From Computor to Electrical Engineer: the Remarkable Career of Edith Clarke

184 • IEEE TRANSACTIONS ON EDUCATION. VOL. E-28. NO. 4. NOVEMBER 1985 From Computor to Electrical Engineer: The Remarkable Career of Edith Clarke

JAMES E. BRITTAIN, SENIOR MEMBER, IEEE

Abstract-Edith Clarke's electrical engineering career had as a cen the development of electronic computers beginning with tral theme the development and dissemination of mathematical meth the ENIAC that was introduced during the same year that ods that served to simplify and reduce the time spent on laborious cal culations in solving problems encountered in the design and operation she retired from General Electric. of large electrical power systems. As an engineer with the General Elec Clarke helped to develop and teach mathematical models tric Company from the early l920' s to 1945, she worked during a time that took advantage of such electromechanical aids as cal when power system analysis was evolving from being labor intensive to culating tables and alternating current network analyzers. being machine intensive, with much of the labor of problem solving In effect, she wrote what now would be called software being shifted from human computors, often women, to electromechan ical computers, such as the network analyzer and differential analyzer. for the machines that set the stage for electronic digital This trend culminated in the development of electronic computers be computers. She became highly skilled in the manipulation ginning with the ENIAC that was completed during the same year that of hyperbolic functions and symmetrical components, and she retired from GE. As a woman who worked in an environment tra was able frequently to simplify their use by preparing ditionally dominated by men, she demonstrated that women could per graphs and tables. Early in her career, she invented and form engineering analysis at least as well as men if given the opportu patented a graphical calculator for the solution of trans nity. Her achievements provided an inspiring example for the next generation of women with aspirations to seek a career in electrical en mission line problems. Her contributions made the "wom gineering. an's work" of unmechanized computing less necessary and, in the process, initiated the arduous task of opening INTRODUCTION the traditionally male-dominated electrical engineering DITH CLARKE (1883-1959) began her career as a culture to women. EComputer Assistant to a Research Engineer at the Am~rican Telephone and Telegraph Company. Eventually, EARLY LIFE AND EDUCATION she overcame formidable entry barriers to women and be Edith Clarke was born on February 10, 1883 and spent came a professional Electrical Engineer. She specialized her early years on a farm in Maryland near Ellicott City. in the analysis of electrical power systems and was em She was one of nine children of Jolfn R. Clarke, a lawyer ployed by the General Electric Company from the early farmer, and Susan Owings Clarke. In her early childhood, 1920's until her retirement in 1945. She then became a Edith Clarke suffered from what probably now would be Professor at the University of Texas where she taught until diagnosed ·as a "learning disability" in reading and spell her second retirement in 1956. Clarke was the.fi;st woman ing, but she exhibited a good aptitude for mathematics and to receive a degree in electrical engineering from the Mas enjoyed puzzles and card games, especially duplicate sachusetts Institute of Technology (MIT), Cambridge, and whist. Both her parents died by the time she was 12 and the first woman to present a technical paper before the an uncle served as her legal guardian. She attended a American Institute of Electrical Engineers (AIEE). boarding school in Montgomery County, MD, until 1899. Clarke directed much of her work as an engineer toward At the age of 18, she received a modest inheritance from the simplification and mechanization of laborious calcu the estate of her parents and decided to use it to continue lations encountered in the analysis of transmission lines her education. She enrolled at Vassar College in Pough and power systems. Somewhat ironically, her most impor keepsie, NY, a college that had opened in 1865 and that tant contributions to engineering analysis tended to reduce provided "the real impetus toward the full collegiate ed or eliminate the need for skilled human computors, an oc ucation of women" [.l]. At Vassar, she concentrated on cupation that had come to be regarded as suitable work for mathematics and astronomy, areas where the college al women at a time when engineering was not. During