Supplement 3REFERENCES
A book like the present one can cover only a part of the subject of machines that think. To obtain more information about these machines and other topics to which they are related there are many references that may be consulted. There are still few books directly on the subject of machines that think, but there are many articles and papers, most of them rather specialized.
The purpose of this supplement is to give a number of these references and to provide a brief, general introduction to some of them. The references are subdivided into groups, each dealing with a branch of the subject. The references in each group are in alphabetical order by name of author (with “anonymous” last), and under each author they are in chronological order by publication date. Some publications, especially a forum or symposium, are listed more than once, according as the topic discussed falls in different groups. In this supplement, the sign three dots ( ...) next to the page numbers for an article indicates that the article is continued on later, nonconsecutive pages.
It seemed undesirable to try to make the group of references dealing with a subject absolutely complete, so long as enough were given to provide a good introduction to the subject. It proved impractical to try to make the citation of every single reference technically complete, so long as enough citation was given so that the reference could certainly be found. Furthermore, in a list of more than 250 references, errors are almost certain to occur. If any reader should send me additions or corrections, I shall be more than grateful.
No one yet knows specifically how particular ideas are thought about in the human brain. The references listed in this section, however, contain some information about such topics as:
The structural differences, development, and evolution of the brains of animals, apes, primitive man, and modern man.The effect on the brain of blood composition, body temperature, supply of oxygen, and other biochemical factors.The structure and physiology of the brain, the nervous system, and nerve impulses.The theory of learning, intelligence, and memory.
The structural differences, development, and evolution of the brains of animals, apes, primitive man, and modern man.
The effect on the brain of blood composition, body temperature, supply of oxygen, and other biochemical factors.
The structure and physiology of the brain, the nervous system, and nerve impulses.
The theory of learning, intelligence, and memory.
Barcroft, Joseph,The Brain and Its Environment, New Haven: Yale University Press, 1948, 117 pp.Beach, Frank A., Payday for Primates,Natural History, vol. 56, no. 10, Dec. 1947, pp. 448-451.Beach, Frank A., Can Animals Reason?Natural History, vol. 57, no. 3, Mar. 1948, pp. 112-116 ...Berry, R. J. A.,Brain and Mind, or the Nervous System of Man, New York: The Macmillan Co., 1928, 608 pp.Boring, Edwin G.,A History of Experimental Psychology, New York: Century Co., 1929, 699 pp.Franz, Shepherd I.,The Evolution of an Idea; How the Brain Works, Los Angeles: University of California, 1929, 35 pp.Herrick, C. Judson,The Thinking Machine, Chicago: University of Chicago Press, 1929, 374 pp.Herrick, C. Judson,Brains of Rats and Men, Chicago: University of Chicago Press, 1930, 382 pp.Lashley, Karl S.,Brain Mechanisms and Intelligence, Chicago: University of Chicago Press, 1929, 186 pp.Pieron, Henri,Thought and the Brain, London: Kegan, Paul, Trench, Trübner & Co., 1927, 262 pp. Also New York: Harcourt, Brace & Co.Schrödinger, Erwin,What is Life?, New York: The Macmillan Co., 1945, 90 pp.Sherrington, Charles S.,The Brain and Its Mechanism, Cambridge, England: The University Press, 1933, 35 pp.Tilney, Frederick,The Brain from Ape to Man, New York: P. B. Hoeber, Inc., 1928, 2 vol., 1075 pp.Wiener, Norbert,Cybernetics, or Control and Communication in the Animal and the Machine, New York: John Wiley & Sons, 1948, 194 pp.Anonymous, Ten Billion Relays,Time, Feb. 14, 1949, p. 67.
Barcroft, Joseph,The Brain and Its Environment, New Haven: Yale University Press, 1948, 117 pp.
Beach, Frank A., Payday for Primates,Natural History, vol. 56, no. 10, Dec. 1947, pp. 448-451.
Beach, Frank A., Can Animals Reason?Natural History, vol. 57, no. 3, Mar. 1948, pp. 112-116 ...
