Chapter XVIII: Conclusion (2)

ECKERT, W. J., The IBM Pluggable Sequence
Relay Calculator, _Mathematical Tables and Other
Aids to Computation_, vol. 3, no. 23, July 1948,
pp. 149-161.

A description of punch-card machinery in rather a light vein is contained in:

ANONYMOUS, Speaking of Pictures: New
Mechanical Monsters Ease _Life’s_ Growing Pains,
_Life_, Sept. 15, 1947, pp. 15-16.

ANONYMOUS, _540_, Chicago:
Time-Life-Fortune Magazine,
Subscription Fulfillment Office, 1948, 15 pp.

New types of punch-card machinery are continually coming into use. Among them are: machines that take in punch cards and make punched paper tape (such as teletype tape), and vice versa—useful for transmitting punch-card information over wires; an electric typewriter operated by punch cards—useful for preparing almanacs for sea and air navigation, etc.; a calculator programmed by punch cards, consisting of an assembly of a tabulator, an electronic calculating punch, and an auxiliary storage unit, all cabled together—useful for some types of long calculation; etc. For information about such machinery, the manufacturers may be consulted.

PUNCH-CARD CALCULATING MACHINERY: APPLICATIONS

There are many articles in scientific journals on applications of punch-card calculating machinery to technical problems. The fields of engineering, education, indexing, mathematics, surveying, statistics, and others are all represented in the following list of sample references:

ALT, FRANZ L., Multiplication of Matrices,
_Mathematical Tables and Other Aids to
Computation_, vol. 2, no. 13, Jan. 1946,
pp. 12-13.

BAILEY, C. F., and others, Punch Cards for
Indexing Scientific Data, _Science_, vol. 104,
Aug. 23, 1946, p. 181.

BOWER, E. C., On Subdividing Tables, _Lick
Observatory Bulletin_, vol. 16, no. 455,
Nov. 1933, pp. 143-144.

BOWER, E. C., Systematic Subdivision of
Tables, _Lick Observatory Bulletin_, vol. 17,
no. 467, Apr. 1935, pp. 65-74.

CLEMENCE, G. M., and PAUL HERGET,
Optimum-Interval Punched-Card Tables,
_Mathematical Tables and Other Aids to
Computation_, vol. 1, no. 6, Apr. 1944,
pp. 173-176.

CULLEY, FRANK L., Use of Accounting Machines
for Mass-Transformation from Geographic to
Military-Grid Coordinates, Washington, D. C.:
National Research Council, _American Geophysical
Union Transactions of 1942_, part 2, pp. 190-197.

DEMING, W. EDWARDS, and MORRIS H.
HANSEN, On Some Census Aids to Sampling,
_Journal of the American Statistical
Association_, vol. 38, no. 225, Sept. 1943,
pp. 353-357.

DUNLAP, JACK W., The Computation of Means,
Standard Deviations, and Correlations by the
Tabulator When the Numbers Are Both Positive
and Negative, _Proceedings of the Educational
Research Forum_, International Business Machines
Corporation, Aug. 1940, pp. 16-19.

DWYER, PAUL S., The Use of Tables in the
Form of Prepunched Cards, _Proceedings of the
Educational Research Forum_, International
Business Machines Corporation, Aug. 1940,
pp. 125-127.

DWYER, PAUL S., Summary of Problems in
the Computation of Statistical Constants with
Tabulating and Sorting Machines, _Proceedings of
the Educational Research Forum_, International
Business Machines Corporation, Aug. 1940, pp. 20-28.

DWYER, PAUL S., and ALAN D. MEACHAM,
The Preparation of Correlation Tables on a
Tabulator Equipped with Digit Selection, _Journal
of the American Statistical Association_, vol.
32, 1937, pp. 654-662.

DYER, H. S., Making Test Score Data Effective
in the Admission and Course Placement of Harvard
Freshmen, _Proceedings of the Research Forum_,
International Business Machines Corporation, 1946,
pp. 55-62.

ECKERT, W. J., and RALPH F. HAUPT,
The Printing of Mathematical Tables,
_Mathematical Tables and Other Aids to
Computation_, vol. 2, no. 17, Jan. 1947,
pp. 196-202.

FEINSTEIN, LILLIAN, and MARTIN
SCHWARZCHILD, Automatic Integration of Linear
Second-Order Differential Equations by Means of
Punched-Card Machines, _Review of Scientific
Instruments_, vol. 12, no. 8, Aug. 1941,
pp. 405-408.

