liquid equation solver for cubic roots
Date1963
Inventory Number1997-1-1605a
ClassificationDemonstration
Subject
Maker
Walter Balcke
Cultural Region
Place of Origin
Place of Use
Dimensions1.5 x 18 x 12 cm (9/16 x 7 1/16 x 4 3/4 in.)
Material
DescriptionThe liquid equation solver consists of a white and clear plexiglass container. In the center, vertically partitioning the container into two parts, is a deck of five laminated construction paper rulers. The rulers slide into a sleeve down the center of the apparatus. Two measurement scales are marked on each side of each ruler - all the markings are hand-drawn in black ink. One of the rules is wood-colored with a black strip at the top. The rest are white with an orange strip at the top.
On either side of the rule is an empty compartment of the container. The two compartments are attached by an opening near the very top such that liquid can be transferred from one side to the other. One compartment, the larger, is triangularly shaped with one outwardly curving edge. Along that edge is a white plexiglass bar with an orange strip across it that serves as a handle for the apparatus. The other compartment is rectangle-shaped, thinner than the rules, with only straight edges.
There is a small round hole on the top edge of the larger compartment, presumably once used to put liquid inside the compartments. However, it has since been filled in. Some clear liquid, slightly more viscous that water, remains in the device demonstrating its function.
The device stands on two plexiglass feet. In between them is a rotating plexiglass bar that can be rotated to various positions for extra stability.
On either side of the rule is an empty compartment of the container. The two compartments are attached by an opening near the very top such that liquid can be transferred from one side to the other. One compartment, the larger, is triangularly shaped with one outwardly curving edge. Along that edge is a white plexiglass bar with an orange strip across it that serves as a handle for the apparatus. The other compartment is rectangle-shaped, thinner than the rules, with only straight edges.
There is a small round hole on the top edge of the larger compartment, presumably once used to put liquid inside the compartments. However, it has since been filled in. Some clear liquid, slightly more viscous that water, remains in the device demonstrating its function.
The device stands on two plexiglass feet. In between them is a rotating plexiglass bar that can be rotated to various positions for extra stability.
Signedunsigned
Curatorial RemarksThis object is clearly visible in a Polaroid photograph taken in August 1961. The photograph is labeled "Exhibit of mathematical models and devices designed and constructed by Mr. Walter H. Balcke of Winchester, Mass. Department of Mathematics, Harvard University. August 1961" (CHSI library, Lib.4927). The display was set up in the Harvard Mathematics Department Library.
FunctionWalter Balcke built and gifted many mathematical models to the Mathematics department at Harvard University. According to substantial correspondence between mathematics professors and Balcke, the models were sometimes used in classes, circulated around the department for observation, and eventually put on display in the mathematics library.
This particular object is designed to solve various algebraic equations for specific values using liquid volume relations. Each side of each rule has a scale along each edge. Users would fill one compartment to the appropriate level and then transfer the liquid to the other side. The compartments are sized such that the liquid level after the transfer would give the solution to the equation presented on the rule currently in use. The models simultaneously solve, and visually demonstrate various algebraic relations.
The scales and equations for each side of each rule are as follows. Each scale is divided into increments of various sizes by small black lines. Only certain increments are marked with a number. The descriptions below indicate how much each scale increases or decreases in a certain number of increments. That number of increments also indicates the frequency of the numerical labels. Each scale is arbitrarily assigned a number from 1 to 4 and each side arbitrarily called a or b. The equation can, of course, only be solved for the values given on the rules, and not for any arbitrary values.
1a: Solves certain cubes and cubic roots. m^3 is on the left edge, beginning with 0 at the top and increasing by 100 every five increments until 1000 at the bottom. m is on the right edge, beginning with 10 at the top and decreasing by 1 every five increments until 0.
1b: Solves certain cubes and cubic roots. m^3 is on the left edge, beginning with 0 at the top and increasing by 0.1 every five increments until 1.0 at the bottom. m is on the right edge, beginning with 1.0 at the top and decreasing 0.1 every five increments until 0 at the bottom.