Berry, R. J. A.,Brain and Mind, or the Nervous System of Man, New York: The Macmillan Co., 1928, 608 pp.
Boring, Edwin G.,A History of Experimental Psychology, New York: Century Co., 1929, 699 pp.
Franz, Shepherd I.,The Evolution of an Idea; How the Brain Works, Los Angeles: University of California, 1929, 35 pp.
Herrick, C. Judson,The Thinking Machine, Chicago: University of Chicago Press, 1929, 374 pp.
Herrick, C. Judson,Brains of Rats and Men, Chicago: University of Chicago Press, 1930, 382 pp.
Lashley, Karl S.,Brain Mechanisms and Intelligence, Chicago: University of Chicago Press, 1929, 186 pp.
Pieron, Henri,Thought and the Brain, London: Kegan, Paul, Trench, Trübner & Co., 1927, 262 pp. Also New York: Harcourt, Brace & Co.
Schrödinger, Erwin,What is Life?, New York: The Macmillan Co., 1945, 90 pp.
Sherrington, Charles S.,The Brain and Its Mechanism, Cambridge, England: The University Press, 1933, 35 pp.
Tilney, Frederick,The Brain from Ape to Man, New York: P. B. Hoeber, Inc., 1928, 2 vol., 1075 pp.
Wiener, Norbert,Cybernetics, or Control and Communication in the Animal and the Machine, New York: John Wiley & Sons, 1948, 194 pp.
Anonymous, Ten Billion Relays,Time, Feb. 14, 1949, p. 67.
There has recently been another approach to the problem: How does a brain think? A group of men, many of them in and near Chicago, have been saying: “We know the properties of nerves, nerve impulses, and simple nerve networks. We know the activity of the brain. What mathematical model of nerve networks is necessary to account for the activity of the brain?” These men have used mathematics, statistics, and mathematical logic in the effort to attack this problem, and they support aBulletin of Mathematical Biophysics.
Householder, Alston S., A Neural Mechanism for Discrimination,Psychometrika, vol. 4, no. 1, Dec. 1939, pp. 45-58.Householder, Alston S., and Herbert D. Landahl,Mathematical Biophysics of the Central Nervous System, Bloomington, Ind.: Principia Press, 1945.Landahl, Herbert D., Contributions to the Mathematical Biophysics of the Central Nervous System,Bulletin of Mathematical Biophysics, vol. 1, no. 2, June 1939, pp. 95-118.Landahl, Herbert D.,Warren S. McCulloch, andWalter Pitts, A Statistical Consequence of the Logical Calculus of Nervous Nets,Bulletin of Mathematical Biophysics, vol. 5, no. 4, Dec. 1943, pp. 135-137.Landahl, Herbert D., A Note on the Mathematical Biophysics of Central Excitation and Inhibition,Bulletin of Mathematical Biophysics, vol. 7, no. 4, Dec. 1945, pp. 219-221.Lettvin, Jerome Y., andWalter Pitts, A Mathematical Theory of the Affective Psychoses,Bulletin of Mathematical Biophysics, vol. 5, no. 4, Dec. 1943, pp. 139-148.McCulloch, Warren S., andWalter Pitts, A Logical Calculus of the Ideas Immanent in Nervous Activity,Bulletin of Mathematical Biophysics, vol. 5, no. 4, Dec. 1943, pp. 115-133.Rashevsky, N.,Mathematical Biophysics, Chicago: University of Chicago Press. Revised edition, 1948, 669 pp.Rashevsky, N., Mathematical Biophysics of Abstraction and Logical Thinking,Bulletin of Mathematical Biophysics, vol. 7, no. 3, Sept. 1945, pp. 133-148.Rashevsky, N., Some Remarks on the Boolean Algebra of Nervous Nets in Mathematical Biophysics,Bulletin of Mathematical Biophysics, vol. 7, no. 4, Dec. 1945, pp. 203-211.Rashevsky, N., A Suggestion for Another Statistical Interpretation of the Fundamental Equations of the Mathematical Biophysics of the Central Nervous System,Bulletin of Mathematical Biophysics, vol. 7, no. 4, Dec. 1945, pp. 223-226.Rashevsky, N., The Neural Mechanism of Logical Thinking,Bulletin of Mathematical Biophysics, vol. 8, no. 1, Mar. 1946, pp. 29-40.
