Coradi's mechanical integraph
Date1916-1926
Inventory Number1996-1-0084
ClassificationIntegraph
Subject
Maker
Keuffel & Esser Company
1867 - 1987
Cultural Region
Place of Origin
Dimensions18 x 37 x 85 cm (7 1/16 x 14 9/16 x 33 7/16 in.)
box: 19.1 × 88.9 × 40.3 cm (7 1/2 × 35 × 15 7/8 in.)
box: 19.1 × 88.9 × 40.3 cm (7 1/2 × 35 × 15 7/8 in.)
Material
Accessorieswood case and key; photocopy of original Keuffel & Esser Co. catalogue in which the model is introduced
DescriptionThe main core of the Coradi integraph is composed of two long, parallel, silver strips connected to a large roller encased in a black frame at each end and connected in the center to a small black square (let these two strips together be called Bar A). That black square supports a pivot to which is attached a long, thin, rectangular, silver bar (let it be called Bar B). There is a small, two-roller mechanism sitting on the top of Bar B. A small bar is suspended from the roller mechanism and attached to one end of a very thin set of parallel silver sheets that are very close to the ground below Bar A. At the other end, the silver sheets are connected to a small wheel encased in a black frame to which is also attached a brass pencil or pen holder.
The black frame that houses the pencil holder is attached to the leftmost end of Bar A. Extending from that end of Bar A is also another, shorter, silver bar (let it be called Bar C) that is attached by a sliding mechanism to Bar B. Bar C is marked as a ruler in both inches and centimeters starting at 1cm where Bar C attaches to Bar A and ending with 38cm where Bar C holds a stylus with which users trace the curve that they wish to integrate. As they trace, the motion is communicated from Bar C to Bar A to Bar B which in turn moves the two thin silver strips that run along the group which impart the final motion to the pencil holder. The motion transfer is mitigated through a mechanism at the leftmost end of Bar A and through the relations of Bars A and B such that a pencil in the pencil holder will trance the integral curve for the curve traced.
The integraph is housed inside the box upon four wooden supports padded with purple felt. The inside of the box is unfinished wood. Written on the inside of the lid in red crayon is "Property of Div. of Mathematics, Written by M. Morse 1929".
The box has one support for each end of Bar A, one for the rightmost end of Bar B, and one that is shared by the leftmost end of Bar B and the stylus end of Bar C. On the right side of the box is a wooden ledge padded in purple felt used to store spare parts, screw, wheels, and accessories.
The outside of the box is finished wood. On the front face of the bottom half of the box there is a small metal key hole. Loose inside the box is the key on a piece of hemp string. There is also a small brass handle attached to the front face of the bottom of the box and two small hooks that swing up to attach the bottom and top halves of the box. There are three brass hinges attaching the top and bottom halves of the box along the back. Loose inside the box there are also three wooden supports padded with purple felt that have come un-nailed from their places.
The original catalogue in which the Model 4298 Coradi Integraph was introduced has been digitized and can be accessed by clicking here. The catalogue describes the materials, specifications, capabilities, and design of the Coradi Integraph.
The black frame that houses the pencil holder is attached to the leftmost end of Bar A. Extending from that end of Bar A is also another, shorter, silver bar (let it be called Bar C) that is attached by a sliding mechanism to Bar B. Bar C is marked as a ruler in both inches and centimeters starting at 1cm where Bar C attaches to Bar A and ending with 38cm where Bar C holds a stylus with which users trace the curve that they wish to integrate. As they trace, the motion is communicated from Bar C to Bar A to Bar B which in turn moves the two thin silver strips that run along the group which impart the final motion to the pencil holder. The motion transfer is mitigated through a mechanism at the leftmost end of Bar A and through the relations of Bars A and B such that a pencil in the pencil holder will trance the integral curve for the curve traced.
The integraph is housed inside the box upon four wooden supports padded with purple felt. The inside of the box is unfinished wood. Written on the inside of the lid in red crayon is "Property of Div. of Mathematics, Written by M. Morse 1929".
The box has one support for each end of Bar A, one for the rightmost end of Bar B, and one that is shared by the leftmost end of Bar B and the stylus end of Bar C. On the right side of the box is a wooden ledge padded in purple felt used to store spare parts, screw, wheels, and accessories.
The outside of the box is finished wood. On the front face of the bottom half of the box there is a small metal key hole. Loose inside the box is the key on a piece of hemp string. There is also a small brass handle attached to the front face of the bottom of the box and two small hooks that swing up to attach the bottom and top halves of the box. There are three brass hinges attaching the top and bottom halves of the box along the back. Loose inside the box there are also three wooden supports padded with purple felt that have come un-nailed from their places.
The original catalogue in which the Model 4298 Coradi Integraph was introduced has been digitized and can be accessed by clicking here. The catalogue describes the materials, specifications, capabilities, and design of the Coradi Integraph.