HOTELLING, HAROLD, Some New Methods in
Matrix Calculation, _The Annals of Mathematical
Statistics_, vol. 14, no. 1, Mar. 1943, pp. 1-34.

INTERNATIONAL BUSINESS MACHINES CORPORATION,
editor, and others, _Proceedings of the
Educational Research Forum_, Endicott, N. Y.:
International Business Machines Corporation, 1941.

INTERNATIONAL BUSINESS MACHINES CORPORATION,
editor, and others, _Proceedings of the Research
Forum_, Endicott, N. Y.: International Business
Machines Corporation, 1946, 94 pp.

KING, GILBERT W., Punched-Card Tables of the
Exponential Function, _Review of Scientific
Instruments_, vol. 15, no. 12, Dec. 1944,
pp. 349-350.

KING, GILBERT W., and GEORGE B.
THOMAS, Preparation of Punched-Card
Tables of Logarithms, _Review of Scientific
Instruments_, vol. 15, no. 12, Dec. 1944, p. 350.

KORMES, MARK, A Note on the Integration of
Linear Second-Order Differential Equations by
Means of Punched Cards, _Review of Scientific
Instruments_, vol. 14, no. 4, Apr. 1943, p. 118.

KORMES, MARK, Numerical Solution of the
Boundary Value Problem for the Potential Equation
by Means of Punched Cards, _Review of Scientific
Instruments_, vol. 14, no. 8, Aug. 1943,
pp. 248-250.

KORMES, MARK, and JENNIE P. KORMES,
Numerical Solution of Initial Value Problems by
Means of Punched-Card Machines, _Review of
Scientific Instruments_, vol. 16, no. 1,
Jan. 1945, pp. 7-9.

KUDER, G. FREDERIC, Use of the IBM Scoring
Machine for Rapid Computation of Tables of
Intercorrelations, _Journal of Applied
Psychology_, vol. 22, no. 6, Dec. 1938,
pp. 587-596.

MAXFIELD, D. K., Library Punched Card
Procedures, _Library Journal_, vol. 71,
no. 12, June 15, 1946, pp. 902-905 ...

MCLAUGHLIN, KATHLEEN, Adding Machines Nip AEF
Epidemics, New York: _New York Times_,
Apr. 27, 1945.

MCPHERSON, JOHN C., On Mechanical Tabulation
of Polynomials, _Annals of Mathematical
Statistics_, Sept. 1941, pp. 317-327.

MCPHERSON, JOHN C., Mathematical Operations
with Punched Cards, _Journal of the American
Statistical Association_, vol. 37, June 1942,
pp. 275-281.

MILLIMAN, WENDELL A., Mechanical
Multiplication by the Use of Tabulating Machines,
_Transactions of the Actuarial Society of
America_, vol. 35, part 2, Oct. 1934, pp.
253-264; for discussion see also vol. 36, part 1,
May 1935, pp. 77-84.

ROYER, ELMER B., A Machine Method for
Computing the Biserial Correlation Coefficient in
Item Validation, _Psychometrika_, vol. 6,
no. 1, Feb. 1941, pp. 55-59.

WHITTEN, C. A., Triangulation Adjustment by
International Business Machines, Washington, D. C.:
National Research Council, _American Geophysical
Union Transactions of 1943_, part 1, p. 31.

The following bibliography may be obtained on request to the Watson Scientific Computing Laboratory, Columbia University, 612 West 116 Street, New York 27, N. Y.:

WATSON SCIENTIFIC COMPUTING LABORATORY,
_Bibliography: The Use of IBM Machines in
Scientific Research, Statistics, and Education_,
New York: International Business Machines
Corporation (form no. 50-3813-0), Sept. 1947, 25 pp.

The organization and equipment of this laboratory are described in:

ECKERT, W. J., Facilities of the Watson
Scientific Computing Laboratory, _Proceedings
of the Research Forum_, International Business
Machines Corporation, 1946, pp. 75-80.

THE DIFFERENTIAL ANALYZER

The basic scientific articles on the two differential analyzers at Massachusetts Institute of Technology are:

BUSH, VANNEVAR, The Differential Analyzer: A
New Machine for Solving Differential Equations,
_Journal of the Franklin Institute_, vol. 212,
no. 4, Oct. 1931, pp. 447-488.

BUSH, VANNEVAR, and SAMUEL H.
CALDWELL, A New Type of Differential Analyzer,
_Journal of the Franklin Institute_, vol. 240,
no. 4, Oct. 1945, pp. 255-326.

