A Report on the Artificial Transmission Line with an Original Design Citation Meyer, Harry Pendleton (1917) A Report on the Artificial Transmission Line with an Original Design. Bachelor's thesis, California Institute of Technology. doi:10.7907/yr66-w875. https://resolver.caltech.edu/CaltechTHESIS:07082024-222516337 Abstract No abstract. Item Type: Thesis (Bachelor's thesis) Subject Keywords: (Electrical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1917 Record Number: CaltechTHESIS:07082024-222516337 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:07082024-222516337 DOI: 10.7907/yr66-w875 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16540 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 11 Jul 2024 19:16 Last Modified: 11 Jul 2024 19:21 Thesis Files PDF - Final Version See Usage Policy. 6MB Repository Staff Only: item control page

THESIS A Report on Artificial Transuission Lines with an original Desicn. by IIarry P. t:eyer. Class of I.Hneteen Hundred and Seventeen. Departr!lent of Electrical Engineering. 'i::HaOOP COLLEGE Oi '1.1:ECH.I.WLOGY Pasadena, California 1917 L The pur pose of this paper is to describe the designs of a few of the artificiil power transmission lines now in use in some of the engineerins collec;es 2.nd universities in this country as laboratory apparatus for imder·u raduate instructional experiments, as well as for researc4, and to design a line for the Electrical Engineering Laboratory at Throop College. The lines herein reported on are of both types: the s1::iooth 1 ine t;ype, and the 11 Lumpy" t;y-pe. In the first type the chief advantage is that it can be 01·r nrated without a c}~ange of electrical di:1e11sions at all frequencies within a reasonable range, making it possible to obtain os.o illograyhic records of surges and transc ient cona"i t ions in the same manner as they 1Jitht occur on actual lines. The '1 Lumpy" type has to have its electrical r.:lfr1ensions corrected for lumpiness at frequencies beyond a certain liuit. On the other hand the Lumpy .Artificial Line is a great deal easier to build and i'.laintain in a good op- erating condition, than is the smooth line, Dhich is ha □pered in both respects by the laree active co ~aenser surface re~uired. The lines considered will be reported on in the following orQex: The Artificial TransDission Line at Union College; The Artificial Power-Transmission Line at Harvard University; The Artificial TransIBission line at the University of 7.'eshington; Characteristics of the Artificial Transmission Line at Massachusetts Institute 2 The method sele c ted for securi nc a smo0th artificial line wa s as follows: ~ire of a suit able diameter was wound o~ class tubes or cylinders which ~ere lin0d with tinfoil. In this way any relation desired between resistance, inductance end capacity wss obtained b~ selectinc the proper lencth and size o:::' v1ire to c o ._,,ith t:1 0 proper size of elass cylinder. Eac h section line as built represents a half-mile line of No 1/0 B.