|Adler, M., "Meccano
||Online description of a demonstration torque amplifier using
standard Meccano parts.
|Amble, O., "On a principle of
Connexion for Bush Integrators," Journal of
Scientific Instruments, 23,
||A survey of regenerative connections of one or two
integrators, by which it is possible to obtain functions such as the
logarithm, square root, or any rational power.
|Anon., "Sir William Thomson's
Analyser," Engineering, 30, 561, 1880.
||A description of a seven integrator version of William
Thomson's harmonic analyser (see Thomson (1878))
|Anon., "With the Editor. Meccano Aids
Scientific Research," Meccano Magazine,
||A one page introduction to a following article Anon. (1934B) discussing the Manchester
analyzer and Bush's prototype at MIT.
|Anon., "Machine Solves Mathematical
Problems. A Wonderful Meccano Mechanism," Meccano
Magazine, XIX, 6,
||A good article, with many excellent pictures of both the Manchester
analyzer and Bush's prototype at MIT. A short
extract from this is reproduced in Wright (1978).
|Anon., "Servo-Mechanism Demonstrated
Today by Professor Harold L. Hazen," The MIT
Tech, LIV, 9, 1, 1934.
||Describes a servo mechanism designed to follow a curve on the
differential analyzer input table. Can be found online here: P1, P4.
|Anon., "A Diligent Machine," The
Manchester Guardian, 25 Jan 1934, p 8.
||A curious short column commenting on the report Anon (1934E) later in the same issue.
|Anon., "A Calculating Machine
by Curves for Manchester University," The
Manchester Guardian, 25 Jan
1934, pp 9-10.
||More than a full column devoted to the full scale analyzer
being built for Manchester University, describing in layman's terms the
kinds of applications it would be used for.
|Anon. "Differential Analyser at
Manchester University," Engineering,
140, 3268, 88-92, 1935.
||A description of the Metropolitan-Vickers
machine at Manchester. Includes good pictures including the digital
revolution counters and time interval camera.
|Anon., "Differential Analyser for
University of Manchester," Nature,
135, 535, 1935.
||A brief column reporting on the opening ceremony for the
|Anon., "The Differential Analyser," The Engineer, 160, 4149, July 19 & 26,
||An excellent two part article describing the mechanical
principles and construction of the differential analyzer.
|Anon. "The Differential Analyser in
Electrical Engineering," Nature, 143,
||A review of the two papers Hartree
(1938C) and Hartree
|Anon., "The Electro-Mechanical Brain
MIT.'s Differential Analyzer Advances Science by Freeing it from
Pick-and-Shovel Work of Mathematics," LIFE,
||A brief article with outstanding pictures describing the
Rockefeller differential analyzer at MIT.
1949-50, pp 44-45.
||Contains a brief mention of Prof. J. C. Cooke's Meccano
differential analyzer; specifically that it then had three integrators,
with a fourth planned.
Meccano Calculating Machine. Solving Complex Mathematical Equations,"
Meccano Magazine, XXXVI, 1, 11,
||A one page article describing the Meccano differential
analyzer built by Prof. J. C. Cooke at the University of Malaya,
|Anon., "Mechanical Differential
Analyser with SKF Bearings," The SKF Ball
#3, 67-72, 1953.
||Description of the Chalmers University DA, with excellent
pictures. This machine is unusual in having the interconnect oriented
vertically with integrators hanging below. The integrator design
is also unconventional.
|Anon., "Differential Analyser," The GMM
Series of Modern Supermodels No. 4, London: The Chief
||The first set of model building instructions published for a
Meccano model of Bush's differential analyzer.
Bulletin, 26, 13,
Jan 23, 1978.
|Reports on the
the UCLA differential analyzer. It was sent to the Smithsonian,
where it remains in storage.
|Anon. "Among the Model Builders," Meccano Magazine, 58, 3, 54-55, 1973.
||Reports on the rediscovery of the Cambridge Meccano
analyzer in New Zealand at MOTAT. Includes a
picture reproduced from the New Zealand Herald (Anon
(1973B)). The text is somewhat confused as to the provenance of
|Anon., "Toy Used to Build 'Brain
in 1930s," New Zealand Herald, 2 June,
||A brief report on the rediscovery of the Cambridge Meccano
analyzer and its installation at MOTAT. Includes a
good picture with Dr. Whale, which is reproduced in Anon (1973).
|Anon., "Computer Display," Museum
News, MOTAT, Sep. 1973.
||A brief report on the then new computer display at MOTAT, featuring
the Cambridge Meccano
|Anon., "Among the Model Builders," Meccano Magazine, 59, 2, 36, 1974.
||A follow up article reproducing a letter from a Mr. Barcroft
who was a laboratory assistant working under the direction of A Porter
operating a Meccano differential analyzer at the Air Defence and
Research Establishment, Malvern in 1942. It is unclear just which
machine he refers to.
|Anon. "New Computer Display,", Museum
News, MOTAT, Sep. 1981.
||A brief report on the recently updated computer display at MOTAT. The
article states that at this time the Meccano
analyzer "is still capable of performing calculus."
