|Adler, M., "Meccano Torque Amplifier", 2001
||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, 284-287, 1946.
||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
Harmonic Analyser," Engineering,
30, 561, 1880.
||A description of a seven integrator version of William
Thomson's harmonic analyser (see Thomson
(1878)) constructed by R. W. Munro for the
Meteorological Office. Contains a detailed engraving.
|Anon., "With the Editor. Meccano
Aids Scientific Research," Meccano
Magazine, XIX, 6, 441, 1934.
||A one page introduction to a following article Anon. (1934B) discussing the Manchester
Meccano differential analyzer and Bush's prototype at
|Anon., "Machine Solves
Mathematical Problems. A Wonderful Meccano Mechanism,"
Meccano Magazine, XIX, 6,
||A good article, with many excellent pictures of both the Manchester
Meccano differential analyzer and Bush's prototype at
MIT. A short extract from this is reproduced in Wright (1978).
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
|Anon., "A Calculating Machine
Working 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
|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
|Anon., "Differential Analyser for
the 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, 1935.
||An excellent two part article describing the mechanical
principles and construction of the differential analyzer.
|Anon. "The Differential Analyser
in Electrical Engineering," Nature,
143, 36, 1939.
||A review of the two papers Hartree
(1938C) and Hartree (1938D).
|Anon., "The Electro-Mechanical
Brain - MIT.'s Differential Analyzer Advances Science by
Freeing it from Pick-and-Shovel Work of Mathematics," LIFE, Jan 14, 1946, pp 73-76.
||A brief article with outstanding pictures describing the
Rockefeller differential analyzer at MIT.
Report of the University of Malaya 1949-50, pp
||Contains a brief mention of Prof. J. C. Cooke's Meccano
differential analyzer; specifically that it then had three
integrators, with a fourth planned.
|Anon., "A 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
|Anon., "Mechanical Differential
Analyser with SKF Bearings," The
SKF Ball Bearing Journal, #3, 67-72,
||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 Meccanoman, 1967.
||The first set of model building instructions published for
a Meccano model of Bush's differential analyzer.
|Anon., "Pioneer Computer Goes To
Washington," USC University
Bulletin, 26, 13, Jan 23, 1978.
|Reports on the
dismantling of the UCLA differential analyzer. It was
sent to the Smithsonian, where it remains in storage.
|Anon. "Among the Model Builders,"
Meccano Magazine, 58, 3,
||Reports on the rediscovery of the Cambridge Meccano
differential 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 this machine.
|Anon., "Toy Used to Build 'Brain
Box' in 1930s," New Zealand Herald,
2 June, 1973.
||A brief report on the rediscovery of the Cambridge Meccano
differential analyzer and its installation at MOTAT. Includes a good picture with
Dr. Whale, which is reproduced in Anon
|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
|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
differential analyzer "is still capable of performing
|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
differential analyzer after it was rediscovered at MOTAT. There are brief notes plus a
reproduction of another article from The Dominion of June
|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.
G. L., and Selig, K. L., "A General Purpose Differential
Analyser Part 1 - Description of Machine," Elliott Journal, 1, 2 44-48, 1951.
||A six integrator machine
using disk-ball-cylinder integrators and magslip based servo
followers. Incorporates photo electric curve followers
on the input tables. See also Hersom
|Asprey, W. (Editor), Computing Before
Computers. Ames, Iowa: Iowa State University Press,
||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
|Beard, R. E. "The Differential
Analyser" Royal College of Science Journal, 12, 127-138,
||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
|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.
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
|Berends, T., "Historic Machine
found by MOTAT,"
New Zealand Herald, 29 June,
||A report on the rediscovery of the Meccano
differential analyzer at MOTAT.
Pictured with the machine are Dr. H. Whale and R. Dearing,
director 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, 195-198, 1944.
||Description of the photo electric follower system used on
the General Electric differential analyzer (see Kuehni (1944)).
|Blackett, P. M. S. and
Williams, F. C., "An Automatic Curve Follower for the
Differential Analyser," Proceedings
of the Cambridge Philosophical Society, 35,
||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.,
"Constructive Use of Friction in Torque Amplifiers and
Constant Torque Devices," Constructor
Quarterly, 4, 24-25, June 1989.
||Describes the principles of the torque amplifier and
related torque limiting devices.
|Bowles, M. D., "U.S. Technological
Enthusiasm and British Technological Skepticism in the Age
of the Analog Brain," IEEE Annals
of the History of Computing, 18, 4, 5-15, 1996.
|This article is
a comparative 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.
|Bückner, H., The Differential Analyser,
develops a 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, 255, 1945.
||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 of the Action, New 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. UK National Archives reference DEFE 15/751
||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, 51-62, 2003.
||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 Electric Review, 52, 8,
||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
|Cook, A. C., "Special Devices Aid
Differential Analyzer Solution of Complex Problems," Transactions of AIEE, 69,
range of special devices added to the GE differential
analyzer. These incluse a curve follower, vector summation
device, sinusoid generator, multiplier, and others.