& s. c uaee copper wire spaced at five feet, and has the follo winc const&nts: resh1tance, 0.25 ohms; henries; c~pacity, 0.007 microfarads. inauctance, 0.001 In clesig-ning the section the follov:in:c forr.mla vn-1,:3 used to find the inductance: in which L = inductance in henries. r = raa_ius of :1ind.ing in inches. 1 n = number of turns. 1 = lenc;th of coil in inches. The capacity was found in a similaY ~anner: i:; C = 4.54 x 1 r k/2 d x 9 x lOD in \"lhich ' .lfrom ]~rans. A. I._~.E. Vol. XXX. p. 245. C = capacitj iL f ~r ~Js . 1 = lonc;tl1 :::; f c l as ,: c;/ l.L1der. r = r ad ius of ; las s c ylinde r. d = thickness of c l ass . k = specific inductive capacity of c l ass. = 4.5 to be h i gh.) The cos t practic ~ble desig n r equ ired a cyli nder s i x i nches in dia~eter, one-eic hth inc h th i ck, un a four and one -11a l f feet lone , \J0uld wit h 2<l:0 turns ofl :i:To. G B.& s. i;uac; e copper v.rire -- t 11r ee i nc hes at e.s.ch 'J nd beinG le f t free of Dind ing . Subs ti tutin0 these values in the rbove fo rmulae gave L = 0.00104 henr i es , and C = 0.00748 ::1 i crofarads. Tho resis t ance of t he 240 t urns of wire is 0 . 24 o1u:.is. '.'!it11 t-:nese constants e ach u:1it re pr es ents one-ha lf mile of No . 00 3. & S. cuag e wire (copver) s paced a t five to six fe et. Because the .we i ght of each vni t ....-m s r1 i g h ( 40 po1.;_nds) a rack of heavy constructi on Y.r as required, and , ,, tho floor s pace was limit ed these r acks v ere constructed as a s possible. Eac i ruc k wss desi cn ed to h : l J 1 00 t u bes or sect ion s , te n in a row e a c h way . Cons iderab le d i ff ic ulty was encounter od in wi n ding the wir e on the tubes , a s thoy we r e eaoily broken. ( G 1/ 4 11 ) inc hes in diamet er ; Jinally 230 turns '. - rn re 1:sed. ( equ i- valcnt t o 240 turns on ~he e l l.SB cyl inder). .:~fte r bei:nz 4 loosened at.d r ,-L'lovcd fr,):.: the ~·or:.1s the so l enoids, or coils of wire , Ticre slippe d over the tube . Cop9cr st r ps !or c0mwcti0 1iS ';1ere used i:n f ~s:, eninc- the coil cn · s to the tuoe: 1 first Jne end w~s ~cdc f as t by me a ns of sevcrs l turns of on.e inch te.pe ; the v1i:cc wt:,s t11en distributed. r: l1d ti c:: tern~d. 0.110 the other '?-nd r:mcl e secure b~r t ~ ) ing . Even ~ore tr0 ub leso ~e was the t 2sk of l i n ine the wit ~ the tinfoil. ,J f raw-hide fib er T:i:e tinfoil \·;us ~,astod t o she~·ts 40 :nils t:i1ick c,:nd 54 inches l one by 17.5 inc hes ~ ide. In order to 0rov ~nt eddy currents , slits v.rerc cut si:s: in :;hcs u~1art , ,.: lter:iatcl,y , hcl:f way ~c ro ss the shen t. Small copper le r ds v1 e r e solc:ierci' to one end of the tinfoil (one le&d per section ). ::1e1.in:· of .9o rcelain ins -:J.lators. After be1nc 'J L,ce .~ in- sioe o.f :::, e tub e , the tinfoil w::.ts :::.n l d. out firmly agL: irn t the tube b; ~sine thre0 ~hosphor - bronze (exa.. uns ion) riru~s . '-' A~ these ringc h eld the tinfoil ae;c j_r: ~; t t1:e tube , thereb ;· dccret,ui:ng the -'.:'. ir g c, p betr,e-"n th e g l m,~, and. tinf o il, the The Dos t i ~rortcnt ob jection to th i s form of line i 2 it s hic h first cost and ~aintuinence or upke ep charce. 