Some of the less technical articles about the second differential analyzer at M.I.T. are:

CALDWELL, SAMUEL H., Educated Machinery,
_Technology Review_, vol. 48, no. 1,
Nov. 1945, pp. 31-34.

GENET, N., 100-Ton Brain at M.I.T.,
_Scholastic_, vol. 48, Feb. 4, 1946, p. 36.

ANONYMOUS, Mathematical Machine; New
Electronic Differential Analyzer, _Science News
Letter_, vol. 48, Nov. 10, 1945, p. 291.

ANONYMOUS, Robot Einstein: Differential
Analyzer at M.I.T., _Newsweek_, vol. 26,
Nov. 12, 1945, p. 93.

ANONYMOUS, M.I.T.’s 100-Ton Mathematical Brain
is Now to Tackle Problems of Peace, _Popular
Science_, vol. 148, Jan. 1946, p. 81.

ANONYMOUS, The Great Electro-Mechanical Brain;
M.I.T.’s Differential Analyzer, _Life_,
vol. 20, Jan. 14, 1946, pp. 73-74 ...

ANONYMOUS, All the Answers at Your Fingertips;
in the Laboratory of M.I.T., _Popular
Mechanics_, vol. 85, Mar. 1946, pp. 164-167 ...

A differential analyzer was built at the Moore School of Electrical Engineering:

TRAVIS, IRVEN, Differential Analyzer
Eliminates Brain Fag, _Machine Design_, July
1935, pp. 15-18.

A differential analyzer was built at the General Electric Company, Schenectady, N. Y. Instead of using a mechanical or electrical amplifier of the motion of the little turning wheel riding on the disc, this machine follows the motion using polarized light. This machine is described in:

BERRY, T. M., Polarized Light Servo System,
_Transactions of the American Institute of
Electrical Engineers_, vol. 63, Apr. 1944,
pp. 195-197.

KUEHNI, H. P., and H. A. PETERSON, A
New Differential Analyzer, _Transactions of the
American Institute of Electrical Engineers_,
vol. 63, May 1944, pp. 221-227.

A differential analyzer has been put into use at the University of California:

BOELTER, L. M. K., and others, _The
Differential Analyzer of the University of
California_, Los Angeles: University of
California, 1947, 25 pp.

A differential analyzer was built at Manchester University, England. It was built first from “Meccano” parts, at a total cost of about 20 pounds, and later refined for more exact work. Some articles dealing with this differential analyzer are:

HARTREE, D. R., The Differential Analyzer,
_Nature_, vol. 135, June 8, 1935, p. 940.

HARTREE, D. R., The Mechanical Integration
of Differential Equations, _The Mathematical
Gazette_, vol. 22, 1938, pp. 342-364.

HARTREE, D. R., and A. PORTER,
The Construction of a Model Differential Analyser,
_Memoirs and Proceedings of the Manchester
Literary and Philosophical Society_, vol. 79,
July 1935, pp. 51-72.

Other small scale differential analyzers built in England are covered in:

BEARD, R. E., The Construction of a Small
Scale Differential Analyser and Its Application to
the Calculation of Actuarial Functions, _Journal
of the Institute of Actuaries_, vol. 71, 1942,
pp. 193-227.

MASSEY, H. S. W., J. WYLIE,
and R. A. BUCKINGHAM, A Small Scale
Differential Analyser: Its Construction and
Operation, _Proceedings of the Royal Irish
Academy_, vol. 45, 1938, pp. 1-21.

A differential analyzer constructed in Germany is briefly described in the following:

SAUER, R., and H. POESCH, Integrating
Machine for Solving Ordinary Differential
Equations, _Engineers Digest_ (American
Edition), vol. 1, May 1944, pp. 326-328.

From the historical point of view there are some interesting papers on a machine for solving differential equations by Sir William Thomson (Lord Kelvin), including one by his brother James Thomson. They are in the _Proceedings of the Royal Society_, vol. 24, Feb. 1876, pp. 262-275. The method of integration by a machine is described, but the state of machine tools at the time was such that no accurate mechanism was constructed. Another interesting paper foreshadowing the differential analyzer is:

WAINWRIGHT, LAWRENCE L., _A Ballistic
Engine_, Chicago: University of Chicago,
thesis for Master’s Degree, 1923, 28 pp.