|Anon., "That Which was Lost has been
Found," New Zealand Federation of Meccano
Modellers Magazine, 17, 3,
||The editorial reproduces a picture from the New Zealand
Herald of the Cambridge Meccano
analyzer after it was rediscovered at MOTAT. There are
brief notes plus a reproduction of another article from The Dominion of
June 23, 1993.
|Anon., "Meccano Differential Analyser
No.2," New Zealand Federation of Meccano
Modellers Magazine, 25, 1,
||Although no author is identified, these notes are edited
from Tee (1993). See also Irwin (2001).
|Ashurst, F. G., Pioneers of
Computing. London: Frederick Muller, 1983.
||An excellent collection of short biographies. Chapter 7 is
devoted to Vannevar Bush and the differential analyzers.
|Asprey, W. (Editor), Computing
Before Computers. Ames, Iowa: Iowa State University Press, 1990.
||Chapter five "Analog Computing Devices" contributed by Alan
G. Bromley provides a good general survey of analog computation
devices, from early planimiters, Kelvin's
harmonic analyzer, differential analyzers, to modern electronic
analog techniques. The full text is available online here.
|Barton, J. C., Campbell, D. A., and
Read, R. C., "An Analog Method for Studying Multiple Scattering," Proceedings of the Physical Society,
LXX, 8A, 605-614, 1957.
||This paper describes a simulation of multiple scattering
conducted using a source of random motion "coupled to a differential
analyser, built in Meccano, which is similar to one built by Hartree and Porter (1935)."
|Beard, R. E. "The Differential
Analyser" Royal College of Science Journal, 12, 127-138, 1942.
||The text of a lecture delivered before the Society on 24
February 1942, describing the basic principles of the differential
analyzer and including a picture of Beard's own machine.
|Beard, R. E., "The Construction of
Small Scale Differential Analyser and its Application to the
Calculation of Actuarial Functions," Journal
of the Institute of
Actuaries. LXXI (part II), 193-227, 1942.
||A brief description of the machine, with a more extensive
discussion on its application to actuarial work. A summary of the
ensuing discussion after the paper was presented is also included.
|Berends, T., "Historic Machine
found by MOTAT,"
New Zealand Herald, 29 June,
||A report on the rediscovery of the Meccano
analyzer at MOTAT.
of the museum, who states that it will
be restored and displayed in a prime position in the museum.
|Berry, T. M., "Polarized-Light Servo
System," AIEE Transactions, 63, 4,
||Description of the photo electric follower system used on the
General Electric differential analyzer (see Kuehni
|Blackett, P. M. S. and Williams,
F. C., "An Automatic Curve Follower for the Differential Analyser," Proceedings of the Cambridge
Philosophical Society, 35, 494-505, 1939.
||This design uses a photoelectric slope detector, a mechanical
arrangement to generate the tangent of an angle, plus an integrator to
follow the slope of the curve more smoothly than with the simple servo
arrangement of Hazen (1936).
|Boerdijk, Ir. A. H.,
Use of Friction in Torque Amplifiers and Constant Torque Devices," Constructor Quarterly, 4, 24-25,
||Describes the principles of the torque amplifier and related
torque limiting devices.
M. D., "U.S. Technological Enthusiasm and British Technological
Skepticism in the Age of the Analog Brain," IEEE
Computing, 18, 4, 5-15, 1996.
|This article is a
analysis of the British and U.S. differential analyzers from 1930 to
1945. The author examines the development of the Bush and Hartree
analyzers in the context of the U.S. engineering community and the
British scientific community. Includes many interesting details.
H., The Differential Analyser,
mathematical theory of set-ups with several free inputs both from a
topological and an analytical point of view using the theory of
Pfaffian systems. It was developed independently of Shannon (1941). It is very remote from
the practicalities of actual machine operation.
|Bush, V., "The Differential Analyzer.
A New Machine for Solving Differential Equations," Journal of the
Franklin Institute, 212, 447-488, 1931.
||Bush's original paper giving a detailed account of the first
differential analyzer built at MIT in 1930.
|Bush, V., and Caldwell, S. H., "A New
Type of Differential Analyzer," Journal of
the Franklin Institute, 240,
||A lengthy paper describing the very large scale second
generation machine at MIT (the Rockefeller DA). This system made
extensive use of shaft angle encoders and servo motors, allowing the
mechanical integrators to be interconnected electrically through a
matrix of telephone switching relays rather than though mechanical
shafting, and programmed from punched paper tape.
|Bush, V., Pieces
York: William Morrow and Company, 1970.
||Bush's autobiography. Contains only brief mention of
the differential analyzer work.
|Cairns, W. J., Crank, J., and
Lloyd, E. C., "Some Improvements in the Construction of a Small Scale
Differential Analyser and a Review of Recent Applications," Armament
Research Department Theoretical Research Memo. No. 27/44, 1944.