5 II. ARTI.llICIAL PO'.VJ:<:R- l RA.ifoi,.iISS I C.i.~ :nrs AT The artificial line herein des c ribed is of the ' 1 Lurnpy 11 type, in sections desicned to repr e sent 49.7 • •,,.. •G• a l ::.'. m1num • • ' r::·1• 1 es 01'"' u'7. /0 .J,.. s ....vr ano.ea. , t ors, o. 47 co nouc inc hes i n diameter (over strands), suspended. p1: r ul le l, on to wers or poles, and spaced at 90.5 i nche s centGrs. The corresponJinc li near constants der wire ~ ile are : Resistance a t 2 5° c·. -------- 0.53 7 o~ns . Line ar I~J~ c t anc e (LI ------- 1.995 ~ illihen~ies . Capac ity (C) --------------- 15.00 ~ illi~ icro farads . The type of line section as orig ina ll y constructed was a T-line, but i L was l ate r chanced t o a -line. It was desired that the i nductance co il s of the unit s hould have l i t tl e or no ::m t ua l ind1.:ctive ac':ion. Close & circular sole no i ds, if properly wound , ~o~ l d h ov e no external macnet ic fi eld and con se~uently would b e devoid of ::rutu al induc tive act io n . >'o r mechan ic a l re&.sons a s ,1uare fo r r:1 'Has n c1 opted, the unit be i nc Ija o.e '--'- P of f our coils wound" on wo oden for~s wh ich were sec urely ~as t ened so as to i:wke a :;10 1:;ed :wgnet ic circuit. By asse~bling the coils i n t he f orrn of an cL.1ci1or r i nt::; in building up the unit, ' J r om the ~lectric a l ~or ld, ?e b. 17, 1 91 2 . G their L:ternal rnac;netic fL:t:: is rolD.tiYely feeble but in orcler to 2:1ini1Lize the r:m"'.:;ual indic'.ive action of adjacent . •., vllO C 01.Lt, of each line were ~ouated on u shelf in units +·· vertical planes alternately perpendicular to ec:.ch other, the even-numbered coil 'J.ni ts b o inc -paralle 1 , lt;u10 s, ,;,;hi le the odd-numbered ones were in a 9lane at right angles to the former. The internal diameter of each coo~oncnt coil was 2.16 inches, the external diameter was about 2.87 inches, while the length was 7. 88 inc hos. Each coil was made up of 1190 turns of #19 d.c.c. wire the covered diameter of 7vhich was 45 ::::1ils. After each cuil was wound it 'i/8.S im- mersed in molten 2araftin wax. The weight of each main coil, after being assembled nas 18.5 lbs., ·::::ile the weight of copper used in tho entire line Das approximately 370 1 • The averace resistance of main c~il or unit was 21:1.6 ohos at 25° C., L'.Lking the resistunce of e1:ch line of ten ~mi ts 246 ohrns, and. giving a nominul liirnur resistance of 0.498 oh~s 2er ~ire Llile at 25° C. T11e aver1:.ge induct :c. nc e o±' each uni-: rn,s a} rro::d::iat ely 90 rnillihenries, :Lwkinc the totcl inductsnce of esch line of ten :mits 0.90 }1enries. represented wa~, 1.82 r:1illihenries ~,er \'lire :::ile. psper s e t 1n a tin~ed iron box 7.9 inches by 2.2 inches by 5.G inches; the □ pace filled with paraffin wax. bet~een ~h0 condenser and box was The average capacity was 0.75 7 a v0ltage corr c s;Jnds <" i t_, ven to a s~ul~ no ~i n<l l l ine& r lo ak~~ e in the act u al line. At ordinary frequencies t ho correct i on factor of th i s li n e is o.o7j i