THE ANNALS OF'THE COMPUTATION LABORATORY OF HARVARD UNIVERSITY

THE ANNALS OF'THE COMPUTATION LABORATORY OF HARVARD UNIVERSITY

VOLUME XXVI

THE ANNALS :OF'THE COMPUTA.TION LABORATORY OF HARVARD UNIVERSITY

I A Manual of Operation for the Automatic Sequence Controlled Calculator 1946 II Tables of the Modified Hankel Fun~tion~ of Order One-Third and of Their

Derivatives 1945

III Tables of the Bessel Functions of the First Kind of Orders Zero and One . 1947 IV Tables of the Bessel Functions of the First Kind of Orders Two and Three 1947 V Tables of the Bessel Functions of the First Kind of Orders Four, Five, and Six. 1947 VI Tables of the Bessel Functions of the First Kind of Orders Seven, Eight, and

Nine 1947

I

VII Tables, of the Bessel Functions of the First Kind of Orders Ten, Eleven, and

Twelve , 1947

VIII Tables of the Bessel Functions of the First Kind of Orders Thirteen, Fourteen,

and Fifteen 1947

IX Tables of the Bessel Functions of the First Kind of Orders Sixteen through

Twenty-Seven 1948

X Tables of the Bessel Functions of the First Kind of Orders Twenty-Eight through

Thirty-Nine . 1948

XI Tables of' the Bessel Functions of the First Kind. of Orders Forty through

Fifty-One 1948

XII Tables of the Bessel Functions of the First Kind of Orders Fifty-Two through

Sixty-Three . 1949

XIII Tables of the Bessel Functions of the First Kind of Orders Sixty-Four through

Seventy-Eight 1949

XIV Tables of the Bessel Functions of the First Kind of Orders Seventy-Nine through

One Hundx:ed Thirty-Five . ' 1951

XV (In preparation)

XVI Proceedings of a. Symposium on Large-Scale Digital Calculating Machinery 1948

XVII Tables for the Design of Missiles 1948

XVIII Tables of Generalized Sine- and Cosine-Integral Functions: Part I 1949 XIX Tables of Generalized Sine- and Cosine:-Integral Functions: Part II 1949

XX Tables of Inverse Hyperbolic Functions . 1949

XXI Tables of Generalized Exponential-Integral Functions

XXII Tables of the Function si: cP and of its First Eleven Derivatives XXIII . (In preparation)

1949 1949 .

,XXIV Description of a Relay Calculator 1949

XXV (In preparation)

XXVI Proceedings of a Second Symposium on Large-Scale Digital Calculating

Machinery 1951

XXVII Synthesis of Electronic Computing and Control Circuits 1951

PROCEEDINGS OF A SECOND SYMPOSIUM ON LARGE-SCALE

DIGITAL CALCULATING MACHINERY

Jointly Sponsored by The Navy Department Bureau of Ordnance and Harvard University

at The Computation Laboratory 13-16 September 1949

CAMBRIDGE, MASSACHUSETTS

HARVARD UNIVERSITY PRESS

~95I

LONDON : GEOFFREY CUMBERLEGE

OXFORD UNIVERSITY PRESS

The opinions or assertions contained herein are the private ones of the writers and are not to be, construed as official or reflecting the views of the Navy Department or the naval service at large.

Composition by The Pitman Press, Bath, England

Printed by offset lithography by the Murray Printing Company, Wakefield, Massachusetts, U.S.A.

PREFACE

InJanuary 1947 the Bureau of Ordnance of the United States Navy and Harvard Univer- sity together sponsored a Symposium on Large-Scale Digital Calculating Machinery as a means of furthering interest in the design, construction, application, and operation of computing machinery. This meeting was attended by over three hundred people, nearly four times the originally expected attendance, and by popular aemand the proceedings were published as Volume XVI of the Annals of the Computation Laboratory.

At the Oak Ridge meeting on computing machinery in April 1949, Mina Rees and John Mauchly, representing the Association for Computing Machinery, suggested that another symposium should be held at Harvard summa~izing. recent and current developments. The staff of the Computation Laboratory had already considered this possibility in connection with the announcement of the completion of Mark III Calculator, and were delighted with the suggestions of Dr. Rees and Dr. Mauchly. Accordingly, the Bureau of Ordnance was again invited to join Harvard University in sponsoring a second symposium with emphasis on the application of digital calculating machinery.

From experience with the first symposium, it was expected that. perhaps three hundred people might attend. The response of more than seven hundred participants clearly indicated the rapidity with which the field of automatic computation is growing.

T~is volume, the twenty-sixth of the Annals of the Computation Laboratory, contains all the papers presented at the second symposium except one. Two of the speakers, Manuel S.

Vallarta and Frederick V. Waugh, found at the last minute that they were unable to attend.

However, their papers were received and were read by J. Curry Street and Leon Moses, respectively, both of Harvard University. Because of the tremendous editorial difficulties experienced with the proceedings of the first symposium, each speaker at the second was requested to supply his manuscript in advance, in order to avoid dependence upon transcription from sound recording. Thirty-nine papers are herein published essentially as submitted.

Thus the work required to prepare this volume for publication was greatly reduced. However, it was necessary to redraw many of the illustrations for offset reproduction; this was done by Carmela M. Ciampa, assisted by Paul Donaldson, photographer of Cruft Laboratory, Harvard University.

Since the symposium was held iIi September, prior to the opening of the fall term, it was possible to make use of the dormitories in the Harvard Yard and the dining facilities of the Harvard Union. Arthur Trottenberg of Harvard University supervised arrangements for the use of these facilities and other accommodations. Preparation of the program and regis-

tration lists and the registration of the members of the symposium after their arrival were carried out by Betty Jennings, Jacquelin Sanborn, Jean Crawford, and Holly Wilkins. It is

v

PREFACE

a pleasure to acknowledge the cooperation of Edmund C. Berkeley, secretary of the Association for Computing Machinery, in this connection.

The staff of the Computation Laboratory wishes to express its appreciation to the members of the symposium for their attendance and for their participation in the discussions, to the chairmen of the several sessions for their assistance, and to the speakers not only for their addresses during the symposium but also for their cooperation in preparing the manuscripts of their papers.

The staff also wishes to express its gratitude to the Bureau of Ordnance and to its repre- sentatives, Captain G. T~ Atkins and Mr. Albert Wertheimer, for many years of pleasant association throughout the building of Mark II and Mark III Calculators, for their continued i~terest and help, and for making possible both the Second Symposium on Large-Scale Digital Calculating Machinery arid the publication of its proceedings.

Cambridge, Massachusetts May 1950

VI

HOWARD H. AIKEN

PROGRAM OF THE SYMPOSIUM MEMBERS OF THE SYMPOSIUM.

FIRST SESSION: Opening Addresses

CONTENTS

SECOND SESSION: Recent Developments in Computing Machinery BANQUET

THIRD SESSION: Recent Developments in Computing Machinery FOURTH SESSION: Numerical Methods.

FIFTH SESSION: Computational Problems in Physics . SIXTH SESSION: Aeronautics and Applied Mechanics . SEVENTH SESSION: The· Economic and Social Sciences EIGHTH SESSION: Discussion and Conclusions

Vll

. ix xv

I

9

7

¹

81 135

213

261

3²¹ 363

PROGRAIvI

FIRST SESSION Tuesday, September 13, 1949

10: 30 A.M. to 12: 00 P.M.

OPENING ADDRESSES Presiding

Howard H. Aiken

Director

of

the Computation Laboratory

7

Edward Reynolds .3 Administrative Vice President of Harvard University

Rear Admiral.F. I. Entwistle, USN

S-

Director of Research, Bureau

of

Ordnance

SECOND SESSION Tuesday, September 13, 1949

2:00 ^P.M. to 5:00 ^P.M.

RECENT DEVELOPMENTS IN COMPUTING MACHINERY Presiding

Mina Rees, Office

of

Naval Research 1. The Mark III Calculator II

Benjamin L. Moore Harvard University 2. The Bell Computer, Model VI '),0

Ernest G. Andrews Bell Telephone Laboratories 3. An Electrostatic Memory System .3'1>-

J.

Presper Eckert, Jr.

Eckert-Mauchly Computer Corporation

4. The Digital Computation Program at Massachusetts Institute of Technology

Lfl-

vv wI:

Jay W. Forrester .-

Massachusetts Institute

of

Technology IX

SECOND SESSION--CONTINUED

5. The Raytheon Electronic Digital Computer _b (J

. Richard M. Bloch Raytheon Manufacturing Company 6. A General Electric Engineering Digital Computer

t 5""

Burton R. Lester .General Electric Company

BANQUET

Tuesday, September 13, 1949 7:00 P.M.

Toastmaster Edward·A. Weeks, Jr.