Signedon frame of the rightmost roller: G. Coradi Zurich
Inscribedon the frame of the rightmost roller: No. 114
in red crayon inside the lid: Property of Div. / of Mathematics / Written by M. Morse 1929
Curatorial RemarksThe Integraph's box contains two cue cards. The first reads "WARNING; Be sure to pick it up by the wheels as well as the frame - The whole weight bears on two fragile, cone-bearings - Bearings broken at some date and replaced December 19, 1984--- E. Gay"
The second reads "For a possible name and purpose for this instrument see the Keuffel & Esser 38th edition of 1936 page 348--"Coradi's Mechanical Integraph" has all the characteristics though differing in detail; E. Gay 1989".
FunctionThis is a Model 4298 Coradi Integraph. Integraphs are mechanical, analog, computing devices used to plot the integral of a graphically defined function. Their close predecessors, mechanical integrators, require the user to construct curves by calculating point by point. Bypassing this tedious process, the Integraph draws the curves directly on paper on its own making its operation automatic, graphical integration. The Integraph was of particular use to mechanical engineers, naval architects, and physicists. It was used to calculate, among other things, centers of gravity and curves of stability.
In order to operate the Integraph, the user traces a figure (the differential curve) and, with the attached writing implement, the device automatically draws the integral curve. The pointed stylus extension of the device is used to trace. A pen or pencil can be fit into the brass holder extended from the base of the larger silver bar then draws the integral curve on a piece of paper or other surface underneath the device. The tracing motion is mediated through the interceding bars such that the pencil will draw precisely the integral curve of the traced function. For example, if the user traces a graphical representation of the curve sin(x), the Integraph will draw -cos(x). The machine is especially helpful when users are taking multiple integrals. Once the first curve has been traced and the integral curve drawn, the user can then trace the mechanically produced curve, and so forth.
The original catalogue in which the first Model 4298 Coradi Integraph was introduced has been digitized and can be accessed by clicking here. The catalogue describes the materials, specifications, capabilities, and design of the Coradi Integraph Model 4298 and compares its abilities with its immediate predecessor, the Model 4296 Integraph.
A variation of the Model 4298 closer to this one is introduced in the Keuffel & Esser Co. Catalogue in 1936 which can be seen here.
In order to operate the Integraph, the user traces a figure (the differential curve) and, with the attached writing implement, the device automatically draws the integral curve. The pointed stylus extension of the device is used to trace. A pen or pencil can be fit into the brass holder extended from the base of the larger silver bar then draws the integral curve on a piece of paper or other surface underneath the device. The tracing motion is mediated through the interceding bars such that the pencil will draw precisely the integral curve of the traced function. For example, if the user traces a graphical representation of the curve sin(x), the Integraph will draw -cos(x). The machine is especially helpful when users are taking multiple integrals. Once the first curve has been traced and the integral curve drawn, the user can then trace the mechanically produced curve, and so forth.
The original catalogue in which the first Model 4298 Coradi Integraph was introduced has been digitized and can be accessed by clicking here. The catalogue describes the materials, specifications, capabilities, and design of the Coradi Integraph Model 4298 and compares its abilities with its immediate predecessor, the Model 4296 Integraph.
A variation of the Model 4298 closer to this one is introduced in the Keuffel & Esser Co. Catalogue in 1936 which can be seen here.
ProvenanceFrom the Mathematics Department, Harvard University, December 14, 1984.
Jakob Amsler
Date: circa 1906
Accessories: instrument is in four (4) parts; the rail is in own box and is inventory # 2006-1-0002b; letter from Prof. William Brower containing the complete history of ownership and use (missing)
Object number: 2006-1-0002a
Gebrüder Haff
Date: circa 1960
Accessories: black storage case
two white cards with conversion tables inside case
Object number: 1997-1-2000
Gottlieb Coradi
Date: 1907
Accessories: carrying case
Object number: 1997-1-0250
Gottlieb Coradi
Date: 1903
Accessories: carrying case
Object number: 1997-1-0247
Adrien Gavard
Date: circa 1860
Accessories: hinged mahogany case with original trade label; extra arm; writing implements; instrument weights; small ivory wheels with brass frames
Object number: 1997-1-1856
Forster
Date: 1950-1960
Accessories: spare ink cartridges; pen attachments
am auxiliary box containing small Allen wrench, scotch tape, extra parts, and storage instructions
Object number: 1999-1-0054
Hammond Typewriter Company
Date: circa 1923
Accessories: four Hammond type shuttles for different type faces, each with a wooden storage box; four laminated paper rectangles with symbol placement guide; instruction book, instruction sheets, advertisements, and correspondence (in object file)
Object number: 1996-1-0373
G. Coradi
Date: circa 1911
Accessories: conversion table on white card in instrument case; instrument case
Object number: 1999-1-0068
W. F. Stanley & Company, Ltd.
Date: circa 1873
Accessories: case
Object number: 5120
Gebrüder Haff
Date: circa 1940
Accessories: card with instrument info and conversion table; photocopy of letter from Dr. Joachim Fischer to William J.H. Andrewes, dated 12 May 1997; photocopy of extract from Dr. Joachim Fischer's inventory of integrating instruments included with the letter
Object number: 1997-1-0444
Gebrüder Haff
Date: circa 1940
Accessories: card with instrument information and conversion table
Object number: 1997-1-0445
Gebrüder Haff
Date: circa 1940
Accessories: case
Object number: 1997-1-0446