|Cossons, N. (ed.), Making of the Modern World,
London: John Murray, 1992.
volume highlighting 100 key inventions from the collections
of the London Science Museum. Includes a beautiful picture
of Hartree's full scale machine.
|Cresswell, J., MOTAT: Museum of Transport and
Technology of New Zealand (Inc.), Auckland, New
Zealand: Hamlyn, 1976.
||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
differential 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
|Croarken, 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.
describes the motivation behind the creation of the
laboratory. It covers the period during which both the
model and full scale differential analyzers were installed
|Croarken, M., "Computing in
Britain During World War II," IEE History of
Technology Summer Meeting 6th July 2002, London, 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 Differential Analyser, London:
||An excellent introduction by the person in charge of
operation of the full
scale differential 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
|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,
||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
|Eyres, 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, No. 16, 4-9, April 1993.
||A small demonstration model from standard Meccano parts
with full construction details. Two integrators and output
table. Uses electro-mechanical servos instead of torque
|Fischer, C. F., "Reminiscences at the end of the Century,"
Molecular Physics, 98,
||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
differential analyzer. Available online here.
|Fischer, C. F., Douglas Rayner Hartree
- His Life in Science and Computing, Singapore: World
||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 using Meccano.
|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
|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 the Meccano
differential 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 the 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 the Meccano
differential analyzer described in Hartree (1935).
|Hartree, D. R., "The
Mechanical Integration of Differential Equations," Mathematical Gazette, 22,
||A comprehensive account of the construction and
application of the Manchester
differential analyzers with a good close up photograph
of the integrators of the full scale machine.
|Hartree, D. R, and Nuttall, A.
K., "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
|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
D. R., "The Bush Differential Analyser and its
Applications," Nature, 146,
3697, 319-323, 1940.
||A general description of the
differential analyzer. Despite the title, the pictures are
actually of the Metropolitan-Vickers
machine at Manchester.
D, R., "A Great Calculating Machine: The Bush Differential
Analyser and its Applications in Science and Industry," Proceedings of the Royal Institution,
31, 151-170, 1940.
||A paper presented at the
Royal Institution weekly evening meeting on May 17, 1940.
Describes the differential analyzer in general, the full
scale Manchester machine specifically, and some of its
applications, including the calculation of train running
times. Mentions the Meccano
|Hartree, D. R., "The
Thirty-fourth Kelvin Lecture: Mechanical Integration in
Electrical Problems," Journal of
the Institution of Electrical Engineers, 90,
||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,
||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, 1949.
||An extensive discussion of differential analyzers with
many photographs including the Meccano
differential 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 provided.
|Hartree, J., and Tee, G., "Toy
Story," New Scientist, 4
||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 of Scientific 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 integrator machine.
S. E., and Selig, K. L., "A General Purpose Differential
Analyser Part II - Application of Machine," Elliott Journal, 1, 3, 76-80, 1952.
||Describes the application of
the Elliott differential analyser to a thermionic microwave
diode. Gives particular attention to scale factors.
See also Ashdown (1951).
|Hey, T., The Quantum Universe,
Cambridge University Press, 1987.
||A brief reference to Hartree's atomic structure
calculations, including a picture of Hartree and Porter with
|Hogle, H., "Torque Amplifier," Canadian MeccaNotes, 6, 19, June
||An unusual torque amplifier design in Meccano parts.
Probably not sensitive enough for use in a differential
|Holst, P. A., "Svein Rosseland
and the Oslo Analyzer," IEEE Annals of the
History of Computing, 18, 4, 16-26, 1996.
||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
No. 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
differential 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
differential analyzer described in Hartree (1935). Available
|Irwin, W., "Meccano Differential
Analyser . . . and New Zealand's First Computer," The International Meccanoman,
||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
Meccano 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".
W., "The Cambridge Meccano Differential Analyser No.2," The Driving Wheel, 5: The
Museum of Transport and Technology Society, 2013. Reprinted
(with fewer photos) in Resurrection.
The Bulletin of the Computer Conservation Society,
64, Winter 2013/4.
||An updated account of the
history of, and the full restoration of the Cambridge
Meccano differential analyzer at MOTAT.
|Jackson, A. S., Analog Computation, New York:
primarily about electronic analog machines, this book
includes a concise section on mechanical
differential analyzers (pp. 573-578).
|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
New Zealand Herald, section
4, page 5, April 20, 1993.
||A half page report on the loss of the Meccano
differential analyzer from MOTAT. Gives a history of the machine
and a picture 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
differential analyzer from MOTAT.
|Kuehni, H. P., and Peterson, H.
A., "A New Differential Analyzer," AIEE
Transactions, 63, 5, 221-228 (discussion 429-431),
||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
|Kryloff, 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
known work, 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
|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, 485,
||A detailed description of the construction and testing of
differential 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 in 500.
|Lowe, I., "Ancient Computer Down
and Out," New Scientist,
138, 1873, p.50, 15 May 1993. (May not appear in all
||A follow up to articles in the New Zealand Herald (King (1993A) and King (1993B)) reporting on the
loss of the Cambridge Meccano
differential 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.