Some of the applications and mathematical limitations of differential analyzers are covered in:

BUSH, V., and S. H. CALDWELL,
Thomas-Fermi Equation Solution by the Differential
Analyzer, _Physical Review_, vol. 38, no. 10,
1931, pp. 1898-1902.

HARTREE, D. R., A Great Calculating Machine:
the Bush Differential Analyser and Its Applications
in Science and Industry, _Proceedings of the
Royal Institution of Great Britain_, vol. 31,
1940, pp. 151-170.

HARTREE, D. R., and A. PORTER,
The Application of the Differential Analyser
to Transients on a Distortionless Transmission
Line, _Journal of the Institute of Electrical
Engineering_, vol. 83, no. 503, Nov. 1938,
pp. 648-656.

HARTREE, D. R., and J. R. WOMERSLEY,
A Method for the Numerical or Mechanical Solution
of Certain Types of Partial Differential Equations,
_Proceedings of the Royal Society of London_,
series A, vol. 161, 1937, pp. 353-366.

MAGINNISS, F. J., Differential Analyzer
Applications, _General Electric Review_,
vol. 48, no. 5, May 1945, pp. 54-59.

SHANNON, CLAUDE E., Mathematical Theory of the
Differential Analyzer, _Journal of Mathematics
and Physics_, Cambridge, Mass.: Massachusetts
Institute of Technology, vol. 20, no. 4, 1941,
pp. 337-354.

HARMONIC ANALYZERS AND SYNTHESIZERS

Another branch of the analogue calculating machine is the harmonic analyzer and synthesizer. These are machines that study wave motions and related physical and mathematical functions. A brief list of articles on this type of machine follows:

ARCHER, R. M., Projecting Apparatus for
Compounding Harmonic Vibrations, _Journal of
Scientific Instruments_, vol. 14, 1937,
pp. 408-410.

BROWN, S. L., A Mechanical Harmonic
Synthesizer-Analyzer, _Journal of the Franklin
Institute_, vol. 228, 1939, pp. 675-694.

BROWN, S. L., and L. L. WHEELER,
A Mechanical Method for Graphical Solution
of Polynomials, _Journal of the Franklin
Institute_, vol. 231, 1941, pp. 223-243.

BROWN, S. L., and L. L. WHEELER, Use
of the Mechanical Multiharmonograph for Graphing
Types of Functions and for Solution of Pairs of
Non-Linear Simultaneous Equations, _Review of
Scientific Instruments_, vol. 13, Nov. 1942,
pp. 493-495.

BROWN, S. L., and L. L. WHEELER,
The Use of a Mechanical Synthesizer to Solve
Trigonometric and Certain Types of Transcendental
Equations, and for the Double Summations Involved
in Patterson Contours, _Journal of Applied
Physics_, vol. 14, Jan. 1943, pp. 30-36.

FÜRTH, R., and R. W. PRINGLE, A
New Photo-Electric Method for Fourier Synthesis
and Analysis, _London, Edinburgh and Dublin
Philosophical Magazine and Journal of Science_,
vol. 35, series 7, 1944, pp. 643-656.

INTERNATIONAL HYDROGRAPHIC BUREAU, _Tide
Predicting Machines_, International Hydrographic
Bureau, Special Publication 13, July 1926.

KRANZ, FREDERICK W., A Mechanical Synthesizer
and Analyzer, _Journal of the Franklin
Institute_, vol. 204, 1927, pp. 245-262.

MARBLE, F. G., An Automatic Vibration
Analyzer, _Bell Laboratories Record_, vol. 22,
Apr. 1944, pp. 376-380.

MAXWELL, L. R., An Electrical Method for
Compounding Sine Functions, _Review of Scientific
Instruments_, vol. 11, Feb. 1940, pp. 47-54.

MILLER, DAYTON C., A 32-Element Harmonic
Synthesizer, _Journal of the Franklin
Institute_, vol. 181, 1916, pp. 51-81.

MILLER, DAYTON C., The Henrici Harmonic
Analyzer and Devices for Extending and Facilitating
Its Use, _Journal of the Franklin Institute_,
vol. 182, 1916, pp. 285-322.

MILNE, J. R., A “Duplex” Form of Harmonic
Synthetiser and Its Mathematical Theory,
_Proceedings of the Royal Society of
Edinburgh_, vol. 39, 1918-19, pp. 234-242.

MONTGOMERY, H. C., An Optical Harmonic
Analyzer, _Bell System Technical Journal_,
vol. 17, no. 3, July 1938, pp. 406-415.