National Archives reference DEFE 15/751 C20779.
||Describes improvements made to the Cambridge model to enhance
reliability and usability: stronger output arms in the torque
amplifiers, lighter integrator discs, clutches in the lead screw
drives, and a double input table similar to Hartree's for time lag
problems. Applications described include problems in heat flow,
explosive detonations, and transmission line simulations.
|Campbell, S. M. "Beatrice Helen
Worsley: Canada's Female Computer Pioneer," IEEE Annals of the History of
Computing, 25, 4,
||A short biography of Beatrice Worsley. Includes a brief
mention of the Meccano differential analyzer she built over a 6 week
period in the summer of 1948.
|Cook, A. C., and Maginniss, F., J.,
"More Differential Analyzer Applications." General
8, 14-20, 1949.
||This paper is a follow up to Maginniss
(1945), reporting on eight more engineering applications of the
General Electric analyzer. The front cover of this issue has an
excellent picture of the analyzer.
Transactions of AIEE, 69,
|Describes a range
devices added to the GE differential analyzer. These incluse a curve
follower, vector summation device, sinusoid generator, multiplier, and
N. (ed.), Making of the Modern World,
London: John Murray, 1992.
highlighting 100 key inventions from the collections of the London
Science Museum. Includes a beautiful picture of Hartree's full scale
|Cresswell, J., MOTAT:
(Inc.), Auckland, New
||Almost too late, a small group of enthusiasts joined together
in an attempt to preserve the remaining relics of New Zealand's
transport and engineering history. The result of their enterprise is
the subject of this book. The Meccano
analyzer is discussed on p102.
|Croarken, M., Early Scientific
Computing in Britain, Oxford: Oxford Science Publications, 1990.
||Chapter 5 is devoted to a discussion of the Manchester and
Cambridge differential analyzers
M., "The Emergence of Computing Science Research and Teaching at
Cambridge, 1936-1949," IEEE
Annals of the History of Computing, 14, 4, 10-15, 1992.
motivation behind the creation of the laboratory. It covers the
period during which both the model and full scale differential
analyzers were installed and operated.
|Croarken, M., "Computing in
Britain During World War II," IEE History of Technology Summer
Meeting 6th July 2002,
||Includes a discussion of the use of the Manchester and
Cambridge differential analyzers for military calculations. Includes a
very extensive set of references.
|Crank, J., The
||An excellent introduction by the person in charge of
operation of the full
analyzer in the Mathematical Laboratory at the
University of Cambridge. Includes many pictures and diagrams and a
fairly detailed account of the construction of the Meccano machines.
|Cundy, H. M., and Rollett, A. P,. Mathematical Models, Oxford: Oxford
University Press, 1961.
||Brief description of the principles of Bush's differential
analyzer. Mentions the possibility of Meccano construction.
|Dalton, J., "Continuing the Saga of
the Differential Analyser," Meccanoman's
Newsmag, #68, 1994.
||Reports on an interview with Maurice Wilkes on the early
history of the Cambridge Meccano differential analyzer.
|Darwin, C. G., "Douglas Rayner
Hartree 1897-1958," Biographical Memoirs of
Fellows of the Royal Society,
4, 103-116, 1958.
||An excellent short biography of Hartree. Includes a
bibliography listing his published works.
|Eames, C., and Eames, R. A., Computer
Perspective, Cambridge, MA: Harvard University Press, 1973.
||This book is based on an exhibition conceived and assembled
for IBM, displaying aspects of the intellectual and socio-economic
environments in the sixty years leading up to the modern
computer. Page 119, titled "Meccano and Quantum Mechanics", is
devoted to the Manchester Meccano differential analyzer.
N. R., "Meccano in the Classroom," Mathematical
Gazette, 54, 389, 282-283, Oct 1970.
|A short article
describing a two
integrator Meccano differential analyzer with no torque amplifiers,
used for educational purposes.
|Fail, R., "Electro-mechanical Servo
for Differential Analyser," Meccanoman's
Journal, #12, 310,1968.
||A rudimentary electro-mechanical servo design to replace a
|Fail, R., "Mini Differential
Analyzer," Midlands Meccano Guild Gazette,
||A small demonstration model from standard Meccano parts with
full construction details. Two integrators and output table. Uses
electro-mechanical servos instead of torque amplifiers.
|Fischer, C. F., "Reminiscences at the end of the Century," Molecular Physics, 98, 1043-1050, 2000
||A collection of auto-biographical notes including an
interesting discussion of the author's work as a research student with
Hartree around the time he was building the first Meccano
analyzer. Available online here.
|Fischer, C. F., Douglas Rayner Hartree - His Life
in Science and
Computing, Singapore: World Scientific, 2003.
||This scientific biography of Douglas R. Hartree not only
describes important events in his life but also outlines his
contributions to a number of fields. Hartree was very interested
in the process of computation. When he learned of a differential
analyzer for solving differential equations, he first built a model
|Ford, H. C., "Mechanical Movement"
United States Patents 1,317,915, 1,317,916, 1919.