Editor of The Atlantic Monthly Speaker

William S. Elliott

Research Laboratories of Elliott Brothers (London) Limited

"The Present Position of Computing-Machine Development in England'· 7

If

THIRD SESSION Wednesday, September 14, 1949

9:00 A.M. to 12:00 P.M.

RECENT DEVELOPMENTS IN COMPUTING MACHINERY

Presiding

E. Leon Chaffee, Harvard University 1. Semiautomatic Instruction on the Zephyr

4'

~

H. D. Huskey

National Bureau of Standards, Institute for Numerical Analysis 2. Static Magnetic Delay Lines

q

1

. Way Dong Woo Harvard University

x

THIRD SESSION-cONTINUED

3. Coordinate Tubes for Use with Electrostatic Storage Tubes

'1 b

R. S. Julian and A. L. Samuel University

of

Illinois 4. Basic Aspects of Special Computational Problems I JE)'

Howard T. Engstrom Engineering Research Associates, Inc.

5. Electrochemical Computing Elements

111

John R. Bowman Mellon Institute

'-ot)~~(tf .s~~,rl(rx ,111111

6. EDVAC Transformation Rules I ~,

GeoJ;ge W. Patterson University of Pennsylvania

FOURTH SESSION Wednesday, September 14, 1949

2:00

P.M. to

5:00

P.M.

NUMERICAL METHODS

Presiding

Raymond C. Archibald, Brown University

1. Notes on the Solution of Linear Systems Involving Inequalities I -S 7 George W. Brown

Rand Corporation

2. Mathematical Methods in Large-scale Computing Units 1£.1-) D. H. Lehmer

University

of

California 3. Empirical Study of Effects of Rounding Errors I if

7

C. Clinton Bramble

U.S. Naval Proving Ground, Dahlgren, Virginia

". Numerical Methods Associated with Laplace's Equation IS" 1- . W. E. Milne

Institutefor Numerical Anafysis, UCLA and Oregon State College

Xl

FOURTH SESSION-cONTINUED

5. An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differentia and Integral Operators I h 4

Cornelius Lanczos

Institute for Numerical Anarysis, UCLA 6. The Monte Carlo Method 1--v7

S. M. Ulani

Los Alamos Scientific Laboratory

FIFTH SESSION Thursday, September 15, 1949

9: 00 A.M. to 12: 00 P.M.

COMPUTATIONAL PROBLEMS IN PHYSICS

Presiding

Karl K. Darrow, Bell Telephone Laboratories

1. The Place of Automatic Computing Machinery in Theoretical Physics

vIS-

Wendell H. Furry . Harvard University

2. Double Refraction of Flow and the Dimensions of Large Asymmetric Molecules 7--1

q

Harold A. Scheraga, John T. Edsall, and J. Orten Gadd, Jr.

Cornell University, Harvard Medical School, and Computation Laboratory

of

Harvard University 3. L-Shell Internal Conversion ').. Lf'O

Morris E. Ro~e

Oak Ridge National Laboratory

4. The Use of Calculating Machines in the Theory of Primary Cosmic Radiation 7 ... t.!',{- Manuel S. Vallarta

University

of

Mexico

(read by J. C. Street, Harvard University) .-. 5. Computational Problems "in Nuclear Physics

,,50

Herman Feshbach Massachusetts Institute qf Technology

XlI

SIXTH SESSION Thursday, September 15, 1949

2: 00 P.M. to 5: 00 P.M.

AERONAUTICS AND ApPLIED MECHANICS

Presiding

Harald M. Westergaard, Harvard Universi~v

1. Computing Machines in Aeronautical R;esearch 1--l3 R. D. O'Neal

University

of

Michigan 2. Problem of Aircraft Dynamics "1. 71

Everett T. Welmers Bell Aircraft Corporation

3. A Statistical Method for Certain Nonlinear Dynamical Systems J... ~

I

George R. Stibitz

Consultant in Applied Mathematics, Burlington, Vermont 4. Combustion Aerodynamics "') ... , ~~

Howard W. Emmons Harvard University

5. Application of Computing Machinery to Research of the Oil Industry '2 D_r' Morris Muskat

Gulf Research & Development Company 6. The 603-405 Computer "3 ) ~

William W. Woodbury Northrop Aircraft, Inc.

SEVENTH SESSION Friday, September 16, 1949 .

9:00 A.M. to 12 :00 P.M.

THE ECONOMIC AND SOCIAL SCIENCES

Presiding

Edwin B. Wilson, Office

of

Naval Research

1. Application of Computing Machinery to the Solution of Problems of the Social Sciences

J

J..

3

Frederick Mosteller Harvard University

XUl

SEVENTH SESSION-cONTINUED

2. Dynamic Analysis of Economic Eq~ilibrium ']. "3

'3

Wassily W. Leontief Harvard Univer-fity

3. Some Computational Problems in Psychology

'33 r:r

Ledyard R. Tucker

Educational Testing Service, Princeton, New Jersey 4. Computational Aspects of Certain Econometric Problems ~~/-r

Herman Ohernoff University

of

Chicago 5. PhysIology and Computing Devices ~ 51

William J. Crozier Harvard University 6. The Science of Prosperity -~ fj 7

Frederick V. Waugh Council of Economic Advisers . (read by Leon Moses, Harvard University)

EIGHTH SESSION

Friday, September 16, 1949

2:00 P.M. to 4:00 P.M.

DISCUSSION AND CONCLUSIONS

Presiding

Willard E. Bleick, U.S. Naval Academy Post Graduate School 1. The Selectron "]

b

b

Jan Rajchman Radio Corporation

of

America

2. Traits Caracteristiques de la Calculatrice de la Machine

a

Calculer Universelle. de l'Institut Blaise Pascal -; 7 tf

Louis Couffignal lnstitut Blaise Pascal

(read by Leon Brillouin, Harvard University) 3. The Future of Computing Machinery J

cr

7

Louis N. Ridenour University qf Illinois

* * *

OPEN DISCUSSION

XIV

MEMBERS OF THE SYMPOSIUM

MATTHEW C. ABBOTT, Engineer, W. S. MacDonald Company, Inc., Cambridge MILTON ABRAMOWITZ, Numerical Mathematics Service, New York

CHARLES W. ADAMS, Massachusetts Institute of Technology, Cambridge

HOWARD H. AIKEN, Professor of Applied Mathematics and Director of the Computation Laboratory, Harvard University, Cambridge

MOE LAWRENCE AITEL, Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts J. CHARLES AJEMIAN, Massachusetts Institute of Technology, Cambridge

MILTON ALDEN, President, Alden Products Company, Brockton, Massachusetts

SAMUEL N. ALEXANDER, Chief, Electronic Computers Section, National Bureau of Standards, Washington, D.C.

WILLIAM R~ ALLEN, Computation Laboratory, Harvard University, Cambridge JAMES C. ALLER, LT., USN, Medford, Massachusetts

R. K. ALLERTON, JR., Public Relations, Underwood Corporation, New York FRANZ L. ALT, National Bureau of Standards, Washington, D.C.

BIAGIO F. AMBROSIO, Engineer, National Bureau of Standards, Los Angeles, California FREDERICK J. ANDERSON, Development Engineer, Sylvania Electric Products, Inc., Boston LOWELL O. ANDERSON, Physicist, Naval Ordnance Test Station, China Lake, California RUTH K. ANDERSON, Mathematician, Naval Ordnance Test Station, China Lake, California ERNEST G. ANDREWS, Technical Staff, Bell Telephone Laboratories, New York .

THOMAS B. ANDREWS, JR., Aeronautic Research Sci~ntist, National A~visory Committee for Aeronautics, Langley Aeronautical Laboratory, Hampton, Virginia

FRANK H. ANDRIX, Engineer, Bell Aircraft Corporation, Buffalo, New York LEONARD J. ANGUS, Consultant, Manhasset, Long Island, New York

RAYMOND C. AItCHIBALD, Professor, Brown University, Providence, Rhode Island

WALTER E. ARNOLDI, Project Engineer, Hamilton Standard Propellers, Wethersfield, Con- necticut

ELEANOR ASMUTH, Badger, Wi"sconsin

JOHN ASMUTH, Instructor, University of Wisconsin, Madison, Wisconsin

ALBERT A. AUERBACH, Design Engineer, Eckert-Mauchly Computer Corporation, Philadelphia, Pennsylvania

ISAAC L~ AUERBACH, Senior Engineer, Burroughs Adding Machine Company, Philadelphia, Pennsy I vania

DONALD E. BABCOCK, Republic Steel Corporation, Youngstown, Ohio

PAUL H. BACKUS, Lt.-Cdr., USN, Chief, Ballistics Research Section, Bureau of Ordnance, Washington, D.C .. '

