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PROCEEDINGS
Industrial
Computation
Seminar
SEPTEMBER
1950
EDITED BY IBM APPLIED SCIENCE DEPARTMENT
CUTHBERT C. HURD, Director
INTERNATIONAL BUSINESS MACHINES CORPORATION
NEW YORK ... NEW YORK
Copyright 1951
International Business Machines Corporation
590 Madison Avenue, New York 22, N. Y.
Form 22-8415-0
P R N TED N THE U N TED S TAT E S o F A MER C A
FORE WORD
AN INDUSTRIAL COMPUTATION SEMINAR, sponsored
..n. by the International Business Machines Corpora-
tion, was held in the IBM Department of Education,
Endicott, New York, from September 25 to September
29, 1950. The ninety research engineers and scientists
who participated in this Seminar met to discuss the
fundamental computational methods which are appli-
cable in a wide variety of research problems. Particular
attention was drawn to computational techniques re-
cently developed in the fields of chemistry and petroleum.
The International Business Machines Corporation wishes
to express its appreciation to all who participated in
this Seminar.
CONTENTS
The Role of the Punched Card in Scientific Computation -WALLACE J. ECKERT 13
Machine Calculation of the Plate-by-Plate Composition
of a Multicomponent Distillation Column -ASCHER OPLER
ROBERT G. HEITZ 18
Continuous Distillation Design Calculations with the IBM -ARTHUR ROSE
Card-Programmed Electronic Calculator THEODORE J. WILLIAMS
WILLIAM S. DYE, III 24
Application of Automatic Computing Methods to
Infrared Spectroscopy -GILBERT W. KING. 32
Correlation and Regression Analysis - E . L. WELKER 36
Pile-Driving Impact -EDWARD A. SMITH 44
Punched Card Mathematical Tables on Standard IBM
Equipment -ELEANOR KRAWITZ. 52
The Solution of Simultaneous Linear Equations Using - J USTUS CHANCELLOR
the IBM Card-Programmed Electronic Calculator JOHN W. SHELDON
G. LISTON TATUM. 57
Two Applications of the IBM Card-Programmed
Electronic Calculator -IRVING C. LIGGETT 62
The Gauss-Seidel Method of Solution of
Simultaneous Linear Equations 62
Approximating the Roots of a Polynominal Equation 65
Matrix by Vector Multiplication on the IBM Type 602-A
Calculating Punch -ELEANOR KRAWITZ. . . . . . . 66
Numerical Solution of Two Simultaneous Second-Order
DiJJerential Equations -WALTER H. JOHNSON 71
Numerical Evaluation of Integrals of the form f ~ f(x)g(x)dx -JOHN W. SHELDON. . 74
The Use of Orthogonal Polynomials in Curve Fitting and
Regression Analysis - J ACK SHERMAN 78
General Purpose Ten-Digit Arithmetic on the IBM Card- -STUART R. BRINKLEY, JR.
Programmed Electronic Calculator G. L. WAGNER
R. W. SMITH, JR. . 81
Remarks on Distillation Calculations -JOHN W. DONNELL. 91
Some Applications of the Monte Carlo Method
Matrix Inversion on the IBM Accounting Machine -ASCHER ()PLER 94
Remarks on Finding Roots of, and Inverting, a Matrix -GILBERT W. KING. 94
Remarks on the Monte Carlo Method -CUTHBERT C. HURD 95
Plotting Punched Card Data Using the IBM Type 405
Accounting Machine -PAUL T. NIMS. . . . . . . . . 96
A Method for Evaluating Determinants and Inverting
Matrices with Arbitrary Polynomial Elements by -L. E. GROSH, JR.