||The disk/ball/cylinder integrator used by Hannibal Ford in
military fire control systems. I am not aware of this type of
integrator ever being used in a differential analyzer, but it has the
advantage of being able to transmit substantial torque without
requiring a torque amplifier. The second patent has a derivative
capable of even greater loading.
|Gray, E., "The Torque Amplifier," New
Zealand Federation of Meccano Modellers Magazine, Oct 1992.
||An unusual application of the torque amplifier to amplify the
outputs of servo motors in a motor chassis.
|Hartree, D. R., F.R.S., and
Porter, A., "The Construction and Operation of a Model Differential
Analyser," Memoirs and Proceedings of the
Manchester Literary &
Philosophical Society, 79, 51-74, 1935.
||A detailed account of the construction and operation of
analyzer at Manchester University including a number
of photographs of the machine.
|Hartree, D. R., F.R.S., and
Ingham, J., "Note on the Application of the Differential Analyser to
Calculation of Train Running times," Memoirs
and Proceedings of the
Manchester Literary & Philosophical Society, 83, 1-15, 1938.
||An interesting paper on a relatively simple second order
equation. Although the work was done on the full scale machine,
reference is made to the fact this would be a suitable problem for
analyzer described in Hartree
|Hartree, D. R., "The Mechanical
Integration of Differential Equations," Mathematical
||A comprehensive account of the construction and application
of the Manchester
analyzers with a good close up photograph of the
integrators of the full scale machine.
|Hartree, D. R, and Nuttall, A.
"The Differential Analyser and its Application in Electrical
Engineering," Journal of the Institution of
Electrical Engineers, 83,
||A fairly detailed account of the Metropolitan-Vickers
machine with good pictures, including of the special input table. A
somewhat briefer section discusses actual applications.
|Hartree, D. R., and Porter, A.,
"The Application of the Differential Analyzer to transients on a
Distortionless Transmission Line," Journal of
the Institution of
Electrical Engineers, 83, 648-656, 1938.
||Examines the behavior of transients on a finite
distortionless transmission line. This problem required use of a
special input table that can feed back a solution after a fixed delay.
Application to lightening arresters is discussed.
|Hartree, D. R., "The Thirty-fourth
Kelvin Lecture: Mechanical Integration in Electrical Problems," Journal
of the Institution of Electrical Engineers, 90, 435-442, 1943.
||Lecture delivered before The Institution on 29, April, 1943.
After a brief description of the differential analyzer (including
mention of Kelvin's contribution) details solutions to several problems
in electrical engineering obtained using the machine.
|Hartree, D. R., "Differential
Analyser," Ministry of Supply Permanent
Records of Research and
Development No. 17-502, 1946/9.
||A detailed account of the use of the Manchester differential
analyzer during the war. Probably the largest collection of
applications gathered in a single document. Section 1.4 documents
other differential analyzers in the UK, including Meccano models.
|Hartree, D. R., F.R.S., Calculating
Instruments and Machines, Urbana: University of Illinois Press,
||An extensive discussion of differential analyzers with many
photographs including the Meccano
analyzer described in Hartree
(1935). Includes a chapter on its application to partial differential equations. There is a
suggestion for the solution of a set of nonlinear simultaneous
equations for a problem in spherical, sound waves remarkable in that it
uses no integrators, just an intricate interconnection if input tables,
output tables and multiplier/divider units. Extensive references are
|Hartree, D. R., "The Bush
Differential Analyser and its Applications," Nature,
||A general description of the differential analyzer. Despite
the title, the pictures are actually of the Metropolitan-Vickers
machine at Manchester.
|Hartree, J., and Tee, G., "Toy
Story," New Scientist, 4 Mar 2000.
||Letters to the editor discussing the differential analyzer,
in response to the question from a reader as to whether any significant
inventions or principles owe their discovery to the use of Meccano.
Available online here.
|Hazen, H. L., Jaeger, J. J., and
Brown, G. S., "An Automatic Curve Follower," Review
Instruments, 7, 353-357, 1936.
||Describes an automatic curve follower using a photocell,
servo motor, and torque amplifier, which can follow the black/white
boundary of a curve on an input table. See also Blackett (1939).
|Heffron, W. G., "Operation and
Application of the Differential Analyzer," Product
Engineering, 23, 4,
||General description of the operation of a differential
analyzer with particular reference to the General Electric 14
|Hey, T., The Quantum Universe, Cambridge
||A brief reference to Hartree's atomic structure calculations,
including a picture of Hartree and Porter with the Meccano
|Hogle, H., "Torque Amplifier," Canadian MeccaNotes, 6, 19, June 1997.
||An unusual torque amplifier design in Meccano parts. Probably
not sensitive enough for use in a differential analyzer.
|Holst, P. A., "Svein Rosseland and
the Oslo Analyzer," IEEE Annals of the History of
Computing, 18, 4,
||At one time the Oslo analyzer was the world's largest;
technically advanced, highly accurate, and used by theoretical
physicists from around the world. A discussion of the machine,
and the man who created it.
|Irwin, W., "Differential Analyser
2," New Zealand Federation of Meccano
Modellers Magazine, 25, 2, 2001.