XV

MEMBERS OF THE SYMPOSIUM

GEORGE A. BALL, Research Assistant, Harvard University, Cambridge

STANLEY S. BALLARD, Professor of Physics, Tufts College, Medford, Massachusetts MELVIN D. BALLER, Engineer, Air Force Cambridge Research Laboratories, Cambridge ROBERT M. BARRETT, Electronic Engineer, Air Force Cambridge Research Laboratories,

Cambridge

JEAN J. BARTIK, Eckert-Mauchly Computer Corporation, Philadelphia, Pennsylvania

STEPHEN D. BATCHELOR, Engineer, Raytheon Manufacturing Company, Waltham, Massa- chusetts

DWIGHT W. BATTEAU, Research Assistant, Harvard University, Cambridge D. T. BELL, Bell Telephone Laboratories, Inc., New York

ALBERT 1. BELLIN, Assistant Professor, Harvard University, Cambridge

LAWRENCE W. BE,LOUNGIE, Raytheon Manufacturing Company, Waltham, Massachusetts J. L. BELYEA, Lt., Royal Canadian Navy, Ottawa, Ontario, Canada

ALBERT A. BENNETT, Professor of Mathematics, Brown University, Providence, Rhode Island

ROBERT J. BERGEMANN, JR., Electronics Engineer, Office of Naval Research, Boston STEFAN BERGMAN, Harvard University, Cambridge

EDMUND C. BERKELEY, President, E. C. Berkeley and Associates, New York

ERIC W. ,BETH, Physicist, Geophysical Research Directorate, Air Force Cambridge Research Laboratories, Cambridge

VICTOR E. BIEBER, JR., Aeronautical Engineer, Bureau of Aeronautics, Washington, D.C.

WALTER J. BINGEL, Mechanical Engineer, Raytheon Manufacturing Company, Waltham, Massach usetts

ROBERT W. BIRGE, Nuclear Laboratory, Harvard University, Cambridge ERNEST W. BIVANS, Air Force Cambridge Research Laboratory, Cambridge GERRIT A. BLAAUW, Computation Laboratory, Harvard University, Cambridge

PAUL B. BLACK, Head of Equipment Engineering, Sylvania Electric Products, Inc., Boston BARTOLOME C.' BLANCO, Harvard University, Cambridge

WILLARD E. BLEICK, Professor, U.S. Naval Postgraduate School, Annapolis, Maryland ALAN BLOCH, Arma Corporation, Brooklyn, N ew York

RICHARD M. BLOCH, Manager, Analytical Section, Raytheon Manufacturing Company, Newton, Massachusetts

H. W. BODE, Bell Telephone Laboratories, New York GEORGE A. W. BOEHM, Science Editor, Newsweek, New York

, JOHN M. BOERMEESTER, John Hancock Mutual Life Insurance Company, Boston MORTON BOISEN, Statistician, Bureau of the Census, Washington, D.C.

ROBERT N. BONNER, Junior Research Chemist, Carter Oil Company, Tulsa, Oklahoma RICHARD C. BOOTON; JR., Research Assistant, Differential Analyzer Computer Laboratory',

Massachusetts Institute of Technology, Cambridge

GUY F. BOUCHER, Computation Laboratory, Harvard University, Cambridge XVI

MEMBERS OF THE ,SYMPOSIUM

JOHN R. BOWMAN, Head, Department of Research in Physical Chemistry, Mellon Institute,

Pittsburgh, Pennsylvania .

HUGH R. BOYD, Research Engineer, Massachusetts Institute of Technology, Cambridge HENRY B. BRAINERD, Massachusetts Institute of Technology, Cambridge

C. CLINTON BRAMBLE, Director of Computation Ballistics, U.S. Naval Proving Ground, Dahlgren, Virginia

C. S. BRAND, Arnold Engineering Company, Chicago, Illinois

LEON BRILLOUIN, International Business Machines Corporation, New York PAUL BROCK, Reeves Instrument Corporation, New York

DOUGLAS A. BROWN, Assistant Director, Harvard University News Office, Harvard University, Cambridge

GEORGE W. BROWN, Rand Corporation, Santa Monica, California

J. H. BROWN, Research Engineer, Massachusetts Institute of Technology, Cambridge

ROBERT G. BROWN, Operations Evaluation Group, CNO, Navy Depar.tment, Washington, D.C.

T. H. BROWN, Professor, Harvard Business School,Harvard University, Boston

T. WISTAR BROWN, Sales Manager, Eckert-Mauchly Computer Corporation, Philadelphia, Pennsylvania

WILLIAM FULLER BROWN, JR., Research Physicist, Sun Oil Company, Newtown Square, Pennsylvania

JOSEPH A. BRUSTMAN, Chief Engineer, Remington Rand, Inc., South Norwalk, Connecticut EDWARD C. BRYANT, Student, Boston University, Boston

RALPH W. BUMSTEAD, Patent Attorney, Westfield, New Jersey

RICHARDS. BURINGTON, Director, Evaluation and Analysis Group, Bureau of Ordnance, Washington, D.C.

WILLIAM BURKHART, Monroe Calculating Machine Company, Orange, New Jersey ROBERT J .. BURNS, Computation Laboratory, Harvard University, Cambridge ROBERT R. BUSH, Research Fellow, Harvard University, Cambridge

SAMUEL H. CALDWELL, Professor of Electrical Engineering, Massachusetts Institute of Tech- nology, Cambridge

FRANK

J.

CAMPAGNA, Computation Laboratory, Harvard University, Cambridge

ELIZABETH JEAN CAMPBELL, Computer,. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge

R. E. CAMPBELL, Liaison Engineer, Signal Corps _Engineering Laboratories, Massachusetts Institute of Technology, Cambridge

ROBERT V. D. CAMPBELL, Department Supervisor, Burroughs Adding Machine Company,

Philadelphia, Pennsylvania. '

E. W. CANNON, Mathematician, National Bureau of Standards, Washington, D.C.

JOEL CARROLL, Geodetic Engineer, U.S. Geological Survey, Washington, D.C.

JOHN B. CARROLL, Assistant Professor of Education, Harvard University, Cambridge

XVll

MEMBERS OF THE SYMPOSIUM

ELBERT P. CARTER,Senior Engineer, Transducer Corporation, Boston

CARL C. CHAMBERS, A~.ting Dean, University of Pennsylvania, Philadelphia, Pennsylvania GEORGE C. CHASE, Research Engineer, Monroe Calculating Machine Company, Orange,

New Jersey

JOSEPH CHEDAKER, Senior Engineer, Burroughs Adding Machine Company, Philadelphia, Pennsylvania

T. C. CHEN, Senior Engineer, Burroughs Adding Machine Company, Philadelphia, Penn- sylvania

HERMAN CHERNOFF, Research Associate, Cowles Commission, University of Chicago, Chicago, Illinois

ALFRED C. CHEVERIE, Computation Laboratory, Harvard University, Cambridge BENJAMIN F. CHEYDLEUR, Mathematician, U.S. Bureau of Ordnance, Washington, D.C.

HENRY W. F. CHIN, Assistant Mechanical Engineer, Raytheon Manufacturing Company, Newton, Massachusetts

MANUEL P. CHINITZ, Mathematician, U.S. Naval Proving Ground, Dahlgren, Virginia ALLEN G. CHRISTENSEN, Computation Laboratory, Harvard University, Cambridge

THOMAS J. CHRISTMAN, Lt., USN, Post-graduate Student, Massachusetts Institute of Tech- nology, Cambridge

J. C. CHU, Senior Scientist, Argonne National Labora.tory, Chicago, Illinois CARMELA M. CIAMPA, Computation Laboratory, Harvard U.niversity, Cambridge

A. G. CLAVIER, Assistant Technical Director, Federal Telecommunication Laboratories, Nutley, New Jersey

GERALD M. CLEMENCE, Director, Nautical Almanac, U.S. Naval Observatory, Washington, D.C.

R.F. CLIPPINGER, Computing Laboratory, Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland

A. M. CLOGSTON, Bell Telephone Laboratories, Murray Hill, New Jersey RICHARD P. COATES, Computation Laboratory, Harvard University, Cambridge

TODD D. COCHRAN, JR., Development Engineer, Eastman Kodak Company, Rochester, New York

R. C. COILE, Operations Evaluation Group, Office of the Chief of Naval Operations, Navy Department, Washington, D.C.

CHARLES F. COIT, Senior Engineer, Raytheon Manufacturing Company, Newton, Massa- chusetts

ARNOLD A. COHEN, Senior Engineer, Engineering Research Associates, Inc., St. Paul, Minnesota CHARLES J., COHEN, Mathematician, Naval Proving Ground, Dahlgren, Virginia

JOHN J. CONNOLLY, Engineering Supervisor, Teleregister Corporation, New York CHARLES A. COOLIDGE, JR., Computation Laboratory, Harvard University, Cambridge JOHN M. COOMBS, Director of Development, Engineering Research Associates, St. Paul.