IBM Punched Card Methods E. USDIN 99
PARTICIPANTS
ACKERMAN, HERMAN A., Geophysicist DEMPSEY, CARL W., Assistant Research Mathematician
Socony-Vacuum Oil Company Sun Oil Company
New York, New York Philadelphia, Pennsylvania
ARONOFSKY, JULIUS S., Senior Research Engineer DONNELL, JOHN W., Professor
Magnolia Petroleum Company Department of Chemical Engineering, Michigan State College
Dallas, Texas East Lansing, Michigan
BEJARANO, GABRIEL G., Research Engineer DuFoRT, EDWARD C., Associate Reservoir Engineer
California Research Corporation Continental Oil Company
Richmond, California Ponca City, Oklahoma
BELL, CLARENCE J., Research Engineer-Mathematician EATON, THOMAS T., Engineering Group Supervisor
Battelle Memorial Institute - Radio Corporation of America, RCA Victor Division
Columbus, Ohio Camden, New Jersey
BLOOM, CHARLES A., Stress Group Leader ECKERT, WALLACE J., Director
Canadair, Limited Department of Pure Science, IBM Corporation
Montreal, Quebec New York, New York
BRILLOUIN, LEON, Director ELKINS, THOMAS A., Geophysicist
Electronic Education, IBM Corporation Gulf Research and Development Company
New York, New York Pittsburgh, Pennsylvania
BRINKLEY, STUART R., JR., Physical Chemist FEIGENBAUM, DAVID, Associate Research Engineer
u.S. Bureau of Mines Cornell Aeronautical Laboratory
Pittsburgh, Pennsylvania Buffalo, New York
BROWN, WILLIAM F., JR., Research Physicist FREUD, OLIVER, Senior Research Engineer
Sun Oil Company The Budd Company
Philadelphia, Pennsylvania Philadelphia, Pennsylvania
BUCHANAN, ALVA C., JR., Chief Accountant FULLERTON, PAUL W., JR.
Tabulating, Magnolia Petroleum Company Applied Science Department, IBM Corporation
Dallas, Texas New York, New York
BUCHHOLZ, WERNER GLAUZ, Roy L., JR., Process Engineer
Engineering Laboratory, IBM Corporation Staqdard Oil Company
Poughkeepsie, New York Cleveland, Ohio
CARLSON, HARRISON C., Research Project Engineer GREENE, CHARLES H., Manager
E. r. duPont deNemours and Company Melting Development, Corning Glass Works
Wilmington, Delaware Corning, New York
CHANCELLOR, JUSTUS GREENFIELD, ALEXANDER, Senior Electronic Engineer
Applied Science Department, IBM Corporation Research Laboratories, Bendix Aviation Corporation
New York, New York Detroit, Michigan
CLAMONS, ERIC H., Research Engineer GREENLAW, DAVID S.
Minneapolis-Honeywell Regulator Company Color Control Department, Eastman Kodak Company
Minneapolis, Minnesota Rochester, New York
COLLINS, FRANCIS, Associate Reservoir Engineer GROSCH, H. R. j., Senior Staff Member .
Atlantic Refining Company Watson Scientific Computing Laboratory, IBM Corporatlon
Dallas, Texas New York, New York
DANFORTH, CLARENCE E., Technical Engineer GROSH, L. E., JR., Research Associate
General Electric Company Statistical Laboratory, Purdue University
Lynn, Massachusetts West Lafayette, Indiana
DE FINETTI, BRUNO, Professor HARRINGTON, ROBERT A., Physicist
Department of Mathematics, University of Trieste B. F. Goodrich Research Center
Trieste, Italy Brecksville, Ohio
HASTINGS, BRIAN T., Project Engineer McINTIRE, ROBERT L., Chemical Engineer
Office of Air Research, USAF, Wright Field Phillips Petroleum Company
Dayton, Ohio Bartlesville, Oklahoma
HOAGBIN, JOSEPH E., Physicist MERRICK, ELSIE V., Engine~r
AC Spark Plug Division, General Motors Corporation Technical Service Division, Standard Oil Company
Flint, Michigan Cleveland, Ohio
HOELZER, HELMUT, Chief MONCREIFF, BRUSE, Junior Methods Analyst
Computing Laboratory, Ordnance Guided Missile Center Methods Division, Prudential Insurance Company of America
Redstone Arsenal Newark, New Jersey
Huntsville, Alabama
NICHOLS, NATHANIEL B., Professor
HUNTER, G. TRUMAN Department of Electrical Engineering, University of Minnesota
Applied Science Department, IBM Corporation Minneapolis, Minnesota
New York, New York
NIMS, PAUL T., Staff Engineer-Research
HURD, CUTHBERT C., Director Chrysler Corporation
Applied Science Department, IBM Corporation Detroit, Michigan
New York, New York
HURLEY, WESLEY V., Air Design Specialist O'BRIAN, WADE B., Supervisor
General Electric Company Payroll, Tabulating, Timekeeping
Lynn, Massachusetts The Cleveland Graphite Bronze Company
Cleveland, Ohio
JOHNSON, WALTER H.