RAYMOND, W. J., An Harmonic Synthesizer Having
Components of Incommensurable Period and Any
Desired Decrement, _Physical Review_, vol. 11,
series 2, 1918, pp. 479-481.

ROBERTSON, J. M., A Simple Harmonic Continuous
Calculating Machine, _London, Edinburgh and
Dublin Philosophical Magazine and Journal of
Science_, vol. 13, 1932, pp. 413-419.

SOMERVILLE, J. M., Harmonic Synthesizer for
Demonstrating and Studying Complex Wave Forms,
_Journal of Scientific Instruments_, vol. 21,
Oct. 1944, pp. 174-177.

STRAITON, A. W., and G. K. TERHUNE,
Harmonic Analysis by Photographic Method,
_Journal of Applied Physics_, vol. 14, 1943,
pp. 535-536.

WEGEL, R. L., and C. R. MOORE, An
Electrical Frequency Analyzer, _Bell System
Technical Journal_, vol. 3, 1924, pp. 299-323.

NETWORK ANALYZERS

A third branch of the analogue calculating machine is the network analyzer. To solve problems, this machine uses the laws governing a network of electrical circuits. For example, an electric power company with a system of power lines over hundreds of miles may have a problem about electrical power: will an accident or a sudden demand cause a breakdown anywhere in the system? In the General Electric Company in Schenectady, N. Y., there is a machine called the A.C. Network Analyzer. All the properties of the power company’s network of lines can be fed on a small scale into the analyzer. Certain dials are turned and certain plugwires are connected. Then various kinds of “accidents” and “sudden demands” are fed into the machine, and the response of the system is noted. The answers given by the machine are multiplied by the proper scale factor, and in this way the problem of the power company is solved.

There are two kinds of problems that network analyzers are built to solve: the steady state conditions and the transient conditions. For example, you may not overload a fuse with an electric iron when it is plugged in and being used, but as you pull out the cord, you may blow the fuse: the steady state does not overstrain the system, but the transient does.

Some articles on network analyzers are:

ENNS, W. E., A New Simple Calculator of Load
Flow in A.C. Networks, _Transactions of the
American Institute of Electrical Engineers_,
vol. 62, 1943, pp. 786-790.

HAZEN, H. L., and others, _The M.I.T.
Network Analyzer_, Cambridge, Mass.:
Massachusetts Institute of Technology, Department
of Electrical Engineering, Serial No. 69, Apr. 1931.

KUEHNI, H. P., and R. G. LORRAINE,
A New A.C. Network Analyzer, _Transactions of the
American Institute of Electrical Engineers_,
vol. 57, 1938, pp. 67-73.

PARKER, W. W., Dual A.C. Network Calculator,
_Electrical Engineering_, May 1945,
pp. 182-183.

PARKER, W. W., The Modern A.C. Network
Calculator, _Transactions of the American
Institute of Electrical Engineers_, vol. 60,
Nov. 1941, pp. 977-982.

PETERSON, H. A., An Electric Circuit Transient
Analyzer, _General Electric Review_,
Sept. 1939, pp. 394-400.

VARNEY, R. N., An All-Electric Integrator
for Solving Differential Equations, _Review of
Scientific Instruments_, vol. 13, Jan. 1942,
pp. 10-16.

Some of the articles on applications of network analyzers to various problems are:

KRON, GABRIEL, Equivalent Circuits of the
Elastic Field, _Journal of Applied Mechanics_,
vol. A11, Sept. 1944, pp. 146-161.

KRON, GABRIEL, Tensorial Analysis and
Equivalent Circuits of Elastic Structures,
_Journal of the Franklin Institute_, vol. 238,
Dec. 1944, pp. 399-442.

KRON, GABRIEL, Numerical Solution of Ordinary
and Partial Differential Equations by Means
of Equivalent Circuits, _Journal of Applied
Physics_, vol. 16, 1945, pp. 172-186.

KRON, GABRIEL, Electric Circuit Models for
the Vibration Spectrum of Polyatomic Molecules,
_Journal of Chemical Physics_, vol. 14, no. 1,
Jan. 1946, pp. 19-31.

KRON, G., and G. K. CARTER, A.C.
Network Analyzer Study of the Schrödinger Equation,
_Physical Review_, vol. 67, 1945, pp. 44-49.

KRON, G., and G. K. CARTER, Network
Analyzer Tests of Equivalent Circuits of Vibrating
Polyatomic Molecules, _Journal of Chemical
Physics_, vol. 14, no. 1, Jan. 1946, pp. 32-34.