Minnesota

XVlll

MEMBERS OF THE SYMPOSIUM

GERALD COOPER, Research Assistant, Massachusetts Institute of Technology, Cambridge CHARLES L. CORDERMAN, Research Assistant, Massachusetts Institute of Technology, Cam-

bridge

DOUGLAS S. CRAIG, Second Vice-President, Metropolitan Life Insurance Company, New York JEAN CRAWFORD, Computation Laboratory, H;;trvard University, Cambridge

JOHN H.· CREDE, Associate Director of Research, Allegheny Ludlum Steel Corporation, Brackenridge, Pennsylvania

. L. P. CROSMAN, Director, Electronic Calculator Research, Remington Rand, Inc., South Norwalk, Connecticut

EDWARD D. CROSS, Director of Engineering, Alden Products Company, Brockton, Massa- chusetts

W. J. CROZIER, Professor, Harvard University, Cambridge

WILLIAM H. CUMMINS, Chief, Classification and Coding Branch, Federal Security Adminis- tration, Washington, D.C.

HASKELL B. CURRY, Professor of Mathematics, The Pennsylvania State College, State College, Pennsy lvania

W. W. CURTIS, Office Supervisor, Aluminium Company of America, Boston

R.J. CYPSER, Instructor, Servomechanisms Laboratory, Massachusetts Institute of Technology, Cambridge

JOHN A. DAELHOUSEN, Staff Member, Massachusetts Institute of Technology, Cambridge EVERETT

J.

DANIELS, Staff Member, Massachusetts Institute of Technology, Cambridge M. DANILOFF, Senior Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts GEORGE B. DANTZIG, Mathematician, US. Air Force Comptroller, Washington, D.C.

KARL K.,DARROW, Physicist, Bell Telephone Laboratories, New York

GERALD W. DAVIS, Electronic Scientist, National Bureau of Standards, Washington, D.C.

MALVIN E. DAVIS, Actuary, Metropolitan Life Insurance Company, New York PHILLIP DAVIS, Mathematician, Harvard University, Cambridge

CHRISTOPHER DEAN, Teaching Fellow, Harvard University, Cambridge

FRANKLIN R. DEAN, Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts J. T. DEBETTENCOURT, Section Manager, Raytheon Manufacturing Company, Waltham,

Massach usetts

L. S. DEDERICK, Associate Director, Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland

GEORGE H. DEPINTO, Harvard University, Cambridge

HENRY DESTEFANO, Harvard University, Cambridge .

JOHN E. DETURK, Senior Engineer, Raytheon Manufacturing Company, Waltham, Massa- chusetts

M. L. DEUTSCH, Physicist, Socony-Vacuum Research Laboratory, Paulsboro, New Jersey A. J. DEVAUD, Engineer, Raytheon Manufacturing Company, 'tValtham, Massachusetts R. L. DEVEER, C. P. Clare and Company, Boston

XIX

MEMBERS OF THE SYMPOSIUM

GEORGE C. DEVOL, Manager, Magnetic Devices Department, Research Laboratory, Reming- ton Rand, Inc., South Norwalk, Connecticut

''''ALTER L. DEVRIES, Actuarial Supervisor, Equitable Life Assurance Society, New York C. B. DEWEY, Vice-President, Reeves Instrument Corporation, New York

ERNEST J. DIETERICH, Junior Engineer, Raytheon Ma.nufacturing Compariy, Waltham, Massachusetts

JOHN D. DILLON,Assistant Chief, Research Services, Air Force, Cambridge Research Labora- tories, Cambridge

BERNARD DIMSDALE, Mathematician, Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland

L. P. DISNEY, Chief, Section of Predictions, U.S. Coast and Geodetic Survey, Washington, D.C.

NATHAN DIVINSKY, Research Associate, Cowles Commission, Chic~go, Illinois

STEPHEN H. DODD, Research Engineer, Massachusetts Institute of Technology, Cambridge CHARLES H. DOERSAM, JR., Mechanical Engineer, Office of Naval Research, Section of

Development Contract, Port Washington, Long Island, New York

FRANCIS W. DRESCH, Assistant Director, Computation and Ballistics, U.S. Naval Proving Ground, Dahlgren, Virginia

L. B. DUMoNT,Engineer, General Electric Company, Lynn, Massachusetts ROBERT F. DUNCAN, Vice-President, John Price Jones Company, New York

S. W. DUNWELL, Future Demands Department, International Business Machines Corporation, New York

J. R. DYER, Colonel, USAF, Staff Officer, Munitions Board, Department of Defense, Wash- ington, D.C.

E. C. EASTON, Dean of Engineering, Rutgers University, New Brunswick, New Jersey

J.

PRESPER ECKERT, JR., Vice-President, Eckert-:NlauchlyComputer Corporation, Phila- delphia, Pennsylvania

W. J. ECKERT, Director, Pure Science, International Business Machines Corporation, New York

ROBERT P. EDDY, Mathematician, Naval Ordnance Laboratory, Silver Spring, Maryland NIELSE. EDLEFSEN, Associate Technical Director, North American Aviation, Santa Monica,

California

JOHN T. EDSALL, Associate Professor of Biological Chemistry, Harvard Medical School, Boston MILTON EFFROS, Management Research, Metropolitan Life Insurance Company, New York ROBERT D. ELBOURN, National Bureau of Standards, ""Vashington, D.C.

PETER ELIAS, Teaching Fellow, Harvard University, Cambridge

WILLIAM S. ELLIOTT, Research "Laboratories of Elliott Brothers (London), Ltd., Borehamwood, Hertfordshire, England

MURRAY ELLIS, Junior Engineer, Raytheon Manufacturing Company, Waltham, Massa- chusetts

xx

MEMBERS OF THE SYMPOSIUM

GEORGE V. ELTGROTH, Vice President, ~ckert-Mauchly Computer Corporation, Philadelphia, Pennsylvania

JOHN O. ELY, Research Associate, Massachusetts Institute of Technology, Cambridge CLAUDE L. EMMERICH, Senior Physicist, Martin-Hubbard Corporation, Cambridge

HOWAR~ EMMONS, Associate Professor, Harvard University, Cambridge

HOWARD T. ENGSTROM, Vice President, Engineering Research Associates, Inc., St. Paul, Minnesota

F. I. ENTWISTLE, Rear Admiral, USN, Director of Research, Bureau of Ordnance, Navy Department, Washington, D.C.

HANS H. ESTIN, Brookline, Massachusetts HELENTY ESTIN, Brookline, Massachusetts

ROBERT R. EVERETT, Research Engineer, Servomechanisms Laboratory, Massachusetts Institute of Technology, Cambridge .

ROBERT G. EVERSEN, Computation Laboratory, Harvard University, Cambridge

HARRIS FAHNESTOCK, Servomechanisms Laboratory, Massachusetts Institute of Technology, Cambridge

R.

M.

FAIRBROTHER, l\fassachusetts Institute of Technology, Cambridge R. S. FALLOWS, Engineer, Sylvania Electric Products, Inc., Boston

JOHN T. FARREN, Computation Laboratory, Harvard University, Cambridge

LOUIS FEIN, Senior Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts ]. H. FELKER, Member of Technical Staff, Bell Telephone Laboratories, Wilippany, New

Jersey

SAMUEL FELTMAN, Ordnance Engineer, Office of Chief of Ordnance, Washington, D.C.

FRED G. FENDER, Professor of Mathematics, Rutgers University, New Brunswick, New Jersey

DAVID T. FERRIER, Lawrence, Long Island, New York

HERMAN FESHBACH, Associate Professor, Massachusetts Institute of Technology, Cambridge F. A. FICKEN, Research Associate, New York University, New York

L. R. FINK, Manager, Electronics Laboratory, General Elec'tric Company, Syracuse, New York

HAROLD A. FINLEY, Manager, Management Research, Metropolitan Life Insurance Company, New York

LYMAN C. FISHER, Naval Ordnance Laboratory, White Oak, Silver Spring, Maryland HARLAND W. FLAGG, Marchant Calculating Machine Company, Boston

DONALD A. FLANDERS, Senior Mathematician, Argonne National Laboratory, Chicago, Illinois

MARGARET I. FLORENCOURT, Research Engineer, Massachusetts Institute of Technology, Cambridge, Massachusetts

WILLIAM B. FLOYD, Sears Roebuck and Company, Chicago, Illinois

J. A. FLYNN, Mechanical Engineer, Cambridge Research Laboratory, Cambridge

XXI

MEMBERS OF T1{E SYMPOSIUM

. JAMES W. FOLLIN, JR., Physicist, Applied Physics Laboratory, Johns Hopkins University, Silver Spring, Mary land

G. DONALD FORBES, Electronics Consultant, Sudbury, l\tlassachusetts . RICHARD E. FORBES, Computation Laboratory, Harvard University, Cambridge

JAY W. FORRESTER, Associate Director, Servomechanisms Laboratory, Massachusetts Institute of Technology, Cambridge