2a: Solves the equation (5/3)x^3 - 2.5x^2 +1.25x = C. C is on the left edge, beginning with 0 at the top and increasing by 20 every two increments until 200 at the bottom. x is on the right edge, beginning with 5 at the top and decreasing by 1 every 5 increments until 1 at the bottom.
2b: Solves the equation x^3 + 1.5x^2 + .75x = C. C is on the left edge, beginning with 0 at the top and increasing by 100 every two increments until 1900 at the bottom. x is on the right edge, beginning with 12 at the top and decreasing by 1 every two increments until 0 at the bottom.
3a: Solves certain cubes and cubic roots. N^3 is on the left edge, beginning with 0 at the top and increasing by 10 every two increments until 120 at the bottom. N is on the right edge, beginning with 5 at the top and decreasing by 1 every ten increments until 0 at the bottom.
3b: Solves certain cubes and cubic roots. N^3 is on the left edge beginning with 0 at the top and increasing by 100 every five increments until 1000 at the bottom. N is on the right edge, beginning with 10 at the top and decreasing by 1 every five increments until 0 at the bottom.
4a: Solves the equation x^3 + 6x^2 + 12x = C. C is on the left edge, beginning with 0 at the top and increasing by 100 every five increments until 100 at the bottom. x is on the right edge beginning with 8 at the top and decreasing by 1 every five increments until -2 at the bottom.
4b: solves the equation x^3 - 15x^2 + 75x = C. C is on the left edge, beginning with 0 at the top and increasing by 1000 every two increments until 15 000 at the bottom. x is on the right edge, beginning with 30 at the top and decreasing by 5 every five increments until 5 at the bottom.
5a: Solves the equation x^3 + 3x^2 + 3x = C. C is on the left edge, beginning with 0 and increasing by 100 every five increments until 1000 at the bottom. x is on the right edge, beginning with 9 at the top and decreasing by 1 every five increments until -1 at the bottom.
5b: Solves the equation x^3 - 6x^2 + 12x = C. C is on the left edge, beginning with 0 at the top and increasing by 100 every five increments until 1000 at the bottom. x is on the right edge, beginning with 12 at the top and decreasing by 1 every five increments until 2 at the bottom.
This particular object is designed to solve various algebraic equations for specific values using liquid volume relations. Each side of each rule has a scale along each edge. Users would fill one compartment to the appropriate level and then transfer the liquid to the other side. The compartments are sized such that the liquid level after the transfer would give the solution to the equation presented on the rule currently in use. The models simultaneously solve, and visually demonstrate various algebraic relations.
The scales and equations for each side of each rule are as follows. Each scale is divided into increments of various sizes by small black lines. Only certain increments are marked with a number. The descriptions below indicate how much each scale increases or decreases in a certain number of increments. That number of increments also indicates the frequency of the numerical labels. Each scale is arbitrarily assigned a number from 1 to 4 and each side arbitrarily called a or b. The equation can, of course, only be solved for the values given on the rules, and not for any arbitrary values.
1a: Solves certain cubes and cubic roots. m^3 is on the left edge, beginning with 0 at the top and increasing by 100 every five increments until 1000 at the bottom. m is on the right edge, beginning with 10 at the top and decreasing by 1 every five increments until 0.
1b: Solves certain cubes and cubic roots. m^3 is on the left edge, beginning with 0 at the top and increasing by 0.1 every five increments until 1.0 at the bottom. m is on the right edge, beginning with 1.0 at the top and decreasing 0.1 every five increments until 0 at the bottom.
2a: Solves the equation (5/3)x^3 - 2.5x^2 +1.25x = C. C is on the left edge, beginning with 0 at the top and increasing by 20 every two increments until 200 at the bottom. x is on the right edge, beginning with 5 at the top and decreasing by 1 every 5 increments until 1 at the bottom.
2b: Solves the equation x^3 + 1.5x^2 + .75x = C. C is on the left edge, beginning with 0 at the top and increasing by 100 every two increments until 1900 at the bottom. x is on the right edge, beginning with 12 at the top and decreasing by 1 every two increments until 0 at the bottom.