Householder, Alston S., A Neural Mechanism for Discrimination,Psychometrika, vol. 4, no. 1, Dec. 1939, pp. 45-58.
Householder, Alston S., and Herbert D. Landahl,Mathematical Biophysics of the Central Nervous System, Bloomington, Ind.: Principia Press, 1945.
Landahl, Herbert D., Contributions to the Mathematical Biophysics of the Central Nervous System,Bulletin of Mathematical Biophysics, vol. 1, no. 2, June 1939, pp. 95-118.
Landahl, Herbert D.,Warren S. McCulloch, andWalter Pitts, A Statistical Consequence of the Logical Calculus of Nervous Nets,Bulletin of Mathematical Biophysics, vol. 5, no. 4, Dec. 1943, pp. 135-137.
Landahl, Herbert D., A Note on the Mathematical Biophysics of Central Excitation and Inhibition,Bulletin of Mathematical Biophysics, vol. 7, no. 4, Dec. 1945, pp. 219-221.
Lettvin, Jerome Y., andWalter Pitts, A Mathematical Theory of the Affective Psychoses,Bulletin of Mathematical Biophysics, vol. 5, no. 4, Dec. 1943, pp. 139-148.
McCulloch, Warren S., andWalter Pitts, A Logical Calculus of the Ideas Immanent in Nervous Activity,Bulletin of Mathematical Biophysics, vol. 5, no. 4, Dec. 1943, pp. 115-133.
Rashevsky, N.,Mathematical Biophysics, Chicago: University of Chicago Press. Revised edition, 1948, 669 pp.
Rashevsky, N., Mathematical Biophysics of Abstraction and Logical Thinking,Bulletin of Mathematical Biophysics, vol. 7, no. 3, Sept. 1945, pp. 133-148.
Rashevsky, N., Some Remarks on the Boolean Algebra of Nervous Nets in Mathematical Biophysics,Bulletin of Mathematical Biophysics, vol. 7, no. 4, Dec. 1945, pp. 203-211.
Rashevsky, N., A Suggestion for Another Statistical Interpretation of the Fundamental Equations of the Mathematical Biophysics of the Central Nervous System,Bulletin of Mathematical Biophysics, vol. 7, no. 4, Dec. 1945, pp. 223-226.
Rashevsky, N., The Neural Mechanism of Logical Thinking,Bulletin of Mathematical Biophysics, vol. 8, no. 1, Mar. 1946, pp. 29-40.
Hardly any field of techniques for thinking is more fascinating than language. The following list of references, of course, is short; it is meant chiefly as an introduction pointing out a number of different paths into the field of language and languages. Such topics as the following are introduced by the references in this list:
Bloomfield, Leonard,Language, New York: Henry Holt & Co., 1933, 564 pp.Bodmer, Frederick, andLauncelot Hogben,The Loom of Language, New York: W. W. Norton & Co., 1944, 692 pp.Flesch, Rudolf,The Art of Plain Talk, New York: Harper & Brothers, 1946, 210 pp.Graff, Willem L.,Language and Languages: An Introduction to Linguistics, New York: D. Appleton & Co., 1932, 487 pp.Hayakawa, S. I.,Language in Action, New York: Harcourt, Brace & Co., 1941, 345 pp.Jespersen, Otto,The Philosophy of Grammar, New York: Henry Holt & Co., 1929 (third printing), 359 pp.Jespersen, Otto,Analytic Syntax,In this book, by means of a well-contrived system of letters and signs, the great linguistic scholar Jespersen depicts all the important inter-relations of English words and parts of words in connected speech.Ogden, C. K.,The System of Basic English, New York: Harcourt, Brace & Co., 1934, 320 pp.Schlauch, Margaret,The Gift of Tongues, New York: Modern Age Books, 1942, 342 pp.Walpole, Hugh R.,Semantics: The Nature of Words and Their Meanings, New York: W. W. Norton & Co., 1941, 264 pp.