GEORGE E. FORSYTHE, National Bureau of Standards, University of California at Los Angeles, Los Angeles, California

FRANKLIN H. FOWLER, JR., Associate Editor, Product Engineering, New York PHILIP FRANKLIN, Professor, Massachusetts Institute of Technology, Cambri~ge

WALTER J. FRANTZ, Research Engineer, Boeing Aircraft, Seattle, Washington

WILLIAM H. FRATER, Director, Wage Analysis, General Motors Corporation, Detroit, Michigan DAVID FRAZIER, Research Chemist, Standard Oil Company, Cleveland, Ohio

R. 0. FREDETTE,Mathematician, Bureau of Ordnance, Navy Department, Washington, D.C.

F. N. FRENKIEL, Naval Ordnance Laboratory, White Oak, Silver Spring, Maryland A. W. FRICK, Radio Corporation of America, Camden, New Jersey

W. BARKLEY FRITZ, Matherriatician, Ballistics Research Laboratory, Aberdeen, Maryland A. E. FROST, Assistant Equipment Research Engineer, Western Union Telegraph Company,

New York

JOSEPH FUCARILE, Computation Laboratory, Harvard University, Cambridge W. H. FURRY, Associate Professor of Physics, Harvard University, Cambridge

IRVING J. GABELMAN, Engineer, Watson Laboratories, USAF, Long Branch, New Jersey EDWIN GABRIEL, Associate Engineer, Air Force Cambridge Research Laboratories, Cambridge j. ORTEN GADD, JR., Computation Laboratory, Harvard University, Cambridge

JAMES A. GEAN, Chief Analytical Engineer, Parsons Corporation, Traverse City, Michigan ARTHUR A. GENTILE, Computation Laboratory, Harvard University, Cambridge

EUGENE M. GETTEL, Research Engineer, United Aircraft Corporation, East Hartford, Con- necticut

N. ELIOT GIBBS, Senior Engineer, Raytheon Manufacturing Company, Waltham, Massa- chusetts

RICHARD C. GIBSON, Assistant Professor of Electrical Engineering, USAF Institute of Tech- nology, Wright-Patterson Air Force Base, Dayton, Ohio

DONALD· B. GILLIES, Computation Centre, Toronto, Canada

DOROTHY F. GILLETTE, Physicist, Air Force Cambridge Research Laboratories, Cambridge H. F. GINGERICH, U.S. Navy Department, Office of Naval Research, Washington, D.C.

G. GLINSKI, Vice-President, Computing Devices of Canada, Ltd.,Ottawa, Canada

SIMON E. Gluck, Research Associate, Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania

THOMAS N. K. GODFREY, National Bureau of Standards, Massachusetts Institute of Technology!

Cambridge

XXll

MEMBERS OF THE SYMPOSIUM

STANFORD GOLDMAN, Prof~ssor of Electrical Engineering, Syracuse University, Syracuse, New York

HARRY H. GOODE, Special Devices Center, Office of Naval Research, Sands Point, Long Island, New York

C. C. GOTLIEB, Assistant Professor, University of Toronto, Toronto, Ontario, Canada R. S. GRAHAM, Bell Telephone Laboratories, Murray Hill, New Jersey

E. F. GRANT, Chief, Applied Mathematics Branch, Air Force Cambridge Research Labora- tories, Cambridge

RANULF W. GRAS, Massachusetts Institute of Technology, Cambridge

HARRY J. GRAY, JR., Instructor of Electrical Engineering, University of Pennsylvania, Moore Sch<;>ol of Electrical Engin.eering, Philadelphia, Pennsylvania

WALTER H. GRAY, JR., Engineer, Raytheon :rvfanufacturing Company, Waltham, Massa- chusetts

BEN F. GREENE, Radio Engineer, Air Force Cambridge Research Laboratories, Cambridge H. VOSE GREENOUGH, JR., Director, Tec9nichordRecords, Brookline, Massachusetts

DARRIN H. GRIDLEY, Naval Research Laboratories, Washington,

D.c.

D. D. GRIEG, Division Head, Federal Telecommunication Laboratories, Nutley, New Jersey B. A. GRIFFITH,Assistant Professor, University of Toronto, Toronto, Canada

IRVING 1. GRINGORTEN, Meteorologist, Air Force Cambridge Research Laboratories, Cam- bridge

H. R. J. GROSCH, Watson Scientific Computing Laboratory, New York

E. V. GULDEN, Research Engineer, National Cash Register Company, Dayton, Ohio WILLIAM F. GUNNING, Engineer, Rand Corporation, Santa Monica., California

DANIEL HAAGENS, Electronics Engineer,Underwood Corporation, Hartford, Connecticut JAMES V. HAGGERTY, Procedural Consultant, Social Security Administration, Baltimore,

Maryland

GILBERT O. HALL, Electronic Scientist, Air Force Cambridge Research Laboratories, Cam- bridge

W. K. HALSTEAD, Chief Engineer, W. S. MacDonald Company, Cambridge

F. E. HAMILTON, Engineer, International Business Machines Corporation, Endicott, New York PRESTON C. HAMMER, Los Alamos Scientific Laboratory, Los Alamos, New Mexico

R. W. HAMMING, Bell Telephone Laboratory, Murray Hill, New Jersey MRS. R. W. HAMMING, Morristown, New Jersey

GARNET HANES, Computation Centre,Universityof Toronto, Toronto, Canada KENNETH C. HANNA, Computation Laboratory, Harvard University, Cambridge

GEORGE A. HARDENBERGH, Assistant Research Engineer, Engineering Research Associates;, St. Paul, Minnesota

E. L. HARDER, Consulting Transmission Engineer, Westinghouse Electric Corporation, East Pittsburgh, Pennsylvania

JOHN A. HARR, Computation Laboratory, Harvard University, Cambridge

XXlll

MEMBERS OF THE SYMPOSIUM

ROBERT W. HART, Electronics Engineer, Office of Naval Research, Boston M. L. HASELTON, Vice President, TeleregisterCorporation, New York SETH HASTINGS, Mutual Life Insurance Company, New York

WILLARD D. HATCH, Ohio State University, Cleveland, Ohio

ROBERT L. HAWKINS, Computation Laboratory, Harvard University, Cambridge MILES V. HAYES, Computation Laboratory, Harvard University, Cambridge

INEZ HAZEL, Assistant Engineer, Raytheon Manufacturing Company, Newton, Massachusetts VERNON

H.

HEAD, National Advisory Committee for Aeronautics Project, Gordon McKay

Laboratory, Harvard University, Cambridge

SAUL D. HEARN, Chief, Employee Statistics Section, Social Security Administration, Baltimore, Maryland

.I.

C. HEBARD, JR., Mechanical Engineer, Raytheon Manufacturing Company, Newton, Massach usetts

MAURICE H. HELLMAN, Engineer, .Air Force Cambridge Research Laboratories, Cambridge, Massachusetts

L. L. HENKEL, Industrial College of Armed Forces, Fort Lesley McNair, Washington, D.C.

H. A. HENNING, Bell Telephone Laboratories, Inc., New York

PAUL HERGET, Director, University of Cincinnati Observatory, Cincinnati, Ohio FRANK C.HERNE, Computation Laboratory, Harvard University, Cambridge ROGER W. HICKMAN, Lecturer, Harvard University, Cambridge

JOHN L. HILL, Engineer, Engineering Research Associates, St. Paul, Minnesota

GEORGE W. HOBBS, Electronics Engineer, General Electric Company, Schenectady, New York

GEORGE G. HOBERG, Research Associate, Burroughs Adding Machine Company, Philadelphia, Pennsylvania

RICHARD HOFHEIMER, Computation Laboratory, Harvard University, Cambridge

MURRAY HOFFMAN, Engineer, Raytheon l\tlanufacturing Company, Waltham, Massachusetts DOUGLAS L. HOGAN, Electronics Engineer, Navy Department, Washington, D.C.

JOHN V. HOLBERTON, Mathematician, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland

A. B. HOLLISTER, Engineer, Underwood Corporation, Hartford, Connecticut

MARVIN R. HOLTER, Research Assistant, University of Michigan, Ann Arbor, Michigan LAWRENCE F. HOPE, Assistant Head, Department ME-6, Research Division, General Motors,

Detroit, Michigan

RALPH HOPKINS, Special Representative, International Business Machines Corporation, Washington, D.C.