the ready had established a strong reputation. Many Vassar time spanned by Clarke's working career, power systems alumnae in the late 19th and early 20th centuries found analysis evolved from being labor intensive to being ma employment at observatories as computational assistants chine intensive, with much of the labor of problem solving to male astronomers [2] . being shifted from human computors, often women, to After receiving an A.B. q.egree from Vassar in 1908, electromechanical computers. This trend culminated in Clarke taught mathematics and physics for a year .at a school for girls in San Francisco, CA. She then taught Manuscript received July 16, 1985. The author is with the School of Social Sciences, Georgia Institute of mathematics for two years at Marshall College in Hun Te_chnology, Atlanta, GA 30332. tington, WV. She expressed her discontent at the pros-

l•. •' BR!TT.' IN: REMARKA3LE CAREER OF EDITH CLARKE 185

pects of a career as a mathematics teacher by enrolling as plify difficult concepts and mathematical methods and ex a sophomore in civil engineering at the University of Wis press them in terms that the average engineer could un consin in the fall of 1911 at age 28 [3]. derstand, a talent that Clarke also displayed as an engineer [7] . Bush came to MIT as a Professor in 1919 and achieved A COMPUTOR AT AT&T AND A STUDENT AT MIT a reputation for his skill in electrical analysis by After spending an enjoyable year as an undergraduate means of operational calculus and for developing the net engineering student, Clarke was hired for the summer as work analyzer and the differential analyzer, electrome a Computer Assistant to George A. Campbell (1870- chanical calculators of the type exploited by Clarke and 1954), an outstanding if somewhat reclusive Research En her colleagues during the 1930's [8] . gineer with AT&T. Clarke found the computing work suf ficiently interesting so that she abandoned her plan to re A COMPUTOR AT GE AND AN INVENTION turn to Wisconsin to complete the requirements for an Despite her newly acquired graduate degree, Clarke ex engineering degree. Campbell had been a Bell employee perienced difficulty finding employment ·as an engineer. since 1897 and already had played a major role in the de Again she became a computor, this time with the Turbine velopment of the loading coil, a major innovation in tele Engineering Department of the General Electric Company communication [4]. At the time Clarke was assigned to in Schenectady, NY. During the period from 1919 to 1921, work for Campbell, his efforts were directed to the anal she trained and directed a small team of women compu ysis of problems related to the use of vacuum-tube ampli tors in the calculation of mechanical stresses in high fiers on long distance telephone lines. The Bell Company speed turbine rotors. As in her earlier computing job at had embarked on a crash program to complete a transcon AT&T, the position with GE resulted from an anomalous tinental line from New York to California, to be opera situation that created a temporary need for skilled calcu tional in time for a planned celebration of the completion lators. The increasingly large turboalternator units man of the Panama Canal. Consequently, the telephone com ufactured by GE just prior to 1920 developed unantici pany was e;v.panding its research P.ffort on related innova pated problems caused by rotor vibrations and metal tions such as repeater amplifiers. Thus, the job opportu fatigue. In response, GE launched an intensive research nity for Clarke was in the context of this accelerated effort directed by C. E. Eveleth that involved the efforts of research program that provided work fo r several women several engineers and members of the GE Research Lab with credentials in mathematics [5] . oratory. The group carried out a program that included Clarke· s time as assistant to Campbell provided her with both experiments and theoretical analysis. The GE re an excellent apprenticeship in the mathematical theory of searchers developed a comprehensive theory of rotor vi transmission lines and electric circuits. Campbell was the brations and developed techniques to overcome the prob- company's leading authority on these topics that involved lem at normal operating speeds. They disseminated their the manipulation of hyperbolic functions, equivalent cir findings in a number of technical papers published during l cuits, and graphical analysis, areas that Clarke pursued for 1924-1925 [9]. I the rest of her career. Among the computational tasks as In June 1921, Clarke filed a patent application describ l signed to her