||Letter to the editor identifying the source of the article in
the preceding issue (Anon (2001)) and
reporting on more recent efforts to restore the Meccano
analyzer at MOTAT.
|Irwin, W., "Differential Analyser
Myths," New Zealand Federation of Meccano
Modellers Magazine, 25, 3,
||A short piece exposing a number of myths circulating about
Meccano differential analyzers.
|Irwin, W., "The Differential Analyzer Explained," New Zealand
Federation of Meccano Modellers Magazine, 26, 3, 2002.
||Describes the principles of operation of a differential
analyzer. Illustrated with a picture of an earlier Meccano
machine by the current author and the Science Museum exhibit of an
integrator from the Meccano
analyzer described in Hartree
(1935). Available online here.
|Irwin, W., "Meccano Differential
Analyser . . . and New Zealand's First Computer," The International
Meccanoman, #46, IX.2005.
||An account of the differential analyzer exhibits at the 2005
NZFMM Easter Convention in Auckland, New Zealand, which included the
restored section of the Cambridge
machine and the author's version of the model in Fail (1993) .
|Irwin, W., "Differential Analyzer -
Adding Unit," New Zealand Federation of
Meccano Modellers Magazine, 31,
6, 8-9, 2007.
||Details of the adding unit used in the original Cambridge
Meccano differential analyzer together with a modern
|Irwin, W., "Propagation of an Urban
Legend, a Differential Analyser Myth," New
Zealand Federation of Meccano
Modellers Magazine, 31, 6, 14-15, 2007.
||Debunks the myth that the Cambridge
Meccano differential analyzer was used by Barnes Wallis for the
design of the "bouncing bomb".
A. S., Analog Computation, New York:
electronic analog machines, this book includes a concise section on
|Janssen, E., and Lebell, D.,
"Applications of the Mechanical Differential Analyzer to Electrical
Engineering," Electrical Engineering,
70, 432-435, 1951.
||Applications for the differential analyzer to magnetic
amplifiers, pulse transformers and electron accelerators.
|King, D., "Historic Computer Lost
from MOTAT," New
Zealand Herald, section 4, page 5, April 20, 1993.
||A half page report on the loss of the Meccano
analyzer from MOTAT.
of it in the museum's former computer display.
|King, D., "Heritage Rusts to Bits in
Rain," New Zealand Herald, section 3,
page 5, April 27, 1993.
||Another report on the events surrounding the loss of the Meccano
analyzer from MOTAT.
|Kuehni, H. P., and Peterson, H. A.,
"A New Differential Analyzer," AIEE
Transactions, 63, 5, 221-228
(discussion 429-431), 1944.
||Detailed technical description of the General Electric 14
integrator differential analyzer which used a Polaroid optical follower
system on the integrators. The follower system is described in Berry (1944).
A., "Sur un intégrateur des
équations différentielles ordinaires," Bulletin de
l'Académie Impériale des Sciences de
St.-Pétersbourg, Ser. V, T.XX, 1, Jan. 1904.
||In this little
Kryloff describes a machine based on the work of Thompson (Thompson (1876A)), but using radically
different integrators. It is unclear if the machine was
successful as the paper was written while it was still under
construction. This paper is in French.
|Lennard-Jones, J. E.,
Wilkes, M. V., and Bratt, J. B., "The Design of a Small Differential
Analyser," Proceedings of the Cambridge
Philosophical Society, 35,
||A detailed description of the construction and testing of the
analyzer at Cambridge University. In an early
test using four integrators, the wave equation of the hydrogen atom was
solved giving the value of the ground state energy correct to one part
|Lowe, I., "Ancient Computer Down and
Out," New Scientist, 138, 1873, p.50,
15 May 1993. (May not appear in
||A follow up to articles in the New Zealand Herald (King (1993A) and King
(1993B)) reporting on the loss of the Cambridge Meccano
analyzer from MOTAT.
|Macauley, T., "Operating the
Meccano Differential Analyser,", unpublished, MOTAT, Auckland,
New Zealand, 1978.
||A brief operating manual for the Meccano differential
analyzer at MOTAT
which indicates that it was in operation in 1978 for
demonstrations. One of the 5 integrators was not functional.
|Maginniss, F.J., "Differential
Analyzer Applications,", General Electric
Review, 48, 5, 54-59, 1945.
||A discussion of eight applications of the differential
analyzer to engineering problems and the techniques used to handle
|Marsh, P., "The Meccano Set
Computer," New Scientist, 80, 1134,
(supplement 28-29), 1978.
||A popular article on the history of the Manchester
|Massey, H. S. W., Wylie, J.,
Buckingham, R. A., and Sullivan, R., "A Small Scale Differential
Analyser - Its Construction and Operation," Proceedings
Academy, 45A, 1, 1-21, 1938.
||A four integrator machine. All the spur gears used in
this machine are of Meccano manufacture. Helical gears and
sprockets are from Bond's. Everything else is of custom design. The
paper contains some excellent pictures.
