,i

224 KENNELLY ON IMPEDANCE. [April 18

tion of equilibrium, we lhave to use a force that will twist theweight out of shape. The momnent of inertia of the weiglht, whentwisted around, is being clhanged. That is just what happenis inan alternating curreint circuit which has no appreciable capacity.The electromotive force working on snlch a circuit producesforced vibrations. But suppose that the stiff wire has elasticity.Then if vou give an impuilse to the weight, it will swing, and theperiod of the swing will depend on the moment of inertia of ttheweight, and on the elasticity of the wire and on tnothing else, pro-vided of couirse that the frictional resistances are not too larg(.We can make that weight swing rapidly by mrakinig the momnentof inertia sinall or the elasticity large, one of the two, or- both.Now the coefficienit of self-inductioni in the eirecuit, corresponds tothe moment of inertia of the swinging weight, and thecapacity in the circuit corresponds to the elasticity of thewire, and just as the elasticity of the wire ai d the mo-ment of inertia of the weighit detelmine th)e period of thecircuit, so the capacity in the circuit, and the self-induction de-terinine thle electrical period of the circuit. That is to say if youcreate a disturbanice in the circuit, say by pulling quickly a per-manient magnet away from the coil, youL will start an electricaldisturbance there. anid the electricity will swing back and forth,just as a penduilum swings back and forth, the period of thatswing depending on the coefficient of self-induction and the ca-pacity of the circuit. The electricity in the circuit will swingback and forth till it is reduced to rest by the ohmic resistance.If you now apply a periodically varying imipulse-not a singleimpuLlse, but a periodically varying impulse to the torsional pen-dulum just mentioned, you will make it oscillate, but theoscillation will be forced, if the period of the aetivg forceis different from the niatural period of the pendulum. But if thetwo periods are exactly the same, then the oscillation of the pen-dulum is a free oscillation, anid the force and pendulumn are inresonanice. Now what is the effect of free oscillation l The effectof free oseillationi is to reach a larger swing thani the forced oscil-lation under the action of a force of the same mean intensity..The swing will continually increase, until the work done againstthe frictional resistances duri-ng one half of the swing is exactlyequal to the work which the moving force does in that time. If,,therefore, the resistance is very small, you see that the swing willincrease indefinitely. Buit what happens to the wire? Resonantswinging means simply this:-The kinetic energy of the swing-ing weight is periodically reduced to zero, that is, transformedentirely into the potential etnergy of the elastic forces of the wireanid vice versa; so that the larger the swing, the larger will bethe maximum elastic force with which the wire reacts; so that the-smaller the frictional resistances the laroer the elastic reactioni.But we must remember that the elastic force in the wirecorresponds to our potential difference in the condenser, so that

1893.] DISC USSIO0N 225

by acting upon the circuit by means of ain electromotive forcewhose period is exactly the same as the natural period of the cir-cuit, we produce an electrical flow which continually increasesuntil it has obtained a maximum vallue and at that time, of course,the potential difference in the condenser may be many tiineshigher than the voltage of the impressed electromotive force.I lhave produiced by very simple means a rise of potential from 60volts to 900 volts just that way, and from 80 volts to nearly 1,200volts by pnitting a condenser in series with a coil, and a properadjuistment of the two. I took the secondary of a transformerand placed with it a large coil, large self-induction, in series, andthen, in series with this, a condeniser; and then I adjusted mycapacity to the self-induction in such a way that I brouLglht theperiod of the circuit in resonan-ce with the frequency of my alter-nator, and thle consequence Avas, that the difference of potential(indicated by a Thomson electrostatic voltineter) went from 80volts to 1,200 volts.

If you create too much rise of potential youn condenser goes.ain working at that problem yet, and I expect to be able verysoon in fact I have alreadv proimised, to read a paper before theInstitute on this very thing. I have no donibt that it is quitepossible to transform 50 or 60 volts into 10,000 or 15,000 or anynumber of volts in that way.On page 178 of the paper it is mentioned tlhiat the reason for

the non-equality of the voltage on the series of the two impe-danices with the arithmetical sum of the voltages imieasured on eachimpedance in turn, is due to tlhe fact tlhat the currenits in the twocoils are usually out of step. I should like to point out that thisis misleading. The curreuit must have at aniy moment the samiephase at every poin:t of an alternating culrrent circuit, otherwisethere would be an accumulation or absorption of electricity at thepoints wlhere a clhange of phase existed. There is evidently ala ps8s linguae in the paragraph referred to, and I have no doubtthat Mr. Kennelly will easily change the paragraph.MR. KENNELLY:-Dr. Pulpin is right conce ruiing the paragraph

on page 178, which by an oversight is misleading. The sentenceshouild read "'due to the fact that 'otherwise the currents inand i2 while of equal strength develop in these cou iter E. M.