PETERSON, H. A., and C. CONCORDIA,
Analyzers for Use in Engineering and Scientific
Problems, _General Electric Review_, vol. 48,
no. 9, Sept. 1945, pp. 29-37.

MACHINES FOR SOLVING ALGEBRAIC EQUATIONS

Another branch of the analogue calculating machine is a type of machine that will solve various kinds of algebraic equations (see Supplement 2). A list of some articles follows. The article by Mallock describes a machine for solving up to 10 linear simultaneous equations in 10 unknowns, and the article by Wilbur, a machine for solving up to 9.

DIETZOLD, ROBERT L., The Isograph—A
Mechanical Root-Finder, _Bell Laboratories
Record_, vol. 16, no. 4, Dec. 1937, pp. 130-134.

DUNCAN, W. J., Some Devices for the Solution
of Large Sets of Simultaneous Linear Equations,
_London, Edinburgh, and Dublin Philosophical
Magazine and Journal of Science_,
vol. 35, series 7, 1944, pp. 660-670.

FRAME, J. SUTHERLAND, Machines for Solving
Algebraic Equations, _Mathematical Tables and
Other Aids to Computation_, vol. 1, no. 9,
Jan. 1945, pp. 337-353.

HART, H. C., and IRVEN TRAVIS,
Mechanical Solution of Algebraic Equations,
_Journal of the Franklin Institute_,
vol. 225, Jan. 1938, pp. 63-72.

HERR, D. L., and R. S. GRAHAM, An
Electrical Algebraic Equation Solver, _Review of
Scientific Instruments_, vol. 9, Oct. 1938, pp.
310-315.

MALLOCK, R. R. M., An Electrical Calculating
Machine, _Proceedings of the Royal Society_,
series A, vol. 140, 1933, pp. 457-483.

MERCNER, R. O., The Mechanism of the Isograph,
_Bell Laboratories Record_, vol. 16, no. 4,
Dec. 1937, pp. 135-140.

STIBITZ, GEORGE R., Electric Root-finder,
_Mathematical Tables and Other Aids to
Computation_, vol. 3, no. 24, Oct. 1948,
pp. 328-329.

WILBUR, J. B., The Mechanical Solution of
Simultaneous Equations, _Journal of the Franklin
Institute_, vol. 222, Dec. 1936, pp. 715-724.

ANALOGUE MACHINES—MISCELLANEOUS

Some articles referring to various other kinds of analogue machines and their applications are here listed together:

BUSH, V., F. D. GAGE, and R. R.
STEWART, A Continuous Integraph, _Journal
of the Franklin Institute_, vol. 203, 1927,
pp. 63-84.

GRAY, T. S., A Photo-Electric Integraph,
_Journal of the Franklin Institute_, vol. 212,
1931, pp. 77-102.

HAZEN, H. L., G. S. BROWN, and W.
R. HEDEMAN, The Cinema Integraph: A Machine
for Evaluating a Parametric Product Integral (two
parts and appendix), _Journal of the Franklin
Institute_, vol. 230, July 1940, pp. 19-44,
and Aug. 1940, pp. 183-205.

MCCANN, G. D., and H. E. CRINER,
Mechanical Problems Solved Electrically,
_Westinghouse Engineer_, vol. 6, no. 2,
March 1946, pp. 49-56.

MYERS, D. M., An Integraph for the Solution
of Differential Equations of the Second-Order,
_Journal of Scientific Instruments_, vol. 16,
1939, pp. 209-222.

PEKERIS, C. L., and W. T. WHITE,
Differentiation with the Cinema Integraph,
_Journal of the Franklin Institute_, vol. 234,
July 1942, pp. 17-29.

SMITH, C. E., and E. L. GOVE,
An Electromechanical Calculator for
Directional-Antenna Patterns, _Transactions of
the American Institute of Electrical Engineers_,
vol. 62, 1943, pp. 78-82.

YAVNE, R. O., High Accuracy Contour Cams,
_Product Engineering_, vol. 19, part 2,
Aug. 1948, 3 pp.

ANONYMOUS, Electrical Gun Director
Demonstrated, _Bell Laboratories Record_,
vol. 22, no. 4, Dec. 1943, pp. 157-167.

ANONYMOUS, Development of the Electric
Director, _Bell Laboratories Record_, vol. 22,
no. 5, Jan. 1944, pp. 225-230.