|Michel, J. G. L., "Extensions in
Differential Analyzer Technique," Journal of
Scientific Instruments, 25,
10, 357-361, 1948.
||In this paper, a constructive technique is developed for
obtaining the results arrived at by Amble (1946)
from analytical considerations. The technique is extended to include
the integral of a quotient, and the inversion of functions. Mentions
that one of these techniques was applied on the Cambridge Meccano
|Michel, J. G. L., "Errors of
Friction Wheel Integrators," Journal of
Scientific Instruments, 32, 2,
||Analyzes the error inherent in a wheel and disk integrator
whenever there is sliding motion of the wheel. This error is
approximately proportional to the torque which must be applied to the
|Mindell, D. A., Between Human and
Machine - Feedback, Control, and Computing Before Cybernetics,
Baltimore: Johns Hopkins University Press, 2002.
||Mindell shows how the modern sciences of systems emerged from
disparate engineering cultures and how they converged during W.W.II.
Chapter 5, Analog Computing at MIT, is devoted to the work of Vannevar
|Myers, D. M., and Blunden, W. R.,
C.S.I.R.O. Differential Analyser," Proceedings
Machines, Sydney Australia, 1951.
||A description of the construction of a 10 integrator
differential analyzer at the University of Sydney. This machine uses
electrical interconnections between the units using a system called
"M-type" transmission. Foe a more detailed account, see Myers (1952).
|Myers, D. M., and Blunden, W. R.,
C.S.I.R.O. Differential Analyser," Journal of
the Institution of
Engineers, Australia, 24, 195-204, Oct-Nov, 1952.
||A more comprehensive description of the C.S.I.R.O. analyzer
than given in Myers (1951). It
includes a section on applications to which the instrument has been
|Nieman, C. W., "Bethlehem Torque
Amplifier," American Machinist, 66,
21, 895-897, 1927.
||Nieman's original description of the torque amplifier, with
application to automobile power steering. The caption of one
figure contains the phrase "adaptable to computing machines" though
there is no other mention in the text, and this article considerably
predates Bush's application. See also US patents 1751645, 1751647, and 1751652.
|O'Neill, R., "Meccano 'Dam Busters' computer stars at MOTAT," Computerworld, 16 July, 2007.
||A review of the new computing exhibit at MOTAT which
features the recently restored Cambridge Meccano
|Owens, L., "Vannevar Bush and the
Differential Analyzer: The Text and Context of an Early Computer," Technology
Culture, 27, 1, 1986, 63-95.
Reprinted in Nyce, J.
M. From Memex To Hypertext, Academic Press, 1991.
||Discusses the background to Bush's machines, from the
early product integraphs through the mechanical analyzer to the mighty
Rockefeller electro-mechanical analyzer.
|Partridge, A., "Torque
Amplifier," Midlands Meccano Guild Gazette,
||A simple servo based design using a motor and differential to
operate electrical contacts.
|Partridge, A., "Torque
Amplifiers," Constructor Quarterly,
19, 40-42, March 1993.
||Constructional details of two torque amplifier designs using
|Paynter, H. M., "The Differential
Analyzer as an Active Mathematical Instrument," IEEE Control Systems
Magazine, 9, 7, 3-8, 1989.
||This presentation features the essential role played by
amplification and control in the successful development of the
differential analyzer. Mentions the Meccano machines, but incorrectly
states that their torque amplifiers were made entirely from Meccano
|Peierls, R., Bird of Passage,
Princeton University Press, 1985.
||The highly readable autobiography of Rudolf Peierls.
Contains a brief mention of Hartree and the Meccano
analyzer (p104). Peierls was the supervisor of
M. Wood when he was building a Meccano machine at Birmingham (see Wood (1942)) and on p137 he confirms this
machine was never completed.
|Porter, A., "An Approximate
Determination of the Atomic Wave Functions of the Chromium Atom," Memoirs and Proceedings of the
Manchester Literary & Philosophical
Society, 79, 75-81, 1934.
||Presents the results of approximate calculations of the wave
functions of the chromium atom, carried out on the Meccano
analyzer described in Hartree
|Porter, A., Differential Analyser
Log Book, MS474 London: Science Museum Library.
||Hand written day to day notes recorded from July to December
1935 as the full scale analyzer at Manchester was being commissioned.
These notes make fascinating reading. It would appear that getting
reliable operation from the machine was very challenging.
A., The Differential Analyser and Some
Applications, University of
Manchester PhD Thesis, 1936.
||Porter's PhD Thesis
in which he
describes both the model and full size machines, including
to handle time-lag problems. He covers in detail numerous
|Porter, A., Introduction to
Servomechanisms, London: Mehuen & Co., 1950.
||This is a general treatment of the theory of servomechanisms.