Bloomfield, Leonard,Language, New York: Henry Holt & Co., 1933, 564 pp.
Bodmer, Frederick, andLauncelot Hogben,The Loom of Language, New York: W. W. Norton & Co., 1944, 692 pp.
Flesch, Rudolf,The Art of Plain Talk, New York: Harper & Brothers, 1946, 210 pp.
Graff, Willem L.,Language and Languages: An Introduction to Linguistics, New York: D. Appleton & Co., 1932, 487 pp.
Hayakawa, S. I.,Language in Action, New York: Harcourt, Brace & Co., 1941, 345 pp.
Jespersen, Otto,The Philosophy of Grammar, New York: Henry Holt & Co., 1929 (third printing), 359 pp.
Jespersen, Otto,Analytic Syntax,
In this book, by means of a well-contrived system of letters and signs, the great linguistic scholar Jespersen depicts all the important inter-relations of English words and parts of words in connected speech.
Ogden, C. K.,The System of Basic English, New York: Harcourt, Brace & Co., 1934, 320 pp.
Schlauch, Margaret,The Gift of Tongues, New York: Modern Age Books, 1942, 342 pp.
Walpole, Hugh R.,Semantics: The Nature of Words and Their Meanings, New York: W. W. Norton & Co., 1941, 264 pp.
For many years, nearly all references about machines as a language for thinking have been specialized and limited. Colleges with scholars who write textbooks usually have not had a variety of expensive and versatile computing machinery. As a result, the main environment for stimulating possible authors has until recently been missing. The list of references is accordingly brief.
Aiken, Howard H., and others,Proceedings of a Symposium on Large-Scale Digital Calculating Machinery, Cambridge, Mass.: Harvard University Press, 1948, 302 pp.Comrie, John Leslie, The Application of Commercial Calculating Machines to Scientific Computing,Mathematical Tables and Other Aids to Computation, vol. 2, no. 16, Oct. 1946, pp. 149-159.Crew, E. W., Calculating Machines,The Engineer, vol. 172, Dec. 1941, pp. 438-441.Fry, Macon,Designing Computing Mechanisms, Cleveland, Ohio: Penton Publishing Co., 1946, 48 pp. (Reprinted fromMachine Design, Aug. 1945 through Feb. 1946.)Hartree, D. R.,Calculating Machines: Recent and Prospective Developments and Their Impact on Mathematical Physics, Cambridge, England: The University Press, 1947, 40 pp.Horsburgh, E. H.,Modern Instruments and Methods of Calculation, London: G. Bell and Sons, Ltd., 1914, 343 pp.Lilley, S., Mathematical Machines,Nature, vol. 149, Apr. 25, 1942, pp. 462-465.Murray, Francis J.,The Theory of Mathematical Machines, New York: King’s Crown Press, 1947, 116 pp.The author states that a mathematical machine is a mechanism that provides information concerning the relationships among a specified set of mathematical concepts.Turck, J. A. V.,The Origin of Modern Calculating Machines, Chicago: Western Society of Engineers, 1921.Recently, however, some magazine and newspaper publishers have seen news value in machines that think, and some good general articles with appeal to a wide audience have appeared. For the references to these articles, see the section of this supplement entitled “Digital Machines—Miscellaneous.”
Aiken, Howard H., and others,Proceedings of a Symposium on Large-Scale Digital Calculating Machinery, Cambridge, Mass.: Harvard University Press, 1948, 302 pp.
Comrie, John Leslie, The Application of Commercial Calculating Machines to Scientific Computing,Mathematical Tables and Other Aids to Computation, vol. 2, no. 16, Oct. 1946, pp. 149-159.
Crew, E. W., Calculating Machines,The Engineer, vol. 172, Dec. 1941, pp. 438-441.