Fs that are out of step."D . GEYER:-Mr. I eunelly has in those plates giveni us very

instructive informatioin tendinLg to show that in t:he alternatingsystem of distribution tllere is a somewhat greater drop than inthe conltinuous cuLrrent system, and he has also called attentioni tottle interesting fact that on account of the distortion of the sinu-soidal wave by the transfor-mer under light load, this extra dropis to some exteimt inereased, so that the distribution is still less uni-form than it would be withoutt this action of tihe transformer. Ibelieve all this applies to the primary part of the circuit. I should


like to consider for a mnoment the secondary part of the eircuit-say the house wiring. I do not at this momrrent recollect whetherthere is a corresponding distortion of the sinusoidal wave in thesecondary part of the circuit, and I should like to ask MAr. Ken-nelly if there is, or if there is not, a corresponding tendencythere to increase the extra drop.MR. KENNELLY :--As Dr. Geyer hlas remarked, the impe-

dance factor increases above the tabular values when the cur-rent waves are not simply sinusoids, and in such cases the drop inthe primary feeders is further augmeented. But if the alterna-tor supplying these feeders generates a wave of E. M. F. that issinusoidal, the transformer mYlust also generate E. M. F'S thatare very nearly -sinusoidal, both in its primary and secondarycoils, even although the primary current wave may be severelydistorted under the iiifluence of hysteresis in the core. Conse-quently, with only incandescent lamps, anid no ferric indulc-ta-nces, in the secondary circuit, the seeondary current waves willbe very nearly siniusoidal, making the impedance factors of thesecondary conductors practically tabuLlar.TnE CHAIRAN:-I want to say just a word in referenice to

Dr. Pupin's remark. The remarks that I made upon the Fer-ranti effect were based entirely upon the statements made to meby parties on the other side of the water, and referred particular-ly to the effect claimed to be produced upon the Ferranti cable,and not alone the peculiarity of a difference of potential whichmight be caused by electrostatic phenomena, and I slhould liketo ask Mr. Kennelly's opinion as to the reliability of the reportsrespecting the Ferranti effect as produced upon his undergroundcable in London.

MR. KENNELLY :-Not having had the pleasure of being pres-ent at the measurements or observations that were made on tlheFeriranti cable, I am unable to give aniy direct eviden ,e whatever,but having carefully read Dr. Fleming's very interesting paper,in which a large number of experimenits were described uponthe pressure as generated and suipplied, I think there is no es-cape from the conelusion that undier certain conditions of loadand transmission, an effect was produced which bears the nameof the Ferranti effect; buit that possibly under conditions whiclwere described by the Chairman that effect did not exist. It isentirely, of couirse, a matter of the resonance in the circuit, asDr. Pupin has described it, antd if you do iot have the right load,that effect may disappear. So it is quite easy to unlderstand thatthe cable, under certain conditions of load or transmissioni, mightbe resoInant and might exalt the pressure ; while under normalload this effect might cease to exist.Mr, C. S. BR&DLEY:-M1r. Chairman, I think the paper is en-

tirely beyond mny scope. I should like to thoroughly uni3erstandit. It has given me a great mrany points and it is very clear in-

1893.1 COMM UVICAT1ONS6 27

deed. I am very glad to have heard it, and I tlilnik it will proveof great value as a reference. I have not digested it yet, to bor-row Mr. Lockwood's phirase, and therefore I am not prepared tosay very muclh about it.MR. LoCKWOOD:-As no one else seems inclined to discuss the

paper, I should like to move that the Institute present to Mr.Kenenelly a very hearty and cordial vote of thanks, for the intel-lectual treat which he has provided for us.MR. SPRAGUE :-I shiould like to second the imotion of Mr.

Lockwood. I am prevented by an impedance in my own h-eadfrom talking any part in the discussion. But I want to thank Mr.Kennelly for placing on the record, where it can be easily ob-tained, so muclh solid information, so clearly expressed, about asubject that is so little understood. While great kniowledge isalways of value if carried in one's own head; if it is placed whereone can get at it with little trouble, anid so that wheni gotten itcan be easily digested, there is perhaps more benefit derivedby the general run of electrical engineers than if they attemptto acquire too much personally. So I heartily second the mo-tion that is made that a vote of thianks be tenidered to Mr.Kennelly for his most initerestinig and valuable paper.

[The motion was cairied.]Adjourned.

[COMMUNICATED AFTER ADJOURNMENT BY MR. CHARLES P.STEIN METZ.]