"Differential Analyzer Applications,", General Electric Review, 48, 5,
||A discussion of eight applications of the differential
analyzer to engineering problems and the techniques used to
|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 of the Royal Irish 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, 43-44, 1955.
||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 wheel.
|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 Bush's lab.
|Myers, D. M., and Blunden, W. R.,
"The C.S.I.R.O. Differential Analyser," Proceedings of Conference on Automatic
Computing 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
|Myers, D. M., and Blunden, W. R.,
"The 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 applied.
|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
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 and Culture, 27, 1, 1986,
63-95. Reprinted in Nyce, J. M. From Memex To Hypertext, Academic
||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, No 7, 5, September 1982.
||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 Meccano parts.
|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 parts.
|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
differential analyzer (p104). Peierls was the
supervisor of A. 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
differential analyzer described in Hartree (1935).
|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.
|Porter, A., The Differential Analyser and Some
Applications, University of Manchester PhD Thesis,
Thesis in which he describes both the model and full size
machines, including modifications to handle time-lag
problems. He covers in detail numerous applications.
|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 differential analyzer.
|Porter, A., "Building the
Manchester Differential Analyzers: A Personal Reflection," IEEE Annals of the
History of Computing, 25, 2, 86-92, 2003.
||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
Beckham 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 (2003).
|Robinson, T. B., "The
Meccano Set Computers," IEEE
Control Systems Magazine, 25, 4, 74-83, 2005.
||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
|Rose, H. E., "The Mechanical
Differential Analyser: Its Principles, Development, and
Applications," Proceedings of the
Institute of Mechanical Engineers, 159, 1948, 46-54
|This is a review
paper which 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
|Rosseland, von S.,
"Mechanische Integration von Differentialgleichungen," Die Naturwissenschaften, 27, 44,
||A description of the 12 integrator full scale machine at
the Institut für Theoretische Astrophysik, Oslo,
Norway. The paper is in German.
|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
||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 Electric Analogue 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
differential analyzer. Extensive references.
|Smillie, K., "People,
Languages, and Computers: A Short Memoir," IEEE Annals of the
History of Computing, 26, 2, 62-74, 2004.
||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.
|Smillie, K., "A
J Simulator for a Meccano Differential Analyzer," Vector, 23, 3 2008.
describes a five-integrator differential analyzer simulator
implemented in J and gives two examples of its use.
|Smillie, K., "Simulation
of Meccano Differential Analyzers", 2008.
|A more extended
version of Smillie (2008a)
published on line. The simulator code is available for
download via this
|Smith, P., "Who sez it cannot be
done!," Meccano Engineer,
#11, March 1996.
||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
|Spackman, L., "A Meccano
Differential Analyser," Meccanoman's
Newsmag, #67, 1993.
||Discussion of the history of the Cambridge Meccano
differential 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
the Development and Use of Differential Analyzers,"
||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
|Tee, G. J., "Meccano Differential
Analyser No. 2," unpublished notes, 1993.
||Notes on the complex history of the Cambridge Meccano
differential 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 of the Royal 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.,
"Mechanical Integration of Linear Differential Equations of
the Second Order with Variable Coefficients," Proceedings of the Royal Society,
24, 269, 1876.
||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
|Thomson, Sir W.,
"Mechanical Integration of the General Linear
Differential Equation of any Order with Variable
Coefficients," Proceedings of the
Royal Society, 24, 271, 1876.
||A generalization of the scheme proposed in Thomson (1876C) to equations of
arbitrary order. Reprinted in Thomson
|Thomson, Sir W.,
"Harmonic Analyzer," Proceedings
of the Royal Society, 27, 371, 1878.
||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 (1878),
|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.
|Wildes, K. L. and Lindgren N. A., A Century of Electrical Engineering and
Computer Science at MIT, 1882-1982, Cambridge: MIT
provides a non-technical historical account of four
generations of analog technology developed under Bush's
guidance, from the early integraphs through to the mighty
|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 1937.
|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
|Williams, M. R., A History of Computing
Technology, 2nd Edition, Wiley-IEEE Computer Society
||Broad survey of computing history. Chapter 5 covers analog
machines in general with a section on the differential
analyzers. Mentions the Hartree Meccano
differential analyzer and has an interesting reference
to a Meccano machine built in Toronto by Beatrice (Trixie)
|Winston, B., Media Technology and
Society: A History: From the Telegraph to the Internet,
||Contains a brief reference to Hartree's construction of a
differential analyser in Meccano after visiting MIT to see
|Wood, A. M., The Design and Construction of a Small
Scale Differential Analyser and its Application to the
Solution of a Differential Equation, University of
Birmingham 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
differential analyzer at Cambridge University. Peierls (1985) confirms it was
|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 (1949).
|Wilson, A. H., "The Binding
Energies of the Hydrogen Isotopes" Proceedings
of the Cambridge Philosophical Society, 34,
||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
|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).