ncreas i nc , however , ~ it h i nc re as ed frequenci e s so that at 200 cycles per s ec o~d it has to CJns i de r a d in ~ak ine t he cclcul c t iuns based on eny rea d i ng s tuken a t tha ~ or l, i [;:i1Cr frequoncios . '.l:hi s line co n s i sts of trienty units c onn ecte d i n s eries. Each un it is crnJ9lete in i ts elf end repre s ents a;Jp ro:c:imately t en :ni les of ~1ower-tran smi:3 ~;ion lkn e. I -t·" ca:n be a &ju s ted. • '~o ~r a ctic a lly c:rq- spc:~cinc u0 to 120 inches, to trn,/ ,:i i ze wi l'e u p to No. cop~)e:c , and mar b e conv 0rted into 4/0 h oro. a-rawn e. stt:nd t: ··c1 telephone line b y i ~s ertinc u 50 - o!~ non -i nduc tive r osistsnce bet -.: : een e &ch unit. J;he li ne i s of the ''lur:ipy !! typ •'.: , sL:. ilar to "':; lrn a rtifici a l line at rrarv~rd Cn iversity, t he co ndens e rs beine con~ected at ths ~ id dl c ~o int of i ~duct ance of euch un it. vo ltaee , under r oson&nt condition s , ~y ~e uns J~ ~ su i tu blc s In Ol'<ler to fulfil the reg_uire~,1e11ts of a unit o.djustable to re 1..)resent an~, 1rnwer-trunsir,i2Tion li:he u9 t ,J 200 :niles in length at o..i.fferent spacings anc1 of dif.1.'erent sizes of hard-drawn cop,er wire up to No. 4/0; the linear co~stants must be adjustcble Tiithin thn follo~ing limits: Resiotance, minit1uE1 value Inductance, Capacity, " = ,r 2.59 ohms. 0.021 henries. = 0.1 to 1.0 m.f. The allowable resistance of ecch coil in the unit ·,·ms found by clivic1inc the rninimur.1 resistunce b,y four (2.59/4 = 0.65 ohms.). By selectinc No. 14 A.'i,'.G. copper 77ire tl1e length 9er coil v1au lk:itec1 to 257 feet. ance w&s :n.lacle for "'.:he resist enc e of c on ;ciec t i:n5 ~sing only 250 feet of nire for each coil. ·wir·es bJ 'J:he hi[)1 resistance re l.luired to re pre~:,cmt lines _; f the smaller c Jnd uc tors is ob t c..ine a. by .~Jving the short circuit c la1:ip on tho 1 O ·J :fl of 11 Adv,.:11c e" resistance -. -: ire . 1he inductance is obtuined by using ~our short uircore solenoids c0nnected in series ana arr2nged in a square. By 1rni Lg Brook I s forrnula the c ir:iens iol:~, of each coil '.','er-e obt.s.ined, a.11 the C•~il:-:: being similar. a. ir:1ens ions are: 'From Electrical World, June 12, 1915. As constructea the 9 Mean radius------------------ 2.20 inches. Lencth of coil --------------- 2.15 inclies. T11ickness Yf winding --------- 0.60 inches. :ie ng th of' v1 i re - - - - - - - - - - - - - 2 5 O. feet. number of turns ------------ ;~1G (Eight layers of 27 turns each.) It was found that with the coils arraneed in a square the mutual induct:.. nee vvas approxiE1a tely 8. o;?i of the total--self.,.induction of each 11:lit. Variations in the induct~nce is obtained by providing one coil with taps at each quarter of the total number of turns, and b:7 mounting one coil so that it can be rotated t1iru 180°. The average maximmn iGductance for the whole line is 0.0213 henries for each unit. Some of the units when measured differed slightly, varying froLl 0.022 to 0.0197 henries. The capacity is obtained from type 21-AA, st andard telephone