3a: Solves certain cubes and cubic roots. N^3 is on the left edge, beginning with 0 at the top and increasing by 10 every two increments until 120 at the bottom. N is on the right edge, beginning with 5 at the top and decreasing by 1 every ten increments until 0 at the bottom.
3b: Solves certain cubes and cubic roots. N^3 is on the left edge beginning with 0 at the top and increasing by 100 every five increments until 1000 at the bottom. N is on the right edge, beginning with 10 at the top and decreasing by 1 every five increments until 0 at the bottom.
4a: Solves the equation x^3 + 6x^2 + 12x = C. C is on the left edge, beginning with 0 at the top and increasing by 100 every five increments until 100 at the bottom. x is on the right edge beginning with 8 at the top and decreasing by 1 every five increments until -2 at the bottom.
4b: solves the equation x^3 - 15x^2 + 75x = C. C is on the left edge, beginning with 0 at the top and increasing by 1000 every two increments until 15 000 at the bottom. x is on the right edge, beginning with 30 at the top and decreasing by 5 every five increments until 5 at the bottom.
5a: Solves the equation x^3 + 3x^2 + 3x = C. C is on the left edge, beginning with 0 and increasing by 100 every five increments until 1000 at the bottom. x is on the right edge, beginning with 9 at the top and decreasing by 1 every five increments until -1 at the bottom.
5b: Solves the equation x^3 - 6x^2 + 12x = C. C is on the left edge, beginning with 0 at the top and increasing by 100 every five increments until 1000 at the bottom. x is on the right edge, beginning with 12 at the top and decreasing by 1 every five increments until 2 at the bottom.
ProvenanceFrom the Department of Mathematics, Harvard University.
Walter Balcke
Date: 1952-1964
Object number: 1997-1-1605b
Charles W. Dixey
Date: circa 1830
Accessories: silver framed green shagreen case
original curatorial cards and photos
Object number: DW0288
Walter Balcke
Date: circa 1958
Accessories: in library folder (Lib 4927):
-twenty-one letters from Joseph L. Walsh, mathematics professor at Harvard University, to Walter Balcke, dated between 27 May 1957 and 24 January 1964 (letters thank Balcke for the many mathematical models he gifted to the Mathematics Department, praise his skill and ingenuity, many invite him to faculty and personal luncheons, and one letter provides an analytic solution to the "13-point problem" behind one of Balcke's models)
-three letters from Garret Birkhoff (then Chairman of the Harvard Mathematics Department) dated 3 March 1954, 4 January 1955, and 10 January 1955, each expressing gratitude (and in one case, an official department thank you) for the many mathematical models he gifted to the mathematics department
-photocopy of original envelope in which correspondence between mathematics department and Walter Balcke was stored (original was destroyed on 13 July 1997)
-photocopy of instructional card for object 1997-1-1671
- seven instructional cards that accompany the following Balcke models: Pascal's Theorem, Brianchon's Concurrent Lines, Trisector, Twelve Point Ellipse, Rolling Parabola, unknown, Equation Solution with a 'Constant' Variable and Thread
- photograph of the display case containing Balcke's models in the Harvard Mathematics department
Object number: 1997-1-1597
Panelvision Corporation
Date: 1984
Accessories: single-board display controller
cable for display (1997-1-0686c)
shipping ticket/ hand carry pass dated June 11, 1997 (in instrument file)
letter to Dr. Richard V. Kollarits from William Andrewes dated June 16, 1997 regarding donation of MiniGraphic display and letter to William Andrewes from Dr. Richard V. Kollarits that accompanied the object upon donation on June 11, 1997 (in instrument file)
four sample color prints made with this display on micro-encapsulated photographic paper. 1. man in business suit, 2. woman crouching next to lawn ornament, 3. two clowns painting a third's face, 4. woman in winter hat and scarf (in instrument file)
copies of two articles by AT&T Bell Laboratories staff (Richard V. Kollarits, William, H. Ninke, David C. Gibbon) on color imaging and printing (in instrument file)
Panelvision pamphlet introducing the MiniGraphic multipurpose flat panel display, including instrument specifications, consumer prices, functioning and features (in instrument file)
