|
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 MIT. |
|
Anon.
"Machine Solves Mathematical Problems. A Wonderful Meccano Mechanism" Meccano Magazine, XIX, 6, 442-444, 1934. |
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).
|
|
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.
|
|
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 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 laymans 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 the University of Manchester" Nature, 135, 535, 1935.
|
A brief column reporting on the
opening ceremony for the Manchester Metropolitan-Vickers
machine. |
|
Anon.
"The Differential Analyser" The
Engineer, 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.
|
|
Anon. Annual Report of the University of Malaya
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.
|
|
Anon. "A
Meccano Calculating Machine. Solving Complex Mathematical Equations"
Meccano Magazine, XXXVI, 1, 11, 1951.
|
A one page article describing
the Meccano differential analyzer built by Prof. J. C. Cooke
at the University of Malaya, Singapore. |
|
Anon.
"Mechanical Differential Analyser with SKF Bearings" The SKF Ball Bearing Journal,
#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 Meccanoman, 1967.
|
The first set of model building
instructions published for a Meccano model of Bush's differential
analyzer.
|
|
Anon.
"Among the Model Buiilders" Meccano
Magazine, 58, 3,
54-55, 1973. |
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 (1973).
|
|
Anon.
"Computer Display", Museum News, MOTAT, Sep. 1973.
|
A brief report on the then new
computer display at MOTAT,
featuring the Cambridge Meccano
differential analyzer.
|
|
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
differential analyzer "is still capable of performing calculus."
|
|
Anon.
"That Which was Lost has been Found", New
Zealand Federation of Meccano Modellers Magazine, 17, 3, 1993. |
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 23, 1993.
|
|
Anon.
"Meccano Differential Analyser No.2", New
Zealand Federation of Meccano Modellers Magazine, 25, 1, 2001. |
Although no author is
identified, these notes are editied 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 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 also included.
|
|
Berends,
T. "Historic Machine found by MOTAT" New
Zealand Herald, 29
June, 1993.
|
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 ot 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, 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. "Constructive Use of Friction in Torque Amplifiers and
Constant Torque Devices" Constructor
Quarterly, 4, 24-25,
June 1989.
|
Describes the principles of the
torque amplifer and related torque limiting devices.
|
|
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 autobigroaphy.
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 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, 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, 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.
|
|
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. "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: Longmans, 1947.
|
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 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.
|
|
Fail, R.
"Electro-mechanical Servo for Differential Analyser", Meccanoman's Journal, #12, 310,1968.
|
A rudimentary electro-mechanical
servo design to replace a torque amplifier.
|
|
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
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
differential 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 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 loading.
|
|
Gray, E.
"The Torque Amplifier", New Zealand
Federation of Meccano Modellers Magazine, Oct 1992.
|
An unusual application of the
torque amplifer 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, 342-364, 1938.
|
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, 643-647, 1938. |
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, 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,
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.
|
|
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 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, 164-170, 1952.
|
General description of the
operation of a differential analyzer with particular reference to the
General Electric 14 integrator machine.
|
|
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 the Meccano
differential analyzer.
|
|
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, 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 preceeding 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, 2001. |
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 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
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
reconstruction. |
|
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".
|
|
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
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),
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).
|
|
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, 1939.
|
A detailed description of the construction and
testing of the Meccano
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 editions.)
|
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.
|
|
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 them.
|
|
Marsh,
P. "The Meccano Set Computer" New
Scientist, 80, 1134,
(supplement 28-29), 1978.
|
A popular article on the history
of the Manchester differential analyzers.
|
|
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
differential analyzer.
|
|
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 Comuting 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 (1952).
|
|
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 iincludes 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 amplifer, 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 newly restored Cambridge Meccano
differential analyzer. |
|
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 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, 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 supersor 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 comissioned. These notes make fascinating reading.
It would appear that getting reliable operation from the machine was
very challenging.
|
|
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 analyzers.
|
|
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.
|
|
Rosseland,
von S. "Mechanische Integration von Differentialgleichungen" Die Naturwissenschaften, 27, 44, 729-735, 1939.
|
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 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 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. |
|
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 references.
|
|
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", 2004, on
line at:
https://turing.iem.thm.de/routeplanning/publications/historyasg1.pdf
. |
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
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 (1879).
|
|
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 (1879).
|
|
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.
|
|
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 adition 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 construction.. |
| |
Williams,
M. R. A
History of Computing Technology, 2nd Edition,
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
differential 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 machine. |
|
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.
|
Details 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 never
completed.
|
|
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, 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, 1978.
|
Reproduced on p31 is a small
extract from Anon (1934B).
|
