Integrators and Integraphs

Instruments for measuring the area under a curve (integrators) and for drawing a curve representing that area (integraphs) date from the nineteenth century and were used well into the twentieth century. Vannevar Bush even designed an integraph that could plot the value of the integral of the product of two functions. Techniques used in planimeters and integraphs would be adopted in more complicated mechanical integrators such as differential analyzers.

This instrument draws the integral of a function that is plotted when the curve representing the function is traced with the tracer. It rests on two German silver rollers attached to a common axle.
Description
This instrument draws the integral of a function that is plotted when the curve representing the function is traced with the tracer. It rests on two German silver rollers attached to a common axle. A framework above the axle carries the tracer arm, the integrating mechanism, and the plotter. A pen point, a pencil point, a calibration bar, a brush, what may be a tracer point and a head for the pencil point are stored in the case.
An inscription on the support for one wheel reads: G. Coradi Zurich. An inscription on the support for the other wheel reads: John R. Freeman (/) No. 121. A paper shed glued to the inside of the lid of the wooden case gives the value in centimeters of the ordinates for curves plotted using different bases.
The integraphs sold by Coradi before about 1903 had a much larger framework surrounding the axle. A similar instrument in the collections of the Science Museum has serial number 173 and dates from 1911. Compare MA.336877.
This instrument may well have been owned by the hydraulic and civil engineer and insurance executive John Ripley Freeman (1855-1932), an 1876 graduate of MIT. Freeman was president of Manufacturer's Mutual Fire Insurance Company of Providence, Rhode Island from the 1890s and also consulted on water power and municipal water supply projects.
References:
Dictionary of American Biography, Supplement 1 (1944).
G. Coradi, Catalogue of Mathematical Precision Instruments, Zurich: Mathematical-Mechanical Institute of G. Coradi, 1915, pp. 27-30. The integraph shown on page 28 is not precisely like this one.
Location
Currently not on view
date made
ca 1910
maker
Coradi, Gottlieb
ID Number
MA.304722.13
catalog number
304722.13
accession number
304722
This instrument draws the integral of a function that is plotted when the curve representing the function is traced with the tracer. The instrument rests on two German silver rollers attached to a common axle.
Description
This instrument draws the integral of a function that is plotted when the curve representing the function is traced with the tracer. The instrument rests on two German silver rollers attached to a common axle. A framework above the axle carries the tracer arm, the integrating mechanism, and the plotter. A pen point, a pencil point, a calibration bar, a screwdriver, and a knob for the pencil point are stored separately in the case. Discussion of instruments used to draw the integral curve of functions dates from the 1830s. In 1878 the engineer Abdank-Abakanowitz introduced the instrument that would be considerably modified and sold by Coradi from about 1890. The integraphs sold by Coradi before about 1903 had a much larger framework surrounding the axle. Although this object was sold by Keuffel & Esser, no model #4295 integraph is listed in K&E catalogs for 1906 through 1944. The device was sold after K&E opened its San Francisco office in 1901, as this office is mentioned on the paper sticker in the lid that gives the model and serial number. The card in the lid of the box indicates that the instrument was purchased from Roebling, who built the Brooklyn Bridge, in 1940. The card has been corrected in pencil to indicate that the vendor was in fact Roebling's son. Neither John Augustus Roebling (1806-1869) nor his son Washington A. Roebling (1837-1926), both of whom worked on the Brooklyn Bridge, was alive in 1940. John A. Roebling II, W.A. Roebling's son, lived from 1867 to 1952. It seems likely that he or possibly a cousin sold the instrument.
References:
Keuffel & Esser Co., Keuffel & Esser Co. its Origin, Growth and Present Scope, New York & Hoboken (1909).
Maurice d'Ocagne, Le Calcul Simplifie (1928).
Horsburgh, ed., Handbook of the Napier Tercentenary Celebration (1914) .
Location
Currently not on view
maker
Coradi, Gottlieb
ID Number
1978.2308.01
catalog number
1978.2308.01
accession number
1978.2308
catalog number
336877
This is the integraph-unit used by Vannevar Bush and his colleagues at MIT before they constructed the first differential analyzer. It consists of a Thomson watthour meter (in a box) with a geat train on under the box that has a crank at the rear.
Description
This is the integraph-unit used by Vannevar Bush and his colleagues at MIT before they constructed the first differential analyzer. It consists of a Thomson watthour meter (in a box) with a geat train on under the box that has a crank at the rear. A nameplate on the meter reads: Thomson watthour meter / direct current / 3 wire / No 5813227 Type 06 / Amp 10 Volts 231-240 / m27778 General Electric Co. U.S.A.
The object was donated to the museum with a large collection of electrical apparatus, much of it in the Electricity collections.
This instrument is a small part of a device that calculated the integral of the product of two functions. It was variously described as a product integraph and a continuous integraph. Illustrations of the system appear in the 1927 paper cited.