was to calculate the first seven terms of an ing her invention of a graphical calculator to be used in infinite series that represented a probability function. An the solution of transmission line problems. The invention other woman computor, Sallie E. Pero, extended the series probably was based on her earlier work at AT&T or as a to eleven terms while Lucy Whitaker used a different student at MIT. Since she was not a salaried engineer, she method to provide an independent check of the work done was not required to assign the patent rights to GE. The by Clarke and Pero [6] . In 1915, Clarke joined the Trans patent description included instructions on how to con II mission and Protection Engineering Department at AT&T struct and assemble the device. She explained that the pur I where sh~ was responsible for training and directing a pose of the calculator was to facilitate the analysis of I small group of computors. During this period, she also transmission lines of different lengths or different char found time to take a course in radio at Hunter College and acteristics by reducing the need for laborious computa several night classes at Columbia, New York, NY. tion. She revealed that the graphical calculator was based In 1918, Clarke took a decisive step toward becoming on line equations that included hyperbolic functions, and an engineer when she left AT&T to enroll in electrical she cited Oliver Heaviside's book, Electromagnetic The engineering at MIT. She completed the senior level un ory, and A. E. Kennelly's The Application of Hyperbolic dergraduate courses by the Fall of 1918 and continued on Functions to Electrical Engineering Problems. The patent to receive the Master of Science degree in electrical en was issued in September 1925 [ 10]. gineering in 1919. Although she was not the first woman Clarke's graphical calculator was the subject of her first to graduate from MIT, she was the first woman to earn a technical paper published in the GE Review in 1923 [11]. degree in electrical engineering from the school. Arthur The paper contained drawings of the parts of the calculator E . Kennelly and Vannevar Bush were leading members of along with instructions on how to mount the parts on card the MIT Faculty while Clarke was a student there. Ken board and assemble. The device included a base chart and nelly taught transmission line and advanced alternating two calibrated radial arms that were attached to the base current circuit theory. He was known for his ability to sim- chart. She stated that her calculator served to reduce "time 186 • IEEE TRANSACTION S ON EDUCATION. VOL. E-28. NO . .J. NOVEMBER !985 and labor" by providing a graphical solution of line equa produce a more exact equivalence with the actual system. tions that took into account distributed resistance, induct The modified equivalent circuit then was used to calculate ance, and capacitance. She explained th at the calculator the maximum power that could be carried without insta gave quite accurate results for power transmission lines of bility. up to 250 miles long, and that a problem solution required During the discussion of Clarke's paper, Charles L. less than a tenth of the time ordinarily required. Her paper Fortescue of the Westinghouse Electric Company ex included a derivation of equations relating line current, pressed his appreciation for the "ingenious method" that voltage, impedance, and admittance that could be solved she had developed. He also complimented the "able way" by means of her calculator. The function of the Clarke in which she had presented material on such a difficult calculator was similar to the well-known " Smith chart" subject. Robert D. Evans, also a Westinghouse engineer, developed by P. H. Smith of the Bell Telephone Labora remarked that the paper was of "very considerable inter tories in the late 1930's. est" and he anticipated that the equivalent circuit method In 1921 , Clarke left GE to accept a one-year appoint would "find general use. " H . H. Spencer commented that ment teaching physics at a woman's college in Istanbul, the profession should be grateful to Clarke for having sim Turkey. She utilized the opportunity to tour several Euro plified such a difficult problem to a "slide rule and arith pean countries and Egypt before returning to Schenectady metical basis" [ 15]. Fortescue and Evans, along with in 1922 to sign a contract as a salaried electrical engineer Clarke, played a major role in the development of the at GE. At age 39, she finally had achieved her goal of method of symmetrical components for power system acceptance as an engineer instead of a computer