Fry, Macon,Designing Computing Mechanisms, Cleveland, Ohio: Penton Publishing Co., 1946, 48 pp. (Reprinted fromMachine Design, Aug. 1945 through Feb. 1946.)
Hartree, D. R.,Calculating Machines: Recent and Prospective Developments and Their Impact on Mathematical Physics, Cambridge, England: The University Press, 1947, 40 pp.
Horsburgh, E. H.,Modern Instruments and Methods of Calculation, London: G. Bell and Sons, Ltd., 1914, 343 pp.
Lilley, S., Mathematical Machines,Nature, vol. 149, Apr. 25, 1942, pp. 462-465.
Murray, Francis J.,The Theory of Mathematical Machines, New York: King’s Crown Press, 1947, 116 pp.
The author states that a mathematical machine is a mechanism that provides information concerning the relationships among a specified set of mathematical concepts.
Turck, J. A. V.,The Origin of Modern Calculating Machines, Chicago: Western Society of Engineers, 1921.
Recently, however, some magazine and newspaper publishers have seen news value in machines that think, and some good general articles with appeal to a wide audience have appeared. For the references to these articles, see the section of this supplement entitled “Digital Machines—Miscellaneous.”
There are a few general references on punch-card calculating machines:
Baehne, G. Walter, editor, and others,Practical Applications of the Punched Card Method in Colleges and Universities, New York: Columbia University Press, 1935, 442 pp.This is a collection of many contributions from a number of authors, describing various applications, chiefly educational.Eckert, W. J.,Punched-Card Methods in Scientific Computation, New York: Columbia University, The Thomas J. Watson Astronomical Computing Bureau, 1940, 136 pp.This is a scientific treatise, chiefly relating to the computation of orbits in astronomy.Hartkemeier, Harry Pelle,Principles of Punch-Card Machine Operation(Subtitle:How to Operate Punch-Card Tabulating and Alphabetic Accounting Machines), New York: Thomas Y. Crowell Co., 1942, 269 pp.This is based on the author’s experience in teaching statistical analysis using IBM tabulators. The book does not deal with the collator or multiplying punch.Hedley, K. J.,The Development of the Punched-Card Method, Actuarial Society of Australasia, 1946, 20 pp.International Business Machines Corporation,International Business Machines(form no. A-4036-6-45), New York: International Business Machines Corporation, 1945, 65 pp.Pages 6 to 31 show pictures and brief descriptions of about 20 punch-card machines, available in 1945.Schnackel, H. G., andH. C. Lang,Accounting by Machine Methods, New York: Ronald Press Co., 1939, 53 pp.Wolf, Arthur W., andEdmund C. Berkeley,Advanced Course in Punched Card Operations, Newark, N. J.: Prudential Insurance Company of America, 1942, 98 pp.A useful and authoritative description of IBM punch-card calculating machinery is the following:International Business Machines Corporation, Department of Education,Machine Methods of Accounting, Endicott, N. Y.: International Business Machines Corporation, 1936-41, 385 pp.This is a collection of 28 separate booklets telling the detailed operation of IBM punch-card machinery. They were written for employees of IBM and users of IBM equipment. The following list of the booklets is useful in locating them:
Baehne, G. Walter, editor, and others,Practical Applications of the Punched Card Method in Colleges and Universities, New York: Columbia University Press, 1935, 442 pp.
This is a collection of many contributions from a number of authors, describing various applications, chiefly educational.
Eckert, W. J.,Punched-Card Methods in Scientific Computation, New York: Columbia University, The Thomas J. Watson Astronomical Computing Bureau, 1940, 136 pp.
This is a scientific treatise, chiefly relating to the computation of orbits in astronomy.
Hartkemeier, Harry Pelle,Principles of Punch-Card Machine Operation(Subtitle:How to Operate Punch-Card Tabulating and Alphabetic Accounting Machines), New York: Thomas Y. Crowell Co., 1942, 269 pp.
This is based on the author’s experience in teaching statistical analysis using IBM tabulators. The book does not deal with the collator or multiplying punch.
Hedley, K. J.,The Development of the Punched-Card Method, Actuarial Society of Australasia, 1946, 20 pp.