condensers guaranteed to st~na 1000 volts. Each unit is protided with ten 1 m.f. condensers connected in series, ~ith taps brought.out at the 5th, 6th, 7th, 8th, 9th and 10th condenser. Each co~plete unit was calibrated and the results were t8bulated for use Dhen con~ections are ms.de for any of the :-:-,any trsts desired. Of all the lines considered ~his type is the easiest and cheapest to construct; there is also practically no 10 ~aintenance charges or upkeep to take care. IV. ARTIFICIAL TRA.iJS:.ass IOH LilIB AT THE Iv.LASS- ACHUSETTS INST ITU TE OF TECRNOLOGY. ' The artificial transmission line at the Llassachusetts Institute is electrically equivalent to 800 ~iles of sinr lephase 500,000 circular 1:111 cop9En- conductor spaced at ten foot cent en;, or it r.my be ·used a~, a 700 uile t:r1ree-_r,hase line ';;ith conductors spaced in an e-luilateral trianc;le. 3y _proper changer:; in the connect ions ~~horter lines represented. r1:2;y be ]he line is made up of thirty sections }1ou:.: 8 d in a cabinet 12 feet lone, 5 feet Ginches high, ano. 2 feet deep, ec.ch u:r~i t occupying a compartE1ent 20 inches long by 12 inches hi[;h. The line inductunce is provided by eight coils (per section) centered on a circular axis, each coil being of No. 12 Tiire wound t6 a diameter of 7 inches and a width of 1 inch. By tl1is method mu t ual inductance effects are secured. Tho &apacity is sec ured by a condenser mounted on the side cf each conpartscnt~ /. _ great raany co::1c,irwtio1rn at' resh,tDnce, induct [mce 2nd cap~city ~ay be secured and studied if the proper con~ections s.re rni,a.e. 'Fro~ the Electrical Jorld, Kay 2, 1914. 11 In order that the Senior Electricals mirht ~et a -...) (_1 ~ore coLlprehcnsive insicht into the Dhysic~l phenomena, and underst~na what actually t~kes 0loce in the trans~issi0n syate~, it was considered that an ~rtificial Line was necessary. ~fter having studied all of the other E.:~cineering Institutions it was a.ecid.ed that the 11 =.ur:1pyn t;y9e would fulfill the conditions of low first cost, low m~intenance, ease construction, and adjustability. The ten-oile unit was selected &s a sufficiently close ap9roximation to the uniformly distributed line const~nts of act:~al :ewer-transmission lin~s.for ordin2ry fre1uencies. As it will be aesireablc to study many st a nd~rd transsission lines, the voriations of line canst ~nts will very over u wide ranee, consequrntly st~ndar& lines v;ere chosen as tho start inc- ,PO int. 1he voltages considered varied fro~ 44,000 to 200,000 volts. The correspondinc standard spacings are given in Table I; the corresponding standard Jencth of line is found by dividing ~he voltage by 1000 (i.e., a drop of 1000 volts is allowed per ~ile). Line resist r nce. In ord.er to r.'