ANONYMOUS, Old Field Fortune Teller:
Electronic Oil Pool Analyzer, _Popular
Mechanics_, vol. 86, Sept. 1946, p. 154.

HARVARD IBM AUTOMATIC SEQUENCE-CONTROLLED CALCULATOR

The basic scientific description of this machine as of September 1, 1945, is contained in:

AIKEN, HOWARD H., and STAFF OF THE
COMPUTATION LABORATORY, _A Manual of
Operation for the Automatic Sequence-Controlled
Calculator_, Cambridge, Mass.: Harvard
University Press, 1946, 561 pp.

The machine has changed rather a good deal since Sept. 1, 1945. Some circuits have been removed. Other circuits have been added. The capacity of the machine to do problems has been greatly increased. The Computation Laboratory at Harvard University is cordial towards scientific inquiries, and some unpublished, mimeographed information is available at the laboratory regarding the details of these changes.

Some shorter scientific and technical descriptions of the machine are contained in:

AIKEN, HOWARD H., and GRACE
M. HOPPER, The Automatic Sequence
Controlled Calculator (3 parts), _Electrical
Engineering_, vol. 65, nos. 8, 9, and 10,
Aug. to Nov. 1946, p. 384 ... (21 pp.).

BLOCH, RICHARD M., Mark I Calculator,
_Proceedings of a Symposium on Large-Scale
Digital Calculating Machinery_, Harvard
University Press, 1948, pp. 23-30.

HARRISON, JOSEPH O., JR., The Preparation of
Problems for the Mark I Calculator, _Proceedings
of a Symposium on Large-Scale Digital Calculating
Machinery_, Harvard University Press, 1948,
pp. 208-210.

INTERNATIONAL BUSINESS MACHINES CORPORATION,
_IBM Automatic Sequence-Controlled
Calculator_, Endicott, N. Y.: International
Business Machines Corporation, 1945, 6 pp.

Some of the less technical articles regarding the machine are:

GENET, N., Got a Problem? Harvard’s Amazing
New Mathematical Robot, _Scholastic_, vol. 45,
Sept. 18, 1944, p. 35.

TORREY, V., Robot Mathematician Knows All the
Answers, _Popular Science_, vol. 145,
Oct. 1944, pp. 86-89....

ANONYMOUS, Giant New Calculator, _Science
News Letter_, vol. 46, Aug. 12, 1944, p. 111.

ANONYMOUS, Mathematical Robot Presented to
Harvard, _Time_, vol. 44, Aug. 14, 1944, p. 72.

ANONYMOUS, World’s Greatest Machine for
Automatic Calculation, _Science News Letter_,
vol. 46, Aug. 19, 1944, p. 123.

ANONYMOUS, Superbrain, _Nation’s
Business_, vol. 32, Sept. 1944, p. 8.

ANONYMOUS, Robot Works Problems Never Before
Solved, _Popular Mechanics_, vol. 82,
Oct. 1944, p. 13.

ENIAC, THE ELECTRONIC NUMERIC INTEGRATOR AND CALCULATOR

There is as yet no full-scale, published scientific account of the Eniac. At the Ballistic Research Laboratories, Aberdeen, Md., where the machine now is, there are a few copies of some long mimeographed reports on the machine and the way it works. These were prepared by H. H. Goldstine and others when at the Moore School of Electrical Engineering, as a part of the contract under which the machine was constructed for the U. S. Government. It is possible that these reports might be consulted on request by serious students.

Some scientific descriptions of the machine and its properties are:

BURKS, ARTHUR W., Electronic Computing
Circuits of the ENIAC, _Proceedings of the
Institute of Radio Engineers_, vol. 35, no. 8,
Aug. 1947, pp. 756-767.

CLIPPINGER, R. F., _A Logical Coding System
Applied to the Eniac_, B. R. L. Report No. 673,
Aberdeen, Md.: Ballistic Research Laboratories,
Sept. 29, 1948, 41 pp.

ECKERT, J. PRESPER, JR., JOHN W.
MAUCHLY, HERMAN H. GOLDSTINE, and
J. G. BRAINERD, Description of the ENIAC
and Comments on Electronic Digital Computing
Machines, Applied Mathematics Panel Report 171.2R,
Washington, D. C.: National Defense Research
Committee, Nov. 1945, 78 pp.