assistant analysis. to engineers. She soon took advantage of the broader ho In May 1926, Clarke published a tutorial paper in the rizon open to an engineer by becoming an active member GE Review entitled " Simplified transmission line calcu of the AIEE and a licensed Professional Engineer in New lations" [ 16] . In an introductory note, the Editor observed York. At GE, she joined the Central Station Engineering that few engineers had mastered some of the more "spe Department [ 12]. She used her early work in telephone cialized branches of higher mathematics." He continued transmission theory to great advantage and helped to ed that Clarke had developed a simpler approach for the use ucate power engineers in analytic methods from telecom of hyperbolic functions in problems frequently encoun munication engineering that increasingly were needed as tered. In the paper, Clarke also noted that "hyperbolic power lines increased in length to appreciable fractions of functions, real or complex, are not popular with engi a wavelength. neers," and that the equivalent series had met wi th "greater favor." However, she pointed out that the labor A GE E NG INEER required increased with the number of terms in the series In April 1925, Clarke applied for a patent on a method and became very great in the case of long lines. Conse designed to regulate the voltage on power transmission quently, she had developed graphs for hyperbolic functions lines. The patent was issued in September 1927 and was of the form often used in engineering analysis. She in assigned to GE. The invention utilized a rotary machine cluded examples of how to use the graphs to obtain quite with special saturable field poles that acted as a synchro accurate results. nous phase modifier. Clarke explained that the phase mod During the 1920's, Clarke learned to use the method of ifier was intended to add sufficient reactive power to the symmetrical components in the analysis of pol yphase system to prevent an excessive drop in the terminal volt power systems. This powerful method essentially did for age. This enabled the transmission line to be operated the analysis of the multiple-phase power system what the nearer its maximum power limit, an important considera method of complex numbers had done for the analysis of tion in long high voltage lines [ 13]. single-phase systems when it was introduced in the 1890's Clarke was the author or co-author of 18 technical pa by A. E. Kennelly and Charles P. Steinmetz. The sym pers published between 1923 and 1945. In February 1926, metrical components method facilitated analysis of unbal she became the first woman to present an AIEE paper. anced three-phase circuits by converting the problem into The paper, later published in the Tran sactions of the A/EE, equivalent symmetrical circuits that were much simpler to was entitled " Steady-state stability in transmission sys analyze. Clarke credited L. G. Stokvis as having been the tems-calculation by means of equivalent circuits or circle first to publish on a method to resolve an unbalanced elec diagrams" [ 14] . She pointed out that the growing trend trical system into positive and negative sequence compo toward longer lines and greater system loading had made nents. He published a paper on the method in a German it necessary to give more attention to the problem of sys periodical in 1912 and a second paper in the Electrical tem stability. She explained how an actual power system World in 1915. In the 1915 paper, Stokvis actually used the . could be analyzed by means of an equivalent circuit with terms synchronous components and inverse components lumped-constant elements. As a source, she cited A. E . for what later were called positive and negative sequence Kennelly who had included a chapter on equivalent cir components [ 17]. cuits in his book Hyperbolic Functions Applied to Elec C. L. Fortescue presented a more general analysis that trical Engineering. Clarke then. introduced a correction included a zero sequence component in addition to the factor containing hyperbolic functions that she used to components used by Stokvis in a classic AIEE paper pub- I . . BRITTA! ' : RE~1ARKABLE CAREER OF EDITH CLARKE 187