.leet th.e regnire::-:ent of being aajustcble to any size of condnctor used in 0nl;y the l c.rc;est o.nc. m.1::1llest c :::n il; ctor o~' e :· :h nur:iue r of strEnds pe r c0n J uctor 7SS ta~en , except i n ~ho c : se oi ~11e con c:v.ctor v;it11 s ev er: strc,ncls • ·11cre only the l ::c rcest c ~ble ~as co~sidered . rabl e II r ives the resi s t s ncc £'or above rnent i oned co 1) ~)Or c O J~c-u c ·- ors for both 1000 ft. ~n d 1 0 miles of line. Th e resist ~nce v ~ryinc from 8 .554 ohr,1s a.t 25° C. for -/;/2 con ductor to O.285 ohms c: t 25 8 C. for a CJ ,, cl uctor of 2,000,000 circuL.u ::dlc~. Table III was then made up froc va lues c; iv en i n Table VIII of circlu a r ~o. 30 of the Ju re&u of St anda rds. ~hen by referr i ng to the Inductan ce Char t, Jig . llb, g iven in Bull etin ~o . 53 of the University of Ill in o is, it was found that the ~ ost economical Ti ire to us e was It was calcula~ed that 2 .54 lbs. De re ne cess a ry, but 2.75 l bs . ~ere ordered f or t ho first un it. Resi ntance: L : orcler to _,b t c in the resist[m di'e n ee ossary to re pre sont an;r 1 ine larcer than -# 2 A. ·,;' . G. copper con duc tor it wi ll be n eces sa ry t o use u rcsi~t~nce i n pbrc.llel ·,c: it h tho indu ct::.:nce. Because of the fe.ct th2.t thL:: ls a ''T " l ine i t i s co:m::iderec1 boGt to :J:..,ke two soJ - erate tections of e ~ch unit an& t ie the resistanc e in a t the go i nt frOQ wh ic h the c~nncct i on t0 the condense rs and neutral ~ ire i s t ake n. ihat beinc the c ~s e, the ~ax i mum resistance in th ~ coils on e it h er si Je of th e neutral r , l .) poi n t will be Cl .554/2 or 4:.277 oh.::rn , nno. a,, th o nnit vm s desi gned to r ep r e s e n t a ten ::1 il e sect io n of )2 A. J . G. co pp er c onductor it will n ot be neces sa ry to u se t ~e r e si Ltsnce loops in D&ra l i el for tha t lin o, but to repr es ent t h e l a r s er c Jndr,ctors th o equ iv s l ent r es i sts.ne e re .u ired i n ecch ha lf-unit will vury from 6.811/2 t o 0.235/2 ohms or 3 ,405 to 0.1425 ohms. Required resi s tance i c parallel wi tl1 ecch h c lf-unit: 1/r = 1/3 .405 - 1/4.277 •(maxirnuml . - 16.67 ohms. (With a 1r. axirn:um of 15 ohms 4 '. YH; equiv 0,lent r es i s ~;::ince 0 ill be 6 .6G7 ohms.) 1/r = 1/0.1425 - 1/4.277 (minimum) = 0.1475 ohr:1s. From the a b ov e calculations it is seen that t Do s lide-wire ty po, of at lea s t 17 ohms, will be required. Induct : nee: In determininc; t ho ::mx imuEl a nc'. ::1 i :r.. , .·~um inductance required for u t An mile s ec t ion OGl y \he c oncluct ors were cons iclereo., t h e> i n s ~Jallest a nd l tn·1:·est u iluctunce b einc calc u l a ted for e ::ic h st trnd u r d spo.cinc . The fo rmula u se d was, in which L = induct&nc e in h cn ries. 14 s = l i::llf; th of 1 i 11 e = l O ::1 i le s . k1;:: 741.13. u = 1.26d or effective s_pa,:;ing in L~ches. R = rudius of conductor in inche s . The results arc shown in tables IV and V. 70 1 1.r - "' s1·-1 ort -t11·r-core 0 n1e~o1· "c nrr auc: --"ea" 1· ·1i e-- SCJ_uc.re .... u 0 "' uv are used to give the induct[~nce. ~he rcsistunce re~u irea li!:ii ts the uax i!:mm lengt}1 of wire 1;~vc..'-1lable for each '.m it to 822.5 feet of ~o. 20 d.c.c. copp er ~ire. 