However, the first chapter uses as examples both the mechanical torque
amplifier of the original Bush differential analyzer, and the
electromechanical servo system used on the later Rockefeller
|Porter, A., "Building the
Differential Analyzers: A Personal Reflection," IEEE Annals of the History of
Computing, 25, 2,
||A delightful memoir by one of the pioneers. Written in
his 93rd year. This memoir is extracted from chapter 4 of Porter (2004).
|Porter, A., So Many Hills to Climb:
My Journey from Cumbria to North Carolina, Silver Spring: The
Publications Group, 2004.
||Arthur Porter describes a remarkable life with eloquent
sensitivity and charming candor. Chapter 4 covers his time at
Manchester University and the building of the differential analyzers.
This chapter was in large part reprinted in Porter
|Robinson, T. B., "The Meccano
Set Computers," IEEE Control Systems Magazine,
||A history of the Meccano based small scale differential
|Robinson, T. B., "A
Reconstruction of the Differential Analyzer in Meccano," IEEE Control
Systems Magazine, 25, 4, 84-89, 2005.
||Description of the author's modern reconstruction in Meccano
of a differential analyzer based on Bush's prototype.
E., "The Mechanical Differential Analyser: Its Principles, Development,
and Applications," Proceedings of the
Institute of Mechanical Engineers,
159, 1948, 46-54 and 62-80.
|This is a review
contributes nothing original. It is followed by a record of the
discussion which ensued when it was presented, in which A. Porter leads
a blistering attack for both its lack of originality and for the
arbitrary change in notation which Rose adopted. It is further followed
by miscellaneous communications relating to mechanical and electrical
|Rosseland, von S., "Mechanische
Integration von Differentialgleichungen," Die
44, 729-735, 1939.
||A description of the 12 integrator full scale machine at the
Institut für Theoretische Astrophysik, Oslo, Norway. The paper is
|Shannon, C. E., "Mathematical
Theory of the Differential Analyzer," Journal
of Mathematics and Physics,
XX, 4, 1941. Reprinted in Claude E. Shannon, Collected Papers
(ed. Wyner A. D. and Sloane, N. J. A.) Wiley-IEEE Press, 1993.
||A heavy duty mathematical analysis of the class of problems
that can be addressed by the differential analyzer, assuming only that
the machine has an unlimited number of integrators and adders. An
interesting paper, but somewhat remote from the practicalities of
actual machine operation.
|Small, J. S., The Analogue Alternative: The
Computer in Britain and the USA, 1930-1975 (Studies in the History of
Science, Technology and Medicine), Routledge, 2001.
||While primarily concerned with electronic analog machines,
chapter 2 provides a good introduction, including Hartree's development
of differential analyzers at Manchester. Includes a picture of the Meccano
analyzer. Extensive references.
|Smillie, K., "People, Languages,
and Computers: A Short Memoir," IEEE Annals of the History of
Computing, 26, 2,
||A biographical memoir which briefly mentions work by Jim
Howland to extend Beatrice Worsley's Meccano differential analyzer in
1951. Essentially the same material can be found online here and here.
Simulator for a Meccano Differential Analyzer," Vector, 23, 3 2008.
five-integrator differential analyzer simulator implemented in J and
gives two examples of its use.
|A more extended
version of Smillie (2008a) published on
line. The simulator code is available
|Smith, P., "Who sez it cannot be
done!," Meccano Engineer, #11, March
||A short article with a picture of a one integrator Meccano DA
constructed by T. Brooker, in which the torque amplifier is constructed
entirely from standard Meccano parts. Probably the first person
to have done it.
|Soroka, W. W., Analog Methods in
Computation and Simulation, New York: Mc Graw-Hill.
||A comprehensive survey a vast array of both mechanical and
electrical methods current at the time of writing. Includes much
material on the differential analyzer with extensive references.
|Spackman, L., "A Meccano
Differential Analyser," Meccanoman's Newsmag,
||Discussion of the history of the Cambridge Meccano
analyzer in New Zealand.
|Strong, C. L., "The Amateur
Scientist: A plan for an analogue computer that can be built for about
$50," Scientific American, June 1968.
||A design for a home built two integrator differential
analyzer with an example application. Construction of the machine would
be greatly simplified by the use of Meccano!
|Schultes, D., "On
Analyzers," April 2004.
||A short essay presenting the development of the differential
analyzer. In addition to discussing the mechanical machines it includes
a section on the later electronic machines and a short comparison with
present day technology.
|Tee, G. J., "Meccano Differential
Analyser No. 2," unpublished notes, 1993.
||Notes on the complex history of the Cambridge Meccano
analyzer, shipped to New Zealand in 1950, almost
dismantled in the 1960's, displayed at MOTAT in the 70's
then lost in 1993 and finally found again in damaged condition.
|Thomson, J., "An Integrating
Machine having a new Kinematic Principle," Proceedings
Society, 24, 262, 1876.
||Description of the ball and disk integrator in which a ball
rests under gravity between a horizontal cylinder and an inclined
integrator disk thus avoiding the sliding necessary in a wheel and disk
integrator. Inspired by the work of Prof. James Clark Maxwell who
applied a similar approach to an improved planimeter design. Reprinted
in Thomson (1879).
|Thomson, Sir W., "An Instrument
for Calculating the Integral of the Product of two Given Functions," Proceedings of the Royal Society,
24, 266, 1876.