lished in 1918 [18]. Fortescue explained that any system tors were used per phase in a three-phase power line. She of three vectors (a term then commonly used for complex mentioned that there had been a revival of interest in such quantities or phasors) could be expressed by three sets of systems and their potential to increase line capacity. She balanced components that he called symmetrical coordi included equations and graphs for lines having from two nates. During the discussion of Fortescue's paper, Vladi to five conductors per phase in various geometrical ar mer Karapetoff suggested that symmetrical components rangements such as three configured as an equilateral tri was a "more correct and descriptive term" for the method angle, four as a square, or five in a vertical collinear array. than symmetrical coordinates. The method was dissemi In her analysis, she compared multiple conductors to sin nated and extended to practical problems in the field of gle conductors with regard to the charging current, no power systems in a number of papers published during the load voltage, and power capacity. She again employed · 1920's. In 1925, R. D. Evans published a paper in Elec symmetrical components in the analysis. trical World on the use of symmetrical components in the A differential analyzer at the Moore School of Electrical determination of short-circuit currents [19]. He also ex Engineering of the University of Pennsylvania was used to plained how the method could be used in conjunction with collect data for an AIEE paper by Clarke and two co-au the so-called "calculating board" that was used to simu thors presented in January 1938 [25]. Her co-authors were late actual power systems. Calculating boards or tables Cornelius N. Weygandt, an instructor at the Moore had been used at least since 1916 to determine short-cir School, and Charles Concordia, a GE colleague. The dif cuit currents in alternating-current systems by simulation ferential analyzer at the Moore School was patterned after using banks of rheostats to represent actual generators, the machine developed by Vannevar Bush, Harold Hazen, lines, and loads [20]. Also published in 1925 was a paper and associates at MIT, by 1930, and it set the stage for by Sadatoshi Bekku, a Japanese engineer, that discussed the famous ENIAC, the electronic digital computer de I the use of symmetrical components and the calculating veloped at the Moore School during World War II. The I: table to determine short-circuit currents in three-phase Moore School differential analyzer had been undertaken !,:1 power systems [21]. Charles F . Wagner and R. D . Evans as an emergency relief project with funding from the Civil I subsequently published a tutorial series on symmetrical Works Administration and Federal Emergency Relief ',, components in the Electric Journal during the period from Administration and had employed 120 men at the peak March 1928 to November 1931. during its construction. The designers were encouraged Clarke presented her first paper using the method of to maximize the " ratio of labor cost to material cost" with symmetrical components at an AIEE meeting in March the result that many parts of the machine were designed 1931 [22]. She extended the method that others had used to be made by machinists assigned to the project that might to determine the effect of single faults to the analysis of have been purchased more cheaply. Somewhat ironically, - two or more simultaneous faults involving a three-phase the ultimate purpose of the machine itself was to reduce transmission system. She mentioned that a calculating ta greatly the labor of engineers and human computors [26]. ble or the MIT network analyzer could be used to facilitate The paper by Clarke and her co-authors dealt with the the analysis. During the discussion of Clarke's paper, an problem of voltage surges produced by unbalanced faults engineer employed by a California utility commented that and how overvoltages could be reduced by means of so the paper had "great practical value" and represented "an called "amortisseur windings" or damper windings on the important step forward in protection engineering." Har generators supplying the fault current. The authors men old W. Bibber credited Clarke with pointing the way to the tioned that the use of the differential analyzer had enabled solution of "almost any problem involving simultaneous them to calculate a wide variation in the key parameters faults that might arise." Clarke and Bibber began work on that would not have been feasible in field tests or without a book on symmetrical components the following year but the aid of the calculating machine. did not complete the project although portions of the man Clarke contributed significantly to the development of uscript eventually were incorporated in Clarke's book the method of modified symmetrical components. She pu bli shed in 1943. Harold L. Hazen, a Professor at MIT published a tutorial paper in the GE Review in 1938 on the \vho had been in charge of the network analyzer