References:
V. Bush, F.D. Gage, and H.R. Stewart, "A Continuous Integraph," Journal of the Franklin Institute, vol. 203 #1, 1927, pp. 63-84.
S. Puchta, "On the Role of Mathematics and Mathematical Knowledge in the Invention of Vannevar Bush's Early Analog Computers," IEEE Annals of the History of Computing, 1996, vol. 18 # 4, pp. 49-59.
Location
Currently not on view
date made
ca 1925
maker
Bush, Vannevar
ID Number
MA.322186
catalog number
322186
accession number
244197
This German silver instrument is designed for measuring the area bounded by a closed curve (the integral of a function y), the moment of the enclosed surface (half the integral of y squared), and the moment of inertia of the enclosed surface (one third the integral of y cubed).
Description
This German silver instrument is designed for measuring the area bounded by a closed curve (the integral of a function y), the moment of the enclosed surface (half the integral of y squared), and the moment of inertia of the enclosed surface (one third the integral of y cubed). The instrument has three tracing points, one fixed to the tracing arm and the other two movable. A heavy metal rail with a groove in it is used to guide the motion of two rollers of the integrator as well as the two movable tracer arms. The rail is stored separately. For related documentation see 1978.1095.02 and 1978.1095.03. This instrument was used by G. Bruce Newby, the father of the donor, who was a naval architect and apparently resided in Long Beach, California, at the time he ordered the device.
A mark on the instrument reads: J. Amsler. Another mark reads: Keuffel & Esser Co. (/) New York. Another mark reads: Alfred J. Amsler & Co. (/) Switzerland. A mark on a paper tag nailed to the inside of the lid reads: KEUFFEL & ESSER CO. Another mark on this tag reads: No. 4286 Serial 1054. A mark on a paper tag pasted to the inside of the lid reads: Property of (/) G. BRUCE NEWBY (/) 83 Stratford Rd. (/) Berkeley, Calif.
For related documentation, see 1978.1095.02 and 1978.1095.03.
Reference: Accession file.
Location
Currently not on view
date made
1930
maker
Alfred J. Amsler & Company
ID Number
1978.1095.01
catalog number
1978.1095.01
accession number
1978.1095
catalog number
336876
This metal guide bar is part of the Amsler integrator (1978.1095.01). It is not shown in the image with the integrator.Currently not on view
Description
This metal guide bar is part of the Amsler integrator (1978.1095.01). It is not shown in the image with the integrator.
Location
Currently not on view
date made
1930
maker
Alfred J. Amsler & Company
ID Number
1978.1095.01.1
catalog number
1978.1095.01.1
accession number
1978.1095
catalog number
336876
This undated, well-worn manual describes the operation of Amsler integrators. It was puslished by Alfred J. Amsler & Co.and is stamped of the first page: G. B. Newby. The last page is annotated.Currently not on view
Description
This undated, well-worn manual describes the operation of Amsler integrators. It was puslished by Alfred J. Amsler & Co.and is stamped of the first page: G. B. Newby. The last page is annotated.
Location
Currently not on view
date made
1930
maker
Alfred J. Amsler & Company
ID Number
1978.1095.02
accession number
1978.1095
catalog number
1978.1095.02
This undated stapled set of sheetsis a typescript describing Amsler's method for determining the polar moments of inertia of a solid of revolution by the use of the integrator.Relates to integrator 1978.1095.01.Currently not on view
Description
This undated stapled set of sheetsis a typescript describing Amsler's method for determining the polar moments of inertia of a solid of revolution by the use of the integrator.
Relates to integrator 1978.1095.01.
Location
Currently not on view
date made
ca 1930
ID Number
1978.1095.03
accession number
1978.1095
catalog number
1978.1095.03
Maximilian Berktold (b. 1929) immigrated from Kempten-Allgäu, West Germany, in 1950 and almost immediately began working for the Los Angeles Scientific Instrument Company.
Description
Maximilian Berktold (b. 1929) immigrated from Kempten-Allgäu, West Germany, in 1950 and almost immediately began working for the Los Angeles Scientific Instrument Company. He oversaw design and production of the firm's planimeters, integrators, pantographs, and various optical instruments until Lasico closed in 2008.
This is the electronic version of the Lasico mechanical integrator 130. It has a metal framework painted green that carries two guide wheels, two reference guides (one for moment of inertia and the other for moment of area) and a tracer arm with two tracer points. The guide wheels fit into a metal guide rail. Two reference guides also fit into the guide rail and a metal counter weight fits into the framework, resting on the other side of the rail.
In addition to these pieces, there are three digital readouts for displaying measurements of area (marked A), moment of area (marked M), and moment of inertia (marked I).
All the pieces of the instrument, other than the rail, fit into a leather-covered wooden case. A photograph of Berktold is taped to the inside lid of the case, as well as a sheet of information about the instrument. This sheet gives a date of 1985. The guide rail is longer than the case is wide (it measures 78.5 cm. w. x 5 cm. d. x 1.3 cm. h.), and is stored separately.
A related pamphlet is entitled “The Lasico Mechanical Integrator.”
Compare 2011.0043.04.
Location
Currently not on view
date made
1985
ID Number
2016.0064.02
accession number
2016.0064
catalog number
2016.0064.02

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