GRACE HOPPER, Chief of Application Department, Eckert-Mauchly Computer Corporation, Philadelphia, Pennsylvania

VIRGIL M. HORN, Assistant Section Head, Actuary Planning, Metropoiitan Life Insurance Company, New York_

XXIV

MEMBERS OF THE SYMPOSIUM

JACOB HOROWITZ, Engineer, Raytheon Manufacturing Company, Newton, Massachusetts JOHN H. HOWARD, Senior Project Engineer, Sperry Gyroscope Company, Great Neck, Long

Island, N ew York

BRADFORD HOWLAND, Graduate Student, Department of Physics, Harvard University, Cambridge

JOHN F. HUBBARD, Treasurer, Martin-Hubbard Corporation, Boston

WILLIAM HULME, Computation Laboratory, Harvard University, Cambridge

j. STUART HUNTER, Statistician, Institute of. Statistics, University of North Carolina, Raleigh, North Carolina

ALLEN HUNTINGTON, Electronics Engineer, U.S. Navy Electronics Laboratory, San Diego, California

C. C. HURD, International Business Machines Corporation, New York

HARRY D. HUSKEY, Mathematician, National Bureau of Standards, Los Angeles, California W. R. HYDEMAN, Mathematician, U.S. Navy, Washington, D.C. .

FR~NK T. INNES, Research Engineer, The Franklin Institute, Philadelphia, Pennsylvania EUGENE ISAACSON, Assistant Professor, Institute for Mathematics 'and Mechanics, New York

University, New York

DAVID R. ISRAEL, Research Assistant, Massachusetts Institute of Technology, Cambridge ARVID W.jACOBSON, Assistant Professor of Mathematics, Wayne University, Detroit, Michigan BETTY JENNINGS, Computation Laboratory, Harvard University, Cambridge

PAUL V. JESTER, Vice President, A. C. Nielsen Company, Chicago, Illinois G. D. JOHNSON, Bell Telephone Laboratories, Ivlurray Hill, New jersey PAUL A. JOHNSON, Engineer, Boeing Airplane Company, Seattle, Washington STANLEY A. JOHNSON, Computation Laboratory, Harvard University, Cambridge, R. F. JOHNSTON, Computation Centre, University of Toronto, Toronto, Canada R. CLARK JONES, Senior Physicist, Polaroid Corporation, Cambridge

ROBERT HUDSON JONES, Head Engineer, Radar Design Branch, Navy Department, Bureau of Ships, Washington, D.C.

THOMAS F. JONES, JR., Assistant Professor, Differential Analyzer Computer Laboratory, Massachusetts Institute of Technology, Cambridge

WILLARD C. JONES, Assistant Chief Engineer, Underwood Corporation, Hartford, Connecticut WILLIAM B. JORDAN, Engineer, General Electric Company, Schenectady, New York

THEODORE A. KALIN, Computation Laboratory, Harvard University, Cambridge SIDNEY KAPLAN, Mathematician, Naval Ordnance Laboratory, Washington

MIDA KARAKASHIAN, Member, joint Computing Group, Massachusetts Institute of Techno- logy, Cambridge

ARTHUR A. KATZ, Mathematician, Eckert-Mauchly Computer Corporation, Philadelphia, Pennsylvania

j. KATZ, Engineer, University of Toronto, Canada

MARTIN KATZ IN, Consultant, Naval Research Laboratory, Washington, D.C.

xxv

MEMBERS OF THE SYMPOSIUM

ALLEN KELLER, Assistant Division Engineer, Turbine Engineering Division, General Electric Company, Lynn, Massachusetts . .

E. G. KELLER, General Electric Company, Schenectady, New York

DANIEL W. KELLIHER, Computation Laboratory, Harvard University, Cambridge

JACQUELIN KELLY, Assistant Engineer, Raytheon Manufacturing Company, Newton, Massa- chusetts

JOHN P. KELLY, Head, Central Statistics Laboratory, Atomic Energy Commission, Oak Ridge, Tennessee

WENTWORTH KENNARD, Technical Editor, Raytheon Manufacturing Company, Waltham, Massach usetts

HARRY KENOSIAN, Research Engineer, Massachusetts Institute of Technology, Cambridge CHESTER H. J. KEPPLER, Captain, USN, Retired, Counsellor for Foreign Students, Harvard

University, Cambridge

J. H. KERFOOT, Civilian Technical Officer, Royal Canadian Navy, Ottawa, Ontario, Canada MARSHALL KINCAID, Computation Laboratory, Harvard University, Cambridge

GILBERT W. KING, Arthur D. Little, Inc., Cambridge R. W. P. KING, Professor, Harvard University, Cambridge

HENRY KINZLER, Supervisor, Procedure Planning, Metropolitan Life Insurance Company, New York

HANS KLEMPERER, Research Engineer, Massachusetts Institute of Technology, Cambridge HERBERT M. KNIGHT, Electronic Engineer, Air Force Cambridge Research Laboratories,

Cambridge

RALPH J. KOCHENBURGER, Instructor, Servomechan:isms Laboratory, Massachusetts Institute of Technology, Cambridge .

FLORENCE K. KOONS, Mathematician, National Bureau of Standards, Washington, D.C.

ZDENEK KOPAL, Massachusetts ,Institute of Technology, Cambridge

JOHN

J.

KORZDORFER, Project Engineer, Red Bank Division, Bendix Aviation Corporation, Red Bank, New Jersey

HANS KRAFT, Aerodynamicist, General Electric Company, Schenectady, New York H. P. KUEHNI, Division Engineer, General Electric Company, Schenectady, New York JosEPH H. KUSNER, Munitions Board, Department of Defense, Washington, D.C.

N. L. KUSTERS, Research Engineer, National Research Council, Ottawa, Ontario, Canada EDWARD LACEY, Electrical Engineer, National Bureau of Standards, Los Angeles, California H. N. LADEN, LT., USN, Research and Development Engineer, Bureau of Ships, Washington,

·D.C.

LEON J. LADER, Radio Engineer, Watson Laboratories, Red Bank, New Jersey

CORNELIUS LANCZOS, Mathematician, Institute for Numerical Analysis, University of Cali-

·fornia at Los Angeles, California

CARNEY LANDIS, Professor of Psychology, Columbia University, New York

GERALD W. LAVIGNE, Computation Laboratory, Harvard University, Cambridge

XXVI

MEMBERS OF THE SYMPOSIUM

TIMOTHY LEARY, Division of Industrial Cooperation, Massachusetts Institute of Technology, Cambridge

PHILIPPE E. LECORBEILLER, Professor of Applied Physics, Harvard University, Cambridge HARRY S. LEE, Engineer, Massachusetts Institute of Technology, Cambridge

DERRICK H. LEHMER, Professor of Mathematics, University of California, Berkeley, California R. A. LEIBLER, USN, Washington, D.C.

POLLY LEIGHTON, Supervisor, Computing Group, Massachusetts Institute of Technology, Cambridge

ALAN L. LEINER, Physicist, National Bureau of . Standards, Electronic Computers Section, Washington, D.C.

MRS. HENRIETTA C. LEINER, Physicist, National Bureau of Standards, Electron Tube Labora- tory, Washington, D.C.

J. PLUMER LEIPHART, Electronic Engineer, Naval Research Laboratory, Washington, D.C.

WASSILY W. LEONTIEF, Professor of Economics, Harvard University, Cambridge

BURTON R. LESTER, Section Engineer, Electronics Laboratory, General Electric Company, Syracuse, N ew York

JOSEPH H. LEVIN, Mathematician, Computation Laboratory, National Bureau of Standards, Washington, D.C.

ARNOLD M. LEVINE, Department Head, Federal Telecommunications Laboratories, Nutley, New Jersey.

FRED C. LEWIS, Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts C. C. LIN, Massachusetts Institute of Technology, Cambridge

PETER L. LINDLEY, Computation Laboratory, Harvard University, Cambridge

HERBERT G. LINDNER, Radio Engineer, Coles Signal Corps Laboratory, Red Bank, New Jersey

S. B. LITTAUER, Associate Professor, Columbia University, New York

ELBERT P. LITTLE, Chief, Computation Section, Office of Air Research, USAF; Computation Laboratory, Harvard University, Cambridge

HUBERT M. LIVINGSTON, Eckert-Mauchly Computer Corporation, Philadelphia, Pennsylvania MRS. HUBERT M. LIVINGSTON, Eckert-Mauchly Computer Corporation, Philadelphia, Penn-

sylvania

CHARLES J. LODA, Physicist, U.S. Navy Underwater Sound Laboratory, New London, Con- necticut

SAMUEL LUBKIN, Electronic Scientist, National Bureau of Standards, Washington, D.C:

E .. E. LUCCHINI, Computation Laboratory, Harvard University, Cambridge

DUNCAN LUCE, Research Center for Group Dynamics, University of Michigan, Ann Arbor, Michigan

W.F. MACDoNAL!l, S. D. Leidesdorf and Company, New York

JOHN H. MACNEILL, Senior Engineer, Raytheon Manufacturing Company, Waltham, Massa- chusetts

XXVll

MEMBERS OF THE SYMPOSIUM

H. M. MACNEILLE, Atomic Energy Commission, Washington, D.C.

W. H. MACWILLIAMS, Jr., Bell Telephone Laboratories, Murray Hill, New Jersey P; J. MAGINNISS, Engineer, General Electric Company, Schenectady, New York ALFRED T. MAGNELL, CDR., USN, Office of Naval Research, Washington, D.C.