1984 article by Panelvision employees (Peter Brody Fang-Chen Luo, Paul Malmberg) on active matrix technology (in instrument file)
Panelvision Corporation Fact Sheet, including details of company history and recent developments (in instrument file)
article about commercial debut of active matrix technology from Design Engineering newspaper, June 18, 1984 (in instrument file)
full circuit diagram and schematic for MiniGraphic Display Controller (in instrument file)
instruction manual and description of MiniGraphic Display Controller (two copies, in instrument file)
circuit diagrams and instruction manuals for the MiniGraphic Display (two booklets, in instrument file)
Object number: 1997-1-0686a
Walter Balcke
Date: 1963
Accessories: mahogany lid
in library folder (Lib 4927):
-twenty-one letters from Joseph L. Walsh, mathematics professor at Harvard University, to Walter Balcke, dated between 27 May 1957 and 24 January 1964 (letters thank Balcke for the many mathematical models he gifted to the Mathematics Department, praise his skill and ingenuity, many invite him to faculty and personal luncheons, and one letter provides an analytic solution to the "13-point problem" behind one of Balcke's models)
- one letter from J.L. Walsh may pertain directly to this object, dated March 21, 1963
-three letters from Garret Birkhoff (then Chairman of the Harvard Mathematics Department) dated 3 March 1954, 4 January 1955, and 10 January 1955, each expressing gratitude (and in one case, an official department thank you) for the many mathematical models he gifted to the mathematics department
-photocopy of original envelope in which correspondence between mathematics department and Walter Balcke was stored (original was destroyed on 13 July 1997)
-photocopy of instructional card for object 1997-1-1671
- seven instructional cards that accompany the following Balcke models: Pascal's Theorem, Brianchon's Concurrent Lines, Trisector, Twelve Point Ellipse, Rolling Parabola, unknown, Equation Solution with a 'Constant' Variable and Thread
- photograph of the display case containing Balcke's models in the Harvard Mathematics department
Object number: 1997-1-1650
Zeiss-Aerotopograph
Date: circa 1950
Accessories: in wooden storage case with metal handles; documentation booklet is now kept in the instrument's file; all other accessories are kept in the box and are included in the description.
Object number: 2009-1-0002b
Walter Balcke
Date: 1952-1964
Accessories: white carboard box
Object number: 1997-1-1637
Walter Balcke
Date: 1953
Accessories: mahogany box; cardboard instruction card;
in library folder (Lib 4927):
-twenty-one letters from Joseph L. Walsh, mathematics professor at Harvard University, to Walter Balcke, dated between 27 May 1957 and 24 January 1964 (letters thank Balcke for the many mathematical models he gifted to the Mathematics Department, praise his skill and ingenuity, many invite him to faculty and personal luncheons, and one letter provides an analytic solution to the "13-point problem" behind one of Balcke's models)
- one letter from J.L. Walsh directly related to this object, the "modified slide rule", dated February 11, 1953
-three letters from Garret Birkhoff (then Chairman of the Harvard Mathematics Department) dated 3 March 1954, 4 January 1955, and 10 January 1955, each expressing gratitude (and in one case, an official department thank you) for the many mathematical models he gifted to the mathematics department
-photocopy of original envelope in which correspondence between mathematics department and Walter Balcke was stored (original was destroyed on 13 July 1997)
-photocopy of instructional card for object 1997-1-1671
- seven instructional cards that accompany the following Balcke models: Pascal's Theorem, Brianchon's Concurrent Lines, Trisector, Twelve Point Ellipse, Rolling Parabola, unknown, Equation Solution with a 'Constant' Variable and Thread
- photograph of the display case containing Balcke's models in the Harvard Mathematics department
Object number: 1997-1-1609
Walter Balcke
Date: 1952-1964
Accessories: mahogany box; cardboard instruction card
Object number: 1997-1-1601
Walter Balcke
Date: 1952-1964
Accessories: mahogany case; two circular protractors; clear plexiglass rule with serated edge
Object number: 1990-5-0028
See also/See also