'r:he .L engt h of wire for each coil is 822.5/4 or 204 ft. find the cliuenu ions of e:::,ch coil in oi·d er to g ive its propo1·tion of the total induct ance of each UL it, formula ._,oras use a.. Brook's As the induct unc e of eecb unit is to be O. 02G•J8 henries or Jess ( no allowance be inr: :::,c:tde for mut ual inductance), the r iven inductance per is 0.02608/4 or 0.00652 honrics. coil By referrine to 15b, V• 55 of Bulletin ~a . 50 of the rnivcrsity of Illin ois, it ~a~ fou nd thut ~he ra dius of the core would be ub out c.70 inches. ·.-Ii th ttis a a bas is tho cJ imcns iJns of' th e coil were found: a= mean r~dius = 1.05 inches. b = coi1 width c = coil thic~ness - 0.84 inches. = C.72 inches. R = r - c = 2r = 1.40 inches. Substituting these va lues in ~he formula, 15 <) L - C.3G6 x (205/1000)"' x F' x F" 'c - C - r Values of F' ~md :'.!... ,, are as follows: F' = lOb - 12c - 2R lOb - lOc - l.4R anJ. Fll 14R - 0.5 log (100 - - - - ) ; 2b - 3c Substitutine the above va lues in the equation, L wa s found to be 0 .00573 henries, wh ich i s too low a v 2l ue. After several attemp ts i t ~as decided to let c = 0.76 in. or 19 lajers (as the d i amete r of the wire was e iven as 0 .04 inches] and b = 0 . 80 inches or t wenty turns, o nk inz the t ot El l 111.r::1 b e r of turns = 1 9 ::-: 2 0 or 3 8 0 . Then by }rn0winc; the nunber of turns and tho l ength of wire the r: e:,m rudius 'a' can be f Juncl b:,r subs:itutinc; in ~he f'un:m l a , feet = 2 alT/12, fro r:, r1hich i nches . 1 a' was f .mnd to equa l 1. 025 1he r r diu J of the coil Tia s than f ]u~J by sub - tracting C.76/2 froc 1.025, which is C.645 inches. By substi,cuti:nc: the above dimensi0 ,1s in Bro ox ' s formula the incLuct c.nce 'L' was i:'ou~1 ~, to be C.00589 hc:nr i0. s . ? orr::rul s 20 , on page 28 of Bul le t in ~o . 52 oi' t ~e ·u ni vers i t;y of Il lino is 1:.rc.:. s then us ca_ g i v i:n_c O. 00605 for the L:1ductsnce. ',7hen the r.'1ut1-,al ind ict ,: nee of th:=: unit i s co ~1:3 idorod '~he i ncluct[rnc c i s ~:uf:'."icicntly close to C.00652 hcnries. Jour c o il s of 19 layers ~ith 20 turns per l aye r were lG l:o tests have beon :.'lDd.e on an~r of the coih~. Tables VI and VII ~ere calculated from the same data as was used in calculat inc Tables IV and V, except that the result shows tho capacity of the largest 1::md mnallest cable co11ductors [ t the st a ndard s_pacinc;s considered. I'he f ollonine f orrrula Yms used: C 38.83 = log (D/R - R/D} X 10 -2 in r:hich D = l.2Gd R = radius of the conductor. C = cupacity in ~icrof~rsds. Of the various r.:io u_ns cons ide:cecl for o bt::.:. in inc this Cal;ac i ty b.nd at the s1:.;r:2e t iuo ce t t inc different ~ot eps th2 li::;its of 0.20 an:l J.11 ::,.f., t~1e telephone cono.ense1· We.ls chosen as the most ctJ01101:1icecl i .Gtrm.:ient. of type No. 21 U Six condensers tested at 1200 volts A.O., and of 0.03 1:1.f. ca;acity ~ere ordered for the first unit. 17 l'he d.iagr cun of co11..'.1ectio1rn for the en.tire unit h , sha~n iL Figure I. 60 44 Length 44000 Spacing Volts 55 72 55000 66 84 66000 88 96 88000 150 1:- s 110 210 144 120 150000 138000 110000 TA.3.LE I. 175 240 175000 200 300 200000 f-' CJ 19 Table II. no A. ·.v.G. 2 1 4/0 7 19 19 37 37 61 AREA 66.40 83.70 212.0 250.0 500.0 550.0 R/1000 ft. 0.162 0.129 0.509 .0431 .0216 .0196 R/10 r:ii les. 8.554 6.811 2.688 2.276 1.141 1.035 Gl 91 91 127 127 AREA 1000 1100 1500 1600 2000 R/1000 ft. .0108 .0098 .0072 .0067 .0054 R/10 Eliles. 