project subject of alpha, beta, and zero components that were de that had been supported financially by GE, was in the au~ rived from the conventional symmetrical components [27] . dience when Clarke's paper was presented and gave a brief She included several examples of problems that were sim commentary on the machine and its use in power system plified by the use of the modified components. She later analysis. The MIT network analyzer was regarded as " the credited Walter W. Lewis with having used the modified most advanced system for transmission network analysis components without the names in a paper published in in the world" in the early 1930's, and approximately 40 1917. The modified components were also sometimes of the machines were built for use by utilities , electrical known as x, y, and z components. In her book published manufacturers , and engineering schools [23] . in 1943, Clarke observed that the definitions and notation Clarke·s third AIEE paper presented in May 1932 was for the modified components still were "not definitely es awa rded a prize as the best paper of the year in the north tablished by usage." She devoted a full chapter of her book ern district of the AIEE [24]. The subject was multiple to the use of alpha, beta, and zero components in the anal conductor transmission lines where two or more conduc- ysis of three-phase systems [28] . 188 . IEEE TRANSACTIONS ON EDUCATION. VOL. E-28. NO . .\. NOVEMBER 1985

In January 1941, Clarke and Selden B. Crary, a GE en Edith Clarke's engineering career had as its central gineer, presented a joint paper at an AIEE meeting in theme the development and dissemination of mathematical Philadelphia, PA, that was awarded a prize as the best methods that tended to simplify and reduce the time spent AIEE paper of the year [29]. Their paper contained a com in laborious calculations in solving problems in the design prehensive analysis of the problem of stability on long and operation of electrical power systems. She translated transmission lines with much of the data being obtained what many engineers found to be esoteric mathematical using a network analyzer. They considered lines with methods into graphs or simpler forms during a time when lengths of up to a full wave length at 60 Hz, and discussed power systems were becoming more complex and when eight different methods that had been proposed to enhance the initial efforts were being made to develop electrome stability of long lines. Their analysis indicated that the use chanical aids to problem solving. As a woman who worked of series capacitance was the most effective method of in an environment traditionally dominated by men, she maintaining stability on long alternating current lines of demonstrated effectively that women could perform at least up to 700 miles in length. as well as men if given the opportunity. Her outstanding In 1943, Clarke published the first of a planned two achievements provided an inspiring example for the next volume work on the circuit analysis of alternating-current generation of women with aspirations to become career power systems. The book was based on her notes for lec engineers. tures given over a period of many years to engineers of REFERENCES the Central Station Engineering Department of GE and [l] M. W. Rossiter, Wom en Scientists in America. Baltimore, MD: The was intended for use as a text by engineering schools or Johns Hopkins University Press, 1982, p. 9. as a reference for power system engineers. The principal [2] - , "'Women's work' in science, 1880-1910, .. ISIS, vol. 71 , pp. focus of the book was on the use of symmetrical compo 381-387, 1980. [3] A. C. Goff, "Women can be engineers," Youngstown, OH, 1946, nents and modified symmetrical components in the solu Edith Clarke File, General Electric Company, Schenectady, NY. I am tion of problems related to polyphase power transmission. indebted to George Wise fo r providing me with a copy of this and In the introduction to the book, she wrote that the prob other documents from the Clarke File. [4] J. E. Brittain. "Tht: introduction of the loading coil: George A. Camp lems encountered by the power transmission engineer at bell and Michael I. Pupin ," Technol. Culture, vol. 11 , pp. 36-57, 1970. any given time could be divided into three classes. Prob [5] L. Hoddeson, " The emergence of basic research in the Bell System, lems of the first class could be "solved analytically by well 1875-1915," Tec/11101. Culture , vol. 22, pp. 512-544, 1981. Also see, Th e Collected Paper of George Ashley Campbell. New York: The known methods in general use" in a reasonable amount of American Telephone and Telegraph Company, 1937, p. 533. ·time. She continued that problems of the _second class "can [6] The Col/ec1ed Papers of George Ashley Ca171 pbe/l. New York: The be solved analytically and the various factors evaluated, American Telephone and Telegraph Company, 1937, p. 236. f?r?i) __E .