GOLDSTINE, HERMAN H., and ADELE
GOLDSTINE, The Electronic Numerical Integrator
and Computer (ENIAC), _Mathematical Tables and
Other Aids to Computation_, vol. 2, no. 15,
July 1946, pp. 97-110.

HARTREE, D. R., The ENIAC, an Electronic
Computing Machine, _Nature_, vol. 158,
Oct. 12, 1946, pp. 500-506.

HARTREE, D. R., _Calculating Machines:
Recent and Prospective Developments and Their
Impact on Mathematical Physics_, Cambridge,
England: The University Press, 1947, 40 pp.
(Pages 14 to 27 are devoted to the Eniac.)

TABOR, LEWIS P., Brief Description and
Operating Characteristics of the ENIAC,
_Proceedings of a Symposium on Large-Scale
Digital Calculating Machinery_, Harvard
University Press, 1948, pp. 31-39.

Some of the less technical articles on Eniac are:

ROSE, A., Lightning Strikes Mathematics:
ENIAC, _Popular Science_, vol. 148,
Apr. 1946, pp. 83-86.

ANONYMOUS, Robot Calculator: ENIAC, All
Electronic Device, _Business Week_,
Feb. 16, 1946, p. 50 ...

ANONYMOUS, Answers by ENY: Electronic
Numerical Integrator and Computer, ENIAC,
_Newsweek_, vol. 27, Feb. 18, 1946, p. 76.

ANONYMOUS, Adds in ¹/₅₀₀₀ Second: Electronic
Computing Machine at the University of
Pennsylvania, _Science News Letter_, vol. 49,
Feb. 23, 1946, p. 113 ...

ANONYMOUS, ENIAC: at the University of
Pennsylvania, _Time_, vol. 47,
Feb. 25, 1946, p. 90.

ANONYMOUS, It Thinks with Electrons; the
ENIAC, _Popular Mechanics_, vol. 85,
June 1946, p. 139.

ANONYMOUS, Electronic Calculator: ENIAC,
_Scientific American_, vol. 174,
June 1946, p. 248.

BELL LABORATORIES RELAY COMPUTERS

As yet no full-scale scientific report is available on the Bell Laboratories general-purpose relay computers that went to Aberdeen and Langley Field. However, there is some information about these and other Bell Laboratories relay computing machines in the following articles:

ALT, FRANZ L., A Bell Telephone Laboratories’
Computing Machine (two parts), _Mathematical
Tables and Other Aids to Computation_, vol. 3,
no. 21, Jan. 1948, pp. 1-13, and vol. 3, no. 22,
Apr. 1948, pp. 69-84.

CESAREO, O., The Relay Interpolator, _Bell
Laboratories Record_, vol. 24, no. 12,
Dec. 1946, pp. 457-460.

JULEY, JOSEPH, The Ballistic Computer, _Bell
Laboratories Record_, vol. 25, no. 1,
Jan. 1947, pp. 5-9.

WILLIAMS, SAMUEL B., A Relay Computer
for General Application, _Bell Laboratories
Record_, vol. 25, no. 2,
Feb. 1947, pp. 49-54.

WILLIAMS, SAMUEL B., Bell Telephone
Laboratories’ Relay Computing System,
_Proceedings of a Symposium on Large-Scale
Digital Calculating Machinery_, Harvard
University Press, 1948, pp. 40-68.

ANONYMOUS, Complex Computer Demonstrated,
_Bell Laboratories Record_, vol. 19, no. 2,
Oct. 1940, pp. v-vi.

ANONYMOUS, _Computer Mark 22 Mod. 0:
Development and Description_, Navord Report
No. 178-45, Washington, D. C.: Navy Department,
Dec. 6, 1945, 225 pp.

ANONYMOUS, Relay Computer for the Army,
_Bell Laboratories Record_, vol. 26, no. 5,
May 1948, pp. 208-209.

THE KALIN-BURKHART LOGICAL-TRUTH CALCULATOR

As yet there are no published references on the Kalin-Burkhart Logical-Truth Calculator.

Some books covering a good deal of mathematical logic are:

QUINE, W. V., _Mathematical Logic_, New
York: W. W. Norton & Co., 1940, 348 pp.

REICHENBACH, HANS, _Elements of Symbolic
Logic_, New York: The Macmillan Co., 1947, 444
pp.

TARSKI, ALFRED, _Introduction to Logic_,
New York: Oxford University Press, 1941, 239 pp.

WOODGER, J. H., _The Axiomatic Method in
Biology_, Cambridge, England: The University
Press, 1937, 174 pp.