||Application of the ball and disk integrator described in Thomson (1876A) to the evaluation of the
integral of a product of functions. Reprinted in Thomson (1879).
|Thomson, Sir W.,
Integration of Linear Differential Equations of the Second Order with
Variable Coefficients," Proceedings of
the Royal Society, 24,
||Sir William Thomson first suggested that the integrators
developed by his brother could be interconnected to produce solutions
of differential equations. The idea was not practical at the time
because of the lack of torque amplifiers. Reprinted in Thomson (1879).
|Thomson, Sir W.,
Integration of the General Linear Differential Equation of any Order
with Variable Coefficients," Proceedings of
the Royal Society, 24, 271,
||A generalization of the scheme proposed in Thomson (1876C) to equations of arbitrary
order. Reprinted in Thomson (1879).
|Thomson, Sir W., "Harmonic
Analyzer," Proceedings of the Royal Society,
||A description of a harmonic analyzer using up to eleven of
the ball and disk integrators described in Thomson (1876A) and the principles detailed
in Thomson (1876B) where one of the
functions in the product is a sine or cosine. This machine was used to
extract the coefficients of a Fourier
series for the purposes of tide prediction. Reprinted with an
addition dated April, 1879 in Thomson (1879).
|Thomson, Sir W., and Tait, P. G., Treatise on Natural Philosophy, Vol.
1, Cambridge: Cambridge
University Press, 1879.
||Although a textbook on physics, it contains an Appendix
(curiously called Appendix B' even though it's the only one) which
contains reprints of several papers on integrating devices previously
published in the Proceedings of the Royal Society. See Thomson (1876A), Thomson
(1876B), Thomson (1876C), Thomson (1876D), and Thomson
|Travis, I., "Differential Analyzer
Eliminates Brain Fag," Machine Design,
7, 7, 15-18, 1935.
||Description of the ten integrator differential analyzer built
at the Moore School of Engineering, University of Pennsylvania. This
machine included two polar input tables.
K. L. and Lindgren N. A., A Century of
Electrical Engineering and
Computer Science at MIT, 1882-1982, Cambridge: MIT Press, 1985.
|Chapter 4 provides
non-technical historical account of four generations of analog
technology developed under Bush's guidance, from the early integraphs
through to the mighty Rockefeller DA.
|Wilkes, M. V., Memoirs of a Computer
Pioneer, Cambridge, MA: The MIT Press, 1985.
||Describes his encounter with the Meccano differential
analyzer at Cambridge and how he came to take responsibility for it. He
also describes the addition of the fifth integrator by Miss E Monroe in
|Williams, M. R., "UTEC and Ferut:
The University of Toronto's Computation Centre," Annals of the History
of Computing, 16, 2, 4-12, 1994.
||Contains a brief reference to Beatrice (Trixie) Worsley's
Meccano differential analyzer at the Unversity of Toronto. There is a
picture of the machine in an early stage of construction..
|Williams, M. R., A History of Computing Technology,
Wiley-IEEE Computer Society Press, 1997
||Broad survey of computing history. Chapter 5 covers analog
machines in general with a section on the differential analyzers.
Mentions the Hartree Meccano
analyzer and has an interesting reference to a Meccano
machine built in Toronto by Beatrice (Trixie) Worsley.
|Winston, B., Media Technology and Society: A
History: From the
Telegraph to the Internet, Routledge, 1998
||Contains a brief reference to Hartree's construction of a
differential analyser in Meccano after visiting MIT to see Bush's
|Wood, A. M., The
Equation, University of
MSc. Thesis, 1942.
||The design of a small scale machine (6 integrators) built
largely of Meccano parts is described. Torque amplifiers and
integrator carriages are custom built. Because of war time material
shortages, only two integrators were completed at the time the thesis
was written. A second section describes the solution of a
equation performed using the Meccano
analyzer at Cambridge University. Peierls
(1985) confirms it was never
|Worsley, B. H., "Construction of a
Model Differential Analyzer," Worsley
Archives, box 3, folder 10,
Queen's University Archives, Ontario, 1948.
||A memo to Dr. B. A. Griffith, Toronto Computation Center,
dated 10 September, 1948 describing the construction of a three
integrator Meccano differential analyzer.
|Worsley, B. H., "Differential
Analyzer," Worsley Archives, box 3,
folder 10, Queen's University
Archives, Ontario, undated.
||A set of course notes from the University of Toronto
Department of Physics, for a 4th year practical course using Worsley's
model differential analyzer. Undated, but must be 1949 or later
because of a reference to Hartree
|Wilson, A. H., "The Binding
of the Hydrogen Isotopes" Proceedings of the
Society, 34, 365-374, 1938.
||Although fundamentally a paper about nuclear physics, it is
interesting because this is the problem which resulted in the addition
of a fifth integrator to the Cambridge Meccano differential analyzer.
|Wright, G., The Meccano Super Models
(The Hornby Companion Series, Vol. 2), London: New Cavendish,
||Reproduced on p.31 is a small extract from Anon (1934B).