Applied Science Department, IBM Corporation OLSEN, JOHN L., Development Engineer
New York, New York Sun Oil Company
Marcus Hook, Pennsylvania
KEEFER, KARL H., Assistant Project Engineer
Aeroproducts Di"ision of General Motors Corporation OPLER, ASCHER, Project Leader
Dayton, Ohio Physics Laboratory, Great Western Division
The Dow Chemical Company
KINCKINER, Roy A., Assistant Director Pittsburg, California
Engineering Research Laboratory, E. I. duPont Experimental Station
Henry Clay, Delaware ORR, S. ROBERT, Assistant Research Physicist
Monsanto Chemical Company
KING, GILBERT W., Research Chemist Miamisburg, Ohio
Arthur D. Little, Inc., and Research Laboratory for Electronics
Massachusetts Institute of Technology
Cambridge, Massachusetts PARKER, ROBERT W.
Engine Performance Calculations, Allison Division
General Motors Corporation
KRAWITZ, ELEANOR Indianapolis, Indiana
Watson Scientific Compu ting Laboratory, IBM Corporation
New York, New York
PETERS, LEO J., Chief
Georhysical Operations Division
LESLIE, JOHN D., Research Engineer Gul Research and Development Company
Standard Oil Development Company Pittsburgh, Pennsylvania
Linden, New Jersey
LEY, DARWIN M., Senior Systems Analyst RAMSER, JOHN H., Physical Chemist
Ford Motor Company The Atlantic Refining Company
Dearborn, Michigan Philadelphia, Pennsylvania
LIGGETT, IRVING C. RANDALL, LAUROS M., Project Engineer
Applied Science Department, IBM Corporation Allison Division, General Motors Corporation
New York, New York Indianapolis, Indiana
LINDLEY, CHARLES A., Development Engineer RANDELS, ROBERT, Physicist
Thompson Aircraft Products Corning Glass Works
Cleveland, Ohio Corning, New York
LUCAS, ROBERT R., Comptroller ROBERTS, JOHN B., Group Supervisor
Monmouth Products Company E. I. duPont deNemours and Company
Cleveland, Ohio Wilmington, Delaware
McADAMS, H. T., Research Chemist ROGGENBUCK, ROBERT A., Research Engineer
Aluminum Ore Company Engine Section, Ford Motor Company
East St. Louis, Illinois Dearborn, Michigan
ROSE, ARTHUR, Associate Professor TAYLOR, CHARLES R., Supervising Metallurgist
Department of Chemical Engineering Armco Steel Corporation
Pennsylvania State College Middletown, Ohio
State College, Pennsylvania
ULLOCK, DONALD S., Staff Engineer
RUBINOFF, MORRIS, Research Assistant Professor Union Carbide and Carbon Corporation
University of Pennsylvania, Moore School of Electrical Engineering South Charleston, West Virgima
Philadelphia, Pennsylvania
WAKEHAM, HELMUT, Section Head
SCHUMACHER, LLOYD E., Assistant Chief Textile Research Institute
Flight Research Section, Headquarters Air Materiel Command Princeton, New Jersey
Dayton, Ohio
WALKER, JACK K., P~'Ysicist
Socony-Vacuum Research and Development
SCIFRES, EUGENE M., Research Engineer Paulsboro, New Jersey
Gates Rubber Company
Denver, Colorado
WATSON, FREDERIC R., Engineer
Products Application Department, Shell Oil Company
SELLS, BERT E., Turbine Engineer San Francisco, California
Aircraft Gas Turbine Division
General Electric Company
West Lynn, Massachusetts WATSON, H. J. MICHAEL, Special Cost Clerk
Steel Company of Canada, Limited
Hamilton, Ontario
SHELDON, JOHN W.
Applied Science Department, IBM Corporation WEINKAMER, WILLIAM A., Test Engineer
New York, New York Harris Products Company
Cleveland, Ohio
SHERMAN, JACK, Mathematician
The Texas Company WELKER, E. L., Associate in Mathematics
Beacon, New York American Medical Association
Chicago, Illinois
SHIVELY, RICHARD D., Assistant Manager
Office Services Department, Gates Rubber Company WHITNEY, ALICE M.
Denver, Colorado Applied Science Department, IBM Corporation
New York, New York
SMITH, EDWARD A., Chief Mechanical Engineer WILLIAMS, THEODORE j., Research Fellow
Raymond Concrete Pile Company Department of Chemical Engineering
New York, New York The Pennsylvania State College
State College, Pennsylvania
SMITH, EDGAR L., JR., Acting Chief
Data Analysis, Long Range Proving Ground Division, USAF WILSON, L.