HENRY M. MALLON, Assistant Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts

HARLAND MANCHESTER, Roving Editor, Reader' s D~gest, New York ROLAND A. MANGINI, John Hancock Life Insurance Company, Boston

CHARLES S. MANNING, Electrical Engineer, Navy Electronics Laboratory, San Diego, California ETHEL Cox MARDEN, Mathematician, National Bureau ofSta:ndards, Washington, D.C.

EMIL MARECKI,Assistant Chief, Machine Tabulation Division, Bureau of the Census, Wash- ington, D.C.

ARTHUR E. MARl, Mari & RentelCompany, Inc., Boston

JOSEPH MARKSTEINER, Computation Laboratory, Harvard University, Cambridge LAWRENCE MARKUS, Harvard University, Cambridge

ELBERT W. MARLOWE, Engineer, Union Switch & Signal Company, Pittsburgh, Pennsylvania H. W. MARSH, Consultant, USN Underwater Sound Laboratory, New London, Connecticut ROBERT H. MARSH, Engineer, Massachusetts Institute of Technology, Cambridge

BYRON O. MARSHALL, Physicist, Air Force Cambridge Research Laboratories, Cambridge DAVID W. MARSHALL, Procedures Analyst, Metropolitan Life Insurance Company, New York W. T. MARTIN, Professor, Massachusetts Institute of Technology, Cambridge

EDWARD MASSELL, Engineer, Electronic Associates, Inc., Long Branch, New Jersey

MORTON P. MATTHEW, Research Engineer, Friden Calculating Machine Company, San Leandro, California

J. W.MAUCHLY, President, Eckert-Mauchly Computer Corporation, Philadelphia, Penn- sylvania

HAROLD F. MAY, Assistant Director, Teleregister Laboratories, New York WILLIAM E. MAY, Department of the Army, Washington, D.C.

J. P. MAYBERRY, Computation Centre, University of Toronto, Toronto, Ontario, Canada H. C. MAYER, Research and Development, Radio Corporation of America, Camden, New

Jersey

ROLLIN POWELL MAYER, Research Engineer,Massachusetts Institute of Technology, Cam- bridge

EVERETT" E. MCCOWN, Electronics Engineer, U.S. Navy Electronics Laboratory, San Diego, California

JAMES O. McDONOUGH, Research Engineer, Massachusetts Institute of Technology, Cambridge WILLIAM D. MCGUIGAN, Engineering Coordinator, Raytheon Manufacturing Company,

Waltham, Massachusetts

E. C. McKAY, Chief, Section of Tides,U.S. Coast and Geodetic Survey, Department of Commerce, Washington, D.C.

XXV111

MEMBERS OF THE SYMPOSIUM

R. O. McMANUS, Mechanical Engineer, Air Force Cambridge Research Laboratory, Cam- bridge

JAMES L. MCPHERSON, Machine Development Officer, Bureau of the Census, Washington, D.C.

JOHN C. MCPHERSON, Vice President, International Business Machines, New York

KENNETH E. MCVICAR, Research Assistant, Electrical Engineering Department, Massachusetts Institute of Technology, Cambridge

LEONARD C. MEAD, Research Coordinator, Tufts College, Medford, Massachusetts RALPH 1. MEADER, Vice President, Engineering Research Associates, St. Paul, Minnesota R. E. MEAGHER, Assistant Professor, University of Illinois, Urbana, Illinois

EUGENE A. MECHLER, Re'search Engineer, Franklin Institute, Philadelphia, Pennsylvania C. S. MERCER, Sales Engineer,' Aluminium Company of America, Boston

DAVID MIDDLETON, Associate Professor of Applied Physics, Harvard University, Cambridge JAMES G. MILES, Engineer, Engineering Research Associates, Inc., St~ Paul, Minnesota

E. J. MILLER, Technical Officer, National Defence, Ottawa, Canada

FREDERICK G. MILLER, Electrical Engineer, Naval Proving Ground, Dahlgren, Virginia HAROLD C~ MILLER, Assistant Chairman, Physics Research, Armour Research Foundation,

Chicago, Illinois

BURTON E. MILLS, Air Force Cambridge Research Laboratories, Cambridge W. E. MILNE, Professor, Oregon State College, Corvallis, Oregon

HARRY R. MIMNO, Professor of Applied Physics, Harvard University, Cambridge

MILTON J. MINNEMAN, Electronic Group Engineer, Glenn L. Martin Company, Baltimore, Maryland

WILLIAM G. MINTY, Computation Laboratory, Harvard University, Cambridge

HERBERT F. MITCHELL, JR., Webb Institute of Naval Architecture, Glenn Cove, Long Island, New York

SAMARENDRA K. MITRA, UNESCO, Calcutta, India

WILLIAM MITTELMAN, Griffiss Air Force Base, Rome, New York

CARLTON A. MIZEN, Project Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts

ELMER B. MODE, Professor of Mathematics, Boston University, Boston

BRUCE MONCREIFF, Systems Reviewer, Prudential Insurance Company of America, Newark, New Jersey

ROBERT J. MONROE, Institute of Statistics, North .carolina State College, Raleigh, North Carolina

N. F. MOODY, National Research Council, Ontario, Canada CALVIN N. MOOERS, President, Zator Company, Boston

C. M. MOONEY, International Business Machines Corporation, New York

BENJAMIN L. MOORE, Assistant Director, Computation Laboratory, Harvard University,

Cambridge .

EDWARD F. MOORE, Graduate Student, Brown University, Providence, Rhode Island

XXIX

MEMBERS OF THE SYMPOSIUM

JOHN MORRIS, Junior Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts REEVES MORRISSON, Head, Analysis Section, Research Department, United Aircraft Corpora-

tion, East Hartford, Connecticut

PAUL L. MORTON, Associate Professor of Electrical Engineering, University of California, Berkeley, California

LEON MOSES, Graduate Student, Harvard University, Cambridge

Z. 1. MOSESSON, Senior Actuarial Assistant, Prudential. Insurance Comp~ny of America, Newark, New Jersey

ROBERT G. Moss, Secretary, Electronic Calculator Committee, M~tropolitan Life Insurance Company, New York

FREDERICK MOSTELLER, Assistant Professor of Mathematical Statistics, Harvard University, Cambridge

HAROLD M. MOTT-SMITH, Assistant . Chief, Reactor Branch, Atomic Energy Commission,

! Washington, I?C.

CLIFTON F. MOUNTAIN, Director, Office of Statistical Research, Boston University, Boston J. D. MOUNTAIN, International Telephone and Telegraph Company, New York

CARL F. MUCKENHOUPT, Head, Scientific Section, Office of Naval Research, Boston RALPH E. MULLENDORE, Bureau of the Census, Washington, D.C.

G. G. MULLER, Bell Telephone Laboratories, New York

ROBERT E. MUMMA, Manager, Electrical Development Laboratory, National Cash Register Company, Dayton, Ohio

J. H. MUNCY, Electronic Engineer, Naval Air Development Station, Johnsville, Pennsylvania MORRIS MUSKAT, Director of Physics Division, Gulf Oil Corporation, Pittsburgh, Pennsylvania FRANKLIN G. MYERS, Design Specialist, Glenn L. Martin Company, Baltimore, Maryland ROBERT A. NELSON, Re~earch Engineer, Servomechanisms Laboratory, Massachusetts Insti-

tute of Technology, Camb~idge

A. J. NEUMANN, Research Associate, University of Pennsylvania, Philadelphia, Pennsylvania HERBERT B. NICHOLS, Science Editor, Christian Science Monitor, Boston

NATALIE N: NICHOLSON, Librarian, Harvard University, Cambridge

R. F. NICHQLSON, Data Utilization Laboratory, Griffiss Air Force Base, Rome, New York EDWIN N. NILSON, Assistant Professor of Mathematics, Trinity College, Hartford, Connecticut WILLIAM J. NOLAN, JR., Division of Industrial Cooperation, Massachusetts Institute of Tech-

nology, Cambridge

R. H. NOYES, Radio Engineer, Signal Corps Engineering Laboratories, Coles Laboratory, Red Bank, New Jersey

ALEXANDER NYMAN, Technical Advisor, Alden Products Company, Brockton, Massachusetts H. NYQuIsT, Bell Telephone Laboratories, New York

JAMES J. O'B~IRNE, Branch Chief, Control, Social Security Administration, Baltimore, Mary- land

JOHN A. O'BRIEN, Research Engineer, Massachusetts Institute of Technology, Cambridge xxx

MEMBERS OF THE SYMPOSIUM

L. A. OHLINGER, Project Engineer, Northrop Aircraft, Inc., Hawthorne, California JOHN A~ O'KEEFE, Mathematician, Army Map Service, Washington, D.C.