0 .570 0.518 0.380 0.356 0.286 STRAifDS STRA~rns In the above table the area is c iven in thousands of circular ~ils. J. e~1ual~3 ohr:is. 20 TABLE III . Resis t ance = 8 . 554. .B . & Leng th = 8 . 554/R/lO OO = 8 . 554 x 1OOO/R Weight = Le ng th x '7 / l OCO . Ho. R w/1OO0 Len6 th Vie i 0 h t 14 2 . 58 1 2 . 40 3315 . 3 41.10 15 3 . 25 9 . 86 2631 . 9 23 . 3 0 16 4 . 09 7 . 82 2091 . 3 l G.4O 18 6 . 51 4 .92 l Z1~; . 9 G. 5O 20 10. 40 3 .09 882 . 5 .. 2 .54 21 13 .1 0 2 . 45 653 . 0 1 . 60 (' ;) 1 21 1ABLE IV In duet D.nc e for 3 2 - 7 strand conductor. iJ R = .148 i11cl1e s; A2 = 83.3 k1 = 741.13; 1·- 1 0- 5 -- .L lotS 60 1.26d 0.148 510.81 2.70826 ::2 173 .77 .02174 55 72 612.97 2.78744 2232.45 .02232 66 84 715.14 2 .85439 2282.07 .02282 88 96 817.30 2.91238 2325.05 .02325 110 120 1021.62 3.00933 2396.9 .02397 138 144 l '.~ 25. 9 3.08845 2455.6 .02456 150 210 1787.83 3.25233 2577.0 . 02577 ,' 175 240 2043.24 3 .31032 2619.97 .0262 () 200 300 2554.1 3 .40723 2608.49 .026085 s a 44 U/R X , 1 Kl-K2 X T 22 ·.:.ABLE V Inductance of ;2, 000, coo C• :,:. 127 st : and cL,b le. = 1. 632/2 = .8155 R k, :: 8 t,)" • .:) k1 = 7Ln o lC r, (.., r:- " l.2GD .8155 log u/R. X 44 60 92. 7036 1.967097 1541.2 .0154 55 72 108.154 2.034043 1590.8 .01591 66 84 129.785 2.113225 1649.5 • 0l6L19 88 96 148.3257 2.17117 1692.3 .01692 110 120 185.4072 2.26811 1764.8 .01765 138 144 222.4886 2.34729 1824.3 .01824 150 210 324.463 2.511162 1944.4 .01944 175 240 370.814 2.569156 1987.4 . 01987 , 200 3CO 4G3.518 2.6660GB 2059. i? .02059 s ,l ,Kl lr -.l.l,,.2 X 10-..J= L 23 TA BLE VI. Capacity fo r .!l 2 it Conductor R .. 0 .14 6 i nc . Small e st. d D U/ R - R/D 60 75 . 60 72 1 0- 2 log Capacit y 5 17. 8063 2 .714 1 67 0 .14306 C. 1 43 9 0 .7 2 62 1. 3682 2 .7 933489 0 .13 9 008 0. 1 39 84 105. 84 7 24. 930 2 . 860296 0 .13 57 55 0. 1 36 9G lh 2 0 . 96 828 . 492 2 .9182883 0 .133 0 5 7 0. 1 33 1 20 1 5 1 .20 1 035 . 61 5 3 . 0 1 5200 0 .1 28 7 81 0. 1 29 1 44 181 . 44 1 242 .73 8 Z.094Z:8C C.1 25486 0 .1 2 5 210 264 . 50 1 8 1 2 . 33 2 . (25823 72 0 .11 9 17 5 0 .119 240 302 . 40 207 0 . ;~? ;(.71G2233 0 .117 09 ili C. 117 300 Z78 . C 2589.04 Z .413 138 8 0~113 76 6 0. 114 U/ R - R/D X 24 TABLE VII. Capacity for 127 strqnd conductor. ~ = 0.8155 Largest. a D U/R - R/D 60 75.60 72 loe Ca pa city ~ 92.69308 1.967047 0.197402 90.72 111. 2358 2 .04 6245 C.18 9762 84 105.84 129.7777 :: .1132011 0.183749 96 120.95 148.:?194 2.1711SG8 0.178841 l ')~vI\ 151.20 185 .40 ~2 2.2 G8 1144 C.1711 99 144 181.44 222 . 484 2 . :7 47 '.~9 88 C.1654 24 210 264..6 324.4 61 2 .5111 625 C•.1 54G;~g 240 3 02.4 370.Gl~ 2 . 5691549 0.1511?9 300 378 . 00 4G3.5 17 2.6GG06b7 0.145G45 D/R-R/u --+- r------ ><. ......... 'X I • , -~ -;II) I -4>); I . I ~~ ~ I+ I 4~ ~ -- "~ L ______ - - ------, ________ _J =J II C\JO -+-le . -. --l- ,,8 ►1 .