I have read Mr. Kennelly's valuable paper on "1Impedaice"with the greatest interest, and am only sorry that I was not ableto be present at its presenitation.One statement, 1however, I would like to emlphasize somewhat

more strongly, since in the paper it is enclosed between so manvremarks of the highest practical value as to be liable to escapedue notice, viz.: that"Any eireuit whatever, consisting of a combilnation of resist-

ances, non-ferric inductances and capaeities, carryinig harmonicallyalternating currents, may be treated by the rules of unvaryingcurrents, if the impedances are expressed by complex nuimbers:

a + bj =r (Cos0 +j sin >) t

the algebraical operations being tlhen performed according to tllelaws controlling complex quantities,"

It is well known that the points of a plane can be represenltedby complex quantities in their rectangular representation

a +dV-1

(*) Where denot;es 1

228 KEIVNEIL Y ON I PEDA CE. [Aprll 18,

or their polar representationi

r (cos so +j sin f),and use has been made hereof repeatedly in the mathematicaltreatment of vector quantities. It is, however, the first instancehere, so far as I know, that attention is drawn by Mr. Kennellyto the correspondence between the electrical ternm " impedance"and the complex numbers.The imuportance hereof lies in the following :-The analysis

of the counplex plane is very well worked out, hence by reducingthe electrical problems to the analysis of complex quantities theyare brought within the scope of a kn-iown and well understoodscience.

Let tis consider an instan-ce hereof whichl will bring us toanother poinit I intend to dwell upon.

In the alterinating current line mentioned on page 187, of Mr.Kennelly's paper, the impedance of the loop can be expressed bythe complex qurantity,

1l 2.57 + 2.87,j = 3.854 (cos 48S +) sini 480),

orj 1.2835 - 1.135)j 1.927 (cos 48° + j sin 48°) per wire,

that iueans, at the liine current C = 10 amperes, between theends of eaelh line a difference of potential will exist of

_ 19.27 volts.2

Let, now, the impedance of the generator be

lo - 1. + 10)j 10.11 (cos 81 + j sin 81fr),then, if the cons1nmer's circuit has an impedance

12 = 23.0 + 27.8j = 37.4 (cos 480 +j sin 48)(containing for instance, miiotors, etc.)then the total impedance of the circuit is

I=lIo +I14 29.07 -+ 40.67j = 50 (cos 54.5'+ sill 54.5Q)In this case a generator potential of F = 500 volts will send

a current of

C = 10 amperes

through the eireinit.The difference of potential at the receiver end of the linie

will beE1 C;= 374 volts.

1893.] COAMUNWCA tONL. 229

At the generator end of the line

E0 (-C(1 + I2) = 412.5 volts,and the drop of potential in the line,

E0- l = 412.54 -374 38.54 volts,

or 19.27 volts per line, 2 I.e., equal to the difference of

potential between the ends of the line, or the true obmic drop,times the im-pedance factor.

if, however, the receiving circuit hlas an impedanceI' = 442

(incandesce-nt lamp load)>the total imnpedance of the circuit is

J_- 48.27 + 12.87j 50 (cos 150 +j sin 15Q).At the generator potential of 500 volts, 10 amperes will flow

tlhrougll thie cirecuit again, bnt the difference of potential at thereceiver end of the line is

E1 = C 1 = 44,2 volts.At thie generator end,

Eo = 0 (1 + 2)= 468.6 volts,sinice

11 +I 46 77 + 2.87)j 46.86 (cos 40 +1j sin 40)so that the drop of potential in the line is 468.6 - 442 26.6ohms, or 13.3 volts per line. That is conisiderably less than thedifference of potential between ends of the line, which still is19.27 volts, so that in this case of the non-inductive, or lamp load,in spite of the impedance factor 1.5 of the line, the drop of po-tential of the line is practically only the true resistance drop, andthe inductance of the line does not count at all.

Still mnore remarkable are the conditions if the receiver circuithas an impedan:e, of a form similar to

12 1 - 60 ) - 61.95 (cos 760-) sin 760),as is the case if the line is feeding into a condenser of the capacityIV= 19 mf. or running a syichronous motor (which under cer-tain conditions of load and excitation acts like a condenser oflarge capacity).

In this case the total impeda-n e of the line is19.0 - 46.22) = 50 (cos 67.7Q-j sin 67.70).

Hlere again 500 volts genierator E. M. F. ill establish 10 amperesof current in the circuit.

30 tENNELLY ON IMPEDANCE. [April 1,

But the difference of potential at the receiver end of the line is

E1 C I, -619.5 volts.At the generator end,

F = C (I, + I,) _98.7 voltsthat is; the drop of potential in the line will be

E0- E, - 20.80 volts,or - 10.4 volts per linae;

that means that, while a continuous current will experience aloss of potential of 12.85 volts per line wire, anid from tlle irnt-pedance of the linie a differencle of potenitial of 19.27 volts perline wire is calculated, we find in this particular case a rise ofpotential of 10.4 volts per line wire, so that the difference ofpotential is rising along the line instead of deereasing, and thatby not less than 20.8 volts.

in this case at an E. M. F. of 500 volts produced in the gene-rator, an E. M. F. of 598.7 volts will appear at the generator termi-nals, and 619.5 at the receiver terminals.'The conclusion thlat we derive herefrom. is, that it is olot per-

m-nissible to calculate the drop of potenitial in an alternating cir-cuit by mnultiplying the resistance dirop by the iinpedance factor.The difference of potential betweenr the ends of the line will in-deed be equal to the current times ihupedance. The losses ofpotential in the line, however, will usually be less than the differ-ence of potential between the ends of the line, and may even benegative; that is, the potential inay rise in the line.