Cocoa, Florida IBM Corporation
New York, New York
SMITH, ROBERT W., JR., Mathematician ZEIGLER, MARTIN L., Assistant Supervisor
U.S. Bureau of Mines Tabulating Division, The Pennsylvania State College
Pittsburgh, Pennsylvania State College, Pennsylvania
TANNICH, RICHARD E., Research Specialist ZIEGLER, GEORGE E., Director of Research
Humble Oil and Refining Company Midwest Research Institute
Baytown, Texas Kansas City, Missouri
The Role of the Punched Card tn Scientific Computation
WALLACE J. ECKERT
International Business Machines Corporation
A S I L 0 0 K over the list of occupations of the members trigonometric tables in order to make his computations.
of this Seminar, I am impressed by the wide range of fields Later, the development of the logarithmic table greatly
represented-engineering, physics, chemistry, accounting, facilitated his arithmetic operations. The adding machine
even astronomy. It is interesting to note how experience in was invented by Pascal in 1642 and the desk calculator by
one field can influence seemingly unrelated activities in Leibnitz in 1693. Thus, we have the invention by scientists
other fields. I might illustrate by a trivial example of a of these two tools that were greatly needed by scientists;
procedure mentioned here in connection with an accounting yet they were of little use to science for over two centuries.
problem which also occurred recently in an astronomical Although the desk calculator of Leibnitz was, in principle,
problem at the Watson Laboratory. It was mentioned that our present-day machine, two centuries were required to
it is frequently more convenient to produce the calendar .: develop it into a generally useful implement.
date on the accounting machine than to copy it from the There are two reasons for this long delay: one is mechan-
calendar. In our problem we required calendar dates at ical, and the other is mental. It is a long, hard pull from
forty-day intervals from 1653 to 2060, taking into account the gleam in the inventor's eye, or even from the first
the complicated leap-year rules of our calendar; the list model, to the point where a scientist can use a device as a
was prepared by a single run on the IBM Type 602-A Cal- help and a tool, rather than as a problem in itself. It is not
culating Punch. difficult for the inventor to make his model work under his
The close relationship between apparently unrelated own benevolent criticism, but to have it developed to the
things is not new in science; it is necessary to look at the point where it is accurate, fool-proof, and efficient is an-
picture in the proper perspective to see the relationship. other matter. Of course, things did not proceed as rapidly
Let us consider the ancient astronomer who was intrigued in those days as they do now, but one should not overlook
by the small spots of light in the sky, called planets. He the great number of technical developments necessary to
spent many hours measuring and recording their positions, fill in the details that make a complicated machine work.
and I am sure that his contemporaries could not see how On the mental side there was the fact that people had
these activities would ever put food into the mouths of men. been trained in the use of logarithms, and computational
His contemporaries could not see enough of the picture. work had been organized for the use of logarithms. If you
We now know how the study of such planetary observa- look through many books in applied mathematics of that
tions has led not only to our understanding of the motions era, you will find that large portions of many of them were
of the planets, but also to our knowledge of the funda- devoted to the conversion of basic formulae into a form
mental principles of mechanics, the basis of all mechanical suitable for the effective use of logarithms. Then, too, there
design. From this vantage point, when we see a farmer was the matter of tables. To replace logarithmic tables with
riding a properly designed tractor and pulling carefully natural tables required some time. This seems like a mod-
designed implements, we realize that the early astronomer ern age, yet I am not an octogenarian and I can remember
has done more to feed the multitudes than all of his con- the dying gasp of the logarithmic table as the standard
temporaries. method of computation. I have seen the desk calculator be-
The computing profession has always incorporated math- come a necessary instrument for every scientist who is
ematical and mechanical techniques; benefits from one field doing quantitative work. They are now so efficient and so
of science have been carried into other fields. At the time reliable that the scientist has merely to insert the proper
of the early astronomical observations computing was being number, push the proper control key to perform his desired
done on a considerable scale, and from that time forward operation, and read the results.