• ~rittain, "Kennelly u?ses complex quantities to simplify AC anal- but the time and labor required are excessive." For prob \../ys1s, Pr2,c. IEEE.J. vol. 1-, p. 462, 1984. · lems of the third class, she noted that "there is no known [8] T. P. Hughes, Networks of Power. Baltimore, MD: The Johns Hop analytic method of evaluating all the factors involved" and, kins University Press. 1983, pp. 376-377. Also see S. Bennett, "Har old Hazen and the theory and design of servomechanisms, " Univ. therefore, "a different and independent problem is en Sheffield, England, Res. Rep. 270, Nov. 1984. countered with each change in given conditions." She ob [9] P. L. Alger, The Human Side of Engineering. Schenectady, NY: Mo served that the calculating table, the network analyzer, and hawk Development Service, Inc., 1972, pp. 71-72 . W. Campbdl, "The. protection of steam-turbine disc wheels from axial vibration," Trans. the methods of symmetrical components had helped move ASME, vol. 46, pp. 31-140, 1924. W. Campbell. " Tangential vibration many problems from class two to class one and some from of steam turbine buckets," Trans. ASME, vol. 47, pp. 643-654, 1925. class three to class two. She pointed out that many prob A . L. Kimball, Jr. , and E. H. Hull, "Variation phenomena of a loaded unbalanced shaft while passi ng through its critical speed," Tran s. lems that involved nonlinear parameters remained in the ASME, vol. 47, pp. 673-688, 1925. third class , although a few such problems had been solved [10] "Calculator," U.S. Patent 1 552 113, Sept. l, 1925. by means of the differential analyzer or a transient ana [11] E. Clarke , "A_!ransmi ssion line calculato,r," General Electric Rev., vol. 26, pp. 380-390, 1923. lyzer [30]. [1 2] Goff, "Women can be °'eiigineers ," Edith Clarke File, pp. 55-57. [ 13] "Electrical power transmission," U.S. Patent l 641 737, Sept. 6, 1927. A PROFESSOR OF ELECTRICAL ENGINEERING [ 14] E. Clarke, "Steady-s tate stability in transmission systems-calculation by means of equivalent circuits or circle diagrams, " Trans. A/EE, vol. Clarke retired from GE on July 31, 1945 but accepted 45, pp. 22-41, 1926. an opportunity to teach electrical engineering at the Uni [15] -, "Steady-state stability in transmission systems-calcul ati on by versity of Texas in the Spring of 1947. Her initial intention means of equivalent circuits or circle diagrams," Trans. A/EE, vol. 45, pp. 80- 86. 1926. -- was to teach for only four months, but she returned to [16] - , " Simplified transmission line calculations." General Electric teach in the Fall and continued to teach at the University Rev., vol. 29, pp. 321-329, 1926. until 1956. In 1948, she became the first woman to be [17] L. G. Stokvis, "Analysis of unbalanced three-phase systems," Elec trical World, vol. 65, pp. 1111-1115, 1915. Also see, E. Clarke, Circuit made a Fellow of the AIEE. The second volume of her Analysis of A-C Power Sys1ems. New York: Wiley. 1943, p. 54. work on power system analysis was published in 1950. She [18) C. L. Fortescue, "Method of symmetrical co-ordinates applied to the was honored by the Society of Women Engineers in 1954 solution of polyphase networks," Trans. A/EE, vol. 37, pp. 1027-1115, 1918. for her significant contributions to engineering. She also [19] R. D. Evans , " Finding single-phase short-circuit currents on calcu became the first alumna member of the Tau Beta Pi and lating boards," Electrical World, m l. 85. pp. 760-765, 1925. Eta Kappa Nu scholastic honorary societies. She again re [20) W. W. Lewis, "Calculation of short-circuit currents in alt ern ating current systems, General Electric Rev. , vol. 22. pp. 140-145, 1919. tired at age 73 in 1956 and returned to her native Mary W. W. Lewis , "A new short circuit calculating table," General Elec- land where she died on October 29, 1959 [31]. tric Rev. , vol. 23, pp. 669-671, 1920. - BRITTAIN: REMARKABLE CAREER OF EDITH CLARKE 189

[21] S. Bekku, " Calculation of short-circuit ground currents on three-phase listed items are all from the Edith Clarke File. Also see an obituary power networks using the method of symmetrical co-ordinates," Gen in E!ec. Eng., vol. 79, p. !08,·1960, and Who's Who in Engineering. eral £/~ Rev., vol. 28, pp. 472-478, !2E· p. 439, 1954. [22] E. Clarl

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