This is due to the difference of )hase between the line impe-dance and the impedanices of the other part of the circuit, asexplained in the paper. I considered it advisable, however, todwell upon this more particularly, since the mistake is madefrequently, to calculate the drop of potential in an alternatingcurrent linle from resistance, impedance factor and current. Inreality the drop of potential in one _part of an alternating cir-cut)n depends not only tTon the constants of th s part of the eir-cuit, but upont the condltions of the other prts of the ercuitalso and may, therefore, at the same current strength varyenormously with different conditiorns of load.Now a few words more on a question of terminology. Peru-

sinof the literature of the last years on this subject, we find every-where the endeavor to establish a suitable name for quantitieslike

2 u?L or n

1. It needs not to be remarked that if the generator contains iron, due tothe variable permeability of iron the nur erical values will, in practice, befound more or less modified.

1893.1 COAM UNICATIONS. 23t

It is of the dimension "speed" or "resistance," is expressedin ohms, and defined by

E. M. F. at right angles to currentcurrent

Tlhis quaitity and the traue or ohmic resistance are tlle catlhetiof a rectangle with the imnpedance as hypothenuse.Kennelly names it " indactane-8peed" (the factor 2 wz n being

an angul]ar velocity).This name, lowever, does not apply well to

2 wFAbont two years ago 1 proposed the rname "1 inductance " for,

this quantity, so that impedance should be the resultant of resis-tance and iniduetance, as compDoneints. Utnfortunately the raname"inductance " lhas now been applied to what we called before thec oeficient of self-induetion." S. P. Thompson in the inew

edition of his book hias adopted the name "inductance" foi2 7r n I also.The name " inductiqye resistance " has been used by Fleminig

anld otihers. This n3ame, however, has been applied also assynonymous with "u e_peld ce." "Ohmiic indutance " has beenproposed, but all these double namnes are too inconvenienlt to beof mnuch practical value. Decidedly the best name would be"inductance, the mnore so as the constant L is so little used inpractice that the ponderous name "c oefclient of se{binduction"will hardly cause any inconvenience.Lynn, Mass., April, 1893.

[REPLY TO IAIR STEINMETZ, COMMUI,NICATED BY THE AUTHOR.]Concerning Mr. Steiurnetz's remarks, oine in partieular is of sulch

practical importaniee that it will not probably suffer by emnphasisor repetitioni. Mr. Steiiinmetz points ouLt that when a eireuit iscomposed of an altern-ator, supply conductor, and load, eachhaving its individual iinpedaanee, their vector sum will generallybe less than their arithmetical sum. Consequently if the gene-rator delivers 1,100 volts at its termiinals, and the drop in thesupply wires allowing for the impedance factor is 100 volts (50oni eaclh conductor, as miglht be indicated by a voltmeter connectedbetweeni the far and near ends of one wire), the voltage at thetransformner terminals would be never less, buit -usually more than1,000 volts, particularly if conde-nsers are in eircuit at the receiv-ing end, and its exact value would depend upon all the impedan-ces in the cirecLit. It is therefore essential to observe that all thetabular impedanec factors given in the paper as applying tosinusoidal currents, or augmented impedance formrulas applyingto non-sinusoidal currents, accurately yield the drop in the con-

232 KENNELL Y ON IMPEDANG J. [April 18,

d aetors so lonig as the static capacity in those conductors is negli-gible. The voltage of delivery at the distant end will always be,yTeater than the difference between this drop and the voltage ofsupply at the near end, unless it happens that the imnpedances ofthe load and of the conductor have the same vector, or timne const-ait. But unless condensers are added to the receiving end ofthe line, this v'ariation of the actual voltage of delivery from thedifferenice between line drop and voltage of supply, is generallysmnall at full load on practical alternating transformer circuits.In other words the time constant of the ordinary suipply wiresdoes not dit er nmateriallv from the apparent time constant of thetransformers when loaded, although obviously this statenment can-nlot be depended -upon too far.

Ctu rent

1.90)6/1.687 Diacritical Poinit

1.236

0 SO 106 2!90 Frcquency 1700

FIG. 13. (See Burnett's Remarks, p. 218.)

april seventy-sixth thle thirty-first thle...

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