BRUCE OLDFIELD, Mathematician, U.S. Naval Ordnance Test Station, China Lake, California THOMAS K. OLIVER, Acting Chief, Office of Air Research, Wright-Patterson Air Force Base,

Ohio

R. D. O'NEAL, Aeronautical Research Center, University of Michigan,Ann Arbor, Michigan ALLAN H. O'NEIL, Mathematician, U.S. Naval Proving Ground, Dahlgren, Virginia

ALEXANDER ORDEN, Research Associate, Massachusetts Institute of Technology, Cambridge SIDNEY OVIATT, John Price Jones Company, Inc., New York

CHESTER H. PAGE, Electronics Consultant, National Bureau of Standards, Washington, D.C.

HENRY E. PAGE, Computation Laboratory, Harvard University, Cambridge

RALPH L. PALMER, Engineer, International Business Machines Corporation, Poughkeepsie, New York

WILLIAM N. PAPIAN,Research Assistant, Servomechanisms Laboratory, Massachusetts Insti- tute of Technology, Cambridge

JOHN E. PARKER, President, Engineering Research Associates, Inc., St. Paul, Minnesota G. B. PARKINSON, Senior Engineer, Raytheon Manufacturing Company, Newton, Massa-

chusetts

JAMES PASTORIZA, Electronic Engineer, Air Force Cambridge Research Laboratory, Cambridge GEORGE W. PATTERSON, Assistant Professor, Moore School, University of Pennsylvania,

Philadelphia, Pennsylvania

ALFRED M. PEISER, Mathematician, Hydrocarbon Research, Inc., New York C. L. PEKERIS, Institute for Advanced Study, Princeton, New Jersey

DAVID P. PERRY, Student, University of Pennsylvania, Philadelphia, Pennsylvania C. G. PETERSON, District Agent, Marchant Calculating lYfachine Company, Boston B. L. PFEFER, Project Manager, General Electric Company, Syracuse, New York

HARRY PFORZHEIMER, Head, Economic Section, Standard Oil Company (Ohio), Cleveland, Ohio.

EDWARD W. PHARO, JR., Engineer, Philadelphia, Pennsylvania J. R. PIERCE, Bell Telephone Laboratories, Murray Hill, New Jersey

ROBERT P. PINCKNEY, Student, Massachusetts Institute of Technology, Cambridge SAMUEL PINES, Design Engineer, Republic Aviation, New York

CHARLES A. PIPER, Sup~rvising Engineer, Bendix Aviation Research Laboratories, Detroit, Michigan

H .. POLACHEK, Mathematician, Naval Ordnance Laboratory, 'Vhite Oak, Silver Spring, Maryland

ROBERT E. POPIEL,Computation Laboratory, Harvard University, Cambridge

H. PORITSKY, Consulting Engineer, General Electric Company, Schenectady,' N ew York WILLIAM A. PORTER, Computation Laboratory, Harvard University, Cambridge

JOHN T. POTTER, President, Potter Instrument Company, Inc., Flushing, New York XXXI

MEMBERS OF THE SYMPOSIUM

F. D. POWELL, Dynamics Engineer, Bell Aircraft Corporation, Buffalo, New York BETTE PREER, Librarian, Boston Public Library, Boston

GEORGE G. PROULX, Computation Laboratory, Harvard University, 'Cambridge C. C. PYNE, Harvard University, Cambridge

E. J. QUINBY, Director, Electronic Research and Development," Monroe Calculating Machine Company, Orange, New Jersey

JAN RAjCHMAN, Research Physicist, Radio Corporation of America, Princeton, New Jersey JOHN H. RAMSER, Senior Physicist, Atlantic Refining Company, Philadelphia, P~nnsylvania

EUGENE A. RASOR, 'Actuarial Mathematician, Social Security Administration, Washington, D.C.

ROBERT RATHBONE, Division of Industrial Cooperation, Servomechanisms Laboratory, Massachusetts Institute of Technology, Cambridge

A. G. RATZ, Research Engineer, University of Toronto, Toronto, Ontario, Canada

KONRAD RAUCH, Special' Application Engineer; National Cash Register Company, Dayton, Ohio

RICHARD W. READ, Massachusetts Institute of Technology, Cambridge DONALD REAM, Electronics Engineer, Navy Department, Washington, D.C.

MINA REES, Director, Mathematic Sciences Division, Office of Naval Research, Washington, D.C.

K. M.REHLER, Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts GEORGE W. REITWIESNER, Mathematician, Ballistic Research. Laboratories, Aberdeen Proving

Ground, Aberdeen, Maryland

THEODORE V. RENTEL, Mari and RentelCompany, Inc., Boston

EDWARD REYNOLDS, Administrative Vice President, Harvard University, Cambridge

GEORGE E. REYNOLDS, Mathematician, Air Force Cambridge Research Laboratories, Cam- bridge

JAMESR.REYNOLDS, Office of Special Advisor to the President, Harvard University, Cambridge

. ROBERT R. REYNOLDS, Assistant Professor, Oklahoma Agricultural and Mechanical College, Stillwater, Oklahoma

CHARLES RHEAMS, Senior Engineer, Raytheon Manufacturing Company, Boston IDA RHODES, Mathematician, National Bureau of Standards, Washington, D.C.

HOPE RICE, University of North Carolina, Chapel Hill, North Carolina

OSCAR K. RICE, Professor of Chemistry, University of North Carolina, Chapel Hill, North Carolina

EDWIN S. RICH, Engineer, Massachusetts Institute of Technology, 'Cambridge C. ,H. RICHARDS, Computation Laboratory, Harvard University, Cambridge

LOUIS N. RIDENOUR, Dean, Graduate College, University of Illinois, Urbana, Illinois

DONALD V. RIDER, Electronics Engineer, Raytheon Manufacturing Company, Waltham, Massachusetts

XXXll

MEMBERS OF THE SYMPOSIUM

LEONARD D. RINALDI, Research Engineer, Cornell Aeronautical Laboratory, Buffalo, New York

E. K. RITTER, Research Engineer, University of Michigan, Ann Arbor, Michigan

GORDON A. ROBERTS, Manager, Future Demands Department, International Business Machines Corporation, New York

REX ROBERTS, Vice President, Transducer Corporation, Boston

JOHN W. ROCHE, Computation Laboratory, Harvard University, Cambridge

NATHANIEL ROCHESTER, Engineering Laboratory, International Business Machines Corpora- tion, Poughkeepsie, New York

HAROLDO AZEVEDO RODRIGUES, Rio de Janeiro, Brazil EDWARD ROGAL, President, Central Records, Inc., Boston

STANLEY ROGERS, Research Engineer, CC?nvair, San Diego, California

THOMAS A. ROGERS, Associate Professor of Engineering, University of California at Los Angeles, Los Angeles, California

E. ROOT, Springfield, Vermont _

MORRIS E. ROSE, Principal Physicist, Oak Ridge National Laboratory, Oak Ridge, Tennessee JOSHUA H. ROSENBLOOM, Physicist, Naval Ordnance Laboratory, Washington, D.C.

CLARENCE Ross, U.S. Naval Proving Ground, Dahlgren, Virginia

JOHN ROTHERY, Air Force Cambridge Research Laboratories, Cambridge

WALTER ROTMAN, Electronic Engineer, Air Force Cambridge Research Laboratories, Cam- bridge

B. G. H. ROWLEY, LT.-CDR., British Naval Staff, Electronics Liaison Officer, Washington, D.C.

D. M. RUBEL, LT.-CDR., USN, Office of the Secretary of Defense, Washington, D.C.

MILTON D. RUBIN, Research Director, G. A. Philbrick Researches, Inc., Boston M. RUBINOFF, Institute for Advanced Study; Princeton, New Jersey

PHILIP RULON, Professor of Education and Acting Dean of the Faculty of Education, Harvard University, Cambridge

HEINZ RUTISHAUSER, S~iss Federal Iri~titute of Technology, Zurich, Switzerland DAVID RUTLAND, Engineer, National Bureau of Standards, Los Angeles, California

HERBERT E. SALZER:, M'athematician, Computation Laboratory, National Bureau of Standards, Washington, D.C.

JOHNM. SALZER, Research Associate, Massachusetts Institute of Technology, Cambridge ARTHUR L. SAMUEL, International Business Machines Corporation, Poughkeepsie, New York PAUL A. SAMUELSON, Professor of Economics, Massachusetts Institute of Technology, Cam-

bridge

JACKIE SANBORN, Computation Laboratory, Harvard University, Cambridge

BERNARD L. SARAHAN, Mathematician, Naval Research Laboratory, Washington, D.C.

EMIL D. SCHELL, Chief, Mathematic and Electronic Computer Branch, U.S. Air Force, Washington, D.C. -

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