International Business Machines Corporation,International Business Machines(form no. A-4036-6-45), New York: International Business Machines Corporation, 1945, 65 pp.
Pages 6 to 31 show pictures and brief descriptions of about 20 punch-card machines, available in 1945.
Schnackel, H. G., andH. C. Lang,Accounting by Machine Methods, New York: Ronald Press Co., 1939, 53 pp.
Wolf, Arthur W., andEdmund C. Berkeley,Advanced Course in Punched Card Operations, Newark, N. J.: Prudential Insurance Company of America, 1942, 98 pp.
A useful and authoritative description of IBM punch-card calculating machinery is the following:
International Business Machines Corporation, Department of Education,Machine Methods of Accounting, Endicott, N. Y.: International Business Machines Corporation, 1936-41, 385 pp.
This is a collection of 28 separate booklets telling the detailed operation of IBM punch-card machinery. They were written for employees of IBM and users of IBM equipment. The following list of the booklets is useful in locating them:
The Department of Education of IBM has begun a second series of booklets on the principles of operation of punch-card calculating machinery:
International Business Machines Corporation, Department of Education,Principles of Operation, Endicott, N. Y.: International Business Machines Corporation, 1942 and later (except for one published in 1939).
Many of the booklets in this series have good examples of machine operation and applications. Also, for the first time, letters and numbers have been used as coordinates to label the hubs on the plugboards. This series includes the following:
In addition to the new types of punch-card machines referred to in the above list, an elaborate punch-card calculating machine is described in the following reference: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 EaseLife’sGrowing Pains,Life, Sept. 15, 1947, pp. 15-16.Anonymous,540, Chicago: Time-Life-Fortune Magazine, Subscription Fulfillment Office, 1948, 15 pp.
In addition to the new types of punch-card machines referred to in the above list, an elaborate punch-card calculating machine is described in the following reference:
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 EaseLife’sGrowing 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.
There are many articles in scientific journals on applications of punch-card calculating machinery to technical problems. The fields ofengineering, 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., andPaul 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, andMorris 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., andAlan 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., andRalph 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, andMartin 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., andGeorge 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, andJennie 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.
There are many articles in scientific journals on applications of punch-card calculating machinery to technical problems. The fields ofengineering, 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., andPaul 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, andMorris 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., andAlan 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., andRalph 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, andMartin 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., andGeorge 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, andJennie 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 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, andSamuel 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., andH. 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., andA. 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, andR. 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., andH. 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 theProceedings of the Royal Society, vol. 24, Feb. 1876, pp. 262-275. The method of integration by a machine is described, but thestate 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., andS. 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., andA. 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., andJ. 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.
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, andSamuel 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., andH. 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., andA. 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, andR. 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., andH. 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 theProceedings of the Royal Society, vol. 24, Feb. 1876, pp. 262-275. The method of integration by a machine is described, but thestate 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., andS. 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., andA. 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., andJ. 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.
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., andL. L. Wheeler, A Mechanical Method for Graphical Solution of Polynomials,Journal of the Franklin Institute, vol. 231, 1941, pp. 223-243.Brown, S. L., andL. 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., andL. 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., andR. 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., andG. K. Terhune, Harmonic Analysis by Photographic Method,Journal of Applied Physics, vol. 14, 1943, pp. 535-536.Wegel, R. L., andC. R. Moore, An Electrical Frequency Analyzer,Bell System Technical Journal, vol. 3, 1924, pp. 299-323.
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., andL. L. Wheeler, A Mechanical Method for Graphical Solution of Polynomials,Journal of the Franklin Institute, vol. 231, 1941, pp. 223-243.
Brown, S. L., andL. 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., andL. 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., andR. 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., andG. K. Terhune, Harmonic Analysis by Photographic Method,Journal of Applied Physics, vol. 14, 1943, pp. 535-536.
Wegel, R. L., andC. R. Moore, An Electrical Frequency Analyzer,Bell System Technical Journal, vol. 3, 1924, pp. 299-323.