man has tried to develop computing aids. The mathema- In medicine there is a well-known phenomenon. While
tician and the scientist have tried to devise both mechanical smallpox and diphtheria were decimating mankind, little
aids and mathematical aids. The first astronomer needed attention was paid to some of the lesser diseases, but now
13
14 INDUSTRIAL COMPUTATiON
that smallpox and diphtheria have been brought under con- ble of handling general scientific calculations such as the
trol the lesser diseases are considered very important. Simi- solution of differential equations, and the reduction of ob-
larly in computation, when multiplication and division were servational data. This laboratory was in full-time operation
performed longhand, or with the aid of logarithms, the on basic research until the advent of the war when it was
computer did not worry about the associated clerical oper- converted to military research. By 1940 a number of labo-
ations. The advent of the desk calculator;however, enabled ratories about the country were using standard punched
him to undertake larger problems, and he has become pain- card machines for technical computation. During the war
fully aware of the details of reading and writing data and new laboratories were quickly established in all phases of
of initiating the proper control operations. The need for the defense effort, including atomic energy, aircraft design
automatic handling of data and instructions becomes impor- and construction, air and sea navigation, and many others
tant for further progress. that are still classified. In 1944 the IBM Automatic Se-
Here again, we have a situation similar to that of the quence Controlled Calculator was completed in Endicott
development of the desk calculator. In 1893, as you have and presented to Harvard University; this machine, known
heard, the punched card was introduced as a means of read- as Mark I, has since been in continuous service. In the
ing data and instructions into a machine, but many years same year two relay calculators were installed at the Aber-
elapsed before the method became accepted as a regular deen Proving Ground; these machines were more limited in
part of scientific research. This delay also has been due to capacity and flexibility but were about twenty times as fast
the necessity of both mechanical and mental development. as the sequence calculator. They are still the fastest relay
When Mr. Watson became president of the International calculators in operation.
Business Machines Corporation in 1914, he immediately In 1945, a special table printing device was installed at
organized a development program to make the machines the Naval Observatory which enabled the scientist to print
more versatile. From 1914 to 1930 there was extensive de- mathematical tables from punched cards in a form suitable
velopment of the various functions of the machines such as for direct reproduction by the printer. In the same year, the
reading cards, sorting, printing, adding, subtracting, multi- recording equipment for the great wind tunnel at California
plying and recording. During the following two decades Institute of Technology was installed so that the observa-
further remarkable technical development in the machines tional data could be recorded directly in cards without
occurred, but in my opinion the mental development among hand transcription. Then came the 603, the first commercial
the scientists and engineers has been more striking. During electronic calculator, which has been replaced by the more
this time there has come the general realization that the versatile IBM Type 604 Electronic Calculating Punch. The
punched card had already provided the means of automati- Selective Sequence Electronic Calculator, which was dedi-
cally handling scientific and engineering data. The recent cated in January, 1948, provided electronic speed of opera-
introduction of the electronic circuit, which has greatly in- tion together with an internal storage capacity of half a
creased the speed of some operations, has dramatized the million digits and completely automatic programming. The
automatic process, but the hundreds of successful automatic Card Programmed Electronic Calculator is the most recent
computing installations now in operation have their roots in addition.
the mental revolution of the past two decades. From such a wide variety of available punched card ma-
It is interesting to note that during this period Mr. chines-:-sorters, accounting machines, collators, reproduc-
Watson saw the importance of automatic computation to ers, the 602, the 602-A, the 604, the CPC, and the SSEC-
science more clearly than the scientist or the engineer, and many of you are probably wondering which equipment you
the present widespread use of such facilities is due in large should use and why. Since much of the later part of the
measure to his early efforts. These efforts included not only program deals with the more recent machines such as the
the rapid development of standard machines to make them 604 and the CPC and their detailed application, I shall con-
more generally useful, but the development of many special fine my attention to some of the more basic uses of the
devices for academic purposes. In 1928 he established the punched card and of the simpler punched card machinf!s.
Columbia University Statistical Bureau for educational re- I shall take my examples from some of the earlier work;
search, and soon after installed there a special statistical it is interesting to note that in many applications these early
calculator. The operation of this machine was very striking techniques are still the most efficient in spite of all the ad-
even by today's standards. It would read data and limited vances that have been made in design. Moreover, many of
operating instructions from the cards at the rate of nearly a these early techniques clearly illustrate basic principles that
million digits an hour; it would add 100 digits simultane- can be readily applied in general.
ously from the cards or from other parts of the machine A question of basic importance in the application of the
according to a complicated program, and print the results punched card is whether the calculation should be done
at the rate of nearly one-half a million digits an hour. In sequentially or in parallel. In a computation with a desk
1933 a second laboratory was established at Columbia capa- calculator the problem also arises, and we shall illustrate it
SEMINAR PROCEEDINGS 15
with a simple calculation. Let us assume that we wish to The simple sorter can rearrange cards at the rate of 500 or
evaluate the formula 600 a minute. When you consider that each card carries
+ + +
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