logarithm model and calculator
Datecirca 1958
Inventory Number1997-1-1671
ClassificationMathematical Model
Subject
Attributed to
Walter Balcke
Cultural Region
Place of Origin
Place of Use
Dimensionsinstrument: 7 × 35 × 1.5 cm (2 3/4 × 13 3/4 × 9/16 in.)
case: 7.4 × 36.4 × 2.5 cm (2 15/16 × 14 5/16 × 1 in.)
case: 7.4 × 36.4 × 2.5 cm (2 15/16 × 14 5/16 × 1 in.)
Material
Accessorieswooden case; blue pencil; pink eraser
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
DescriptionThe model is stored in a rectangular wooden case that opens with three brass hinges along one of the long edges. There are two brass hooks attached to the front of the bottom of the case that each hook into a brass loop on the front edge of the lid when the case is closed. The inside of the case is contoured to fit the various instrument pieces and is painted yellow. Pieces of cotton are stuffed into certain of the instrument contours to protect instrument pieces and hold them in place.
The model consists of three components: a right scalene plexiglass triangle, and two plexiglass attachment. One attachment, the "limiter" has one rounded, smooth edge. Centered near the top is attached a blue plexiglass piece. The other edge consists of three prongs. The leftmost prong (when the smooth edge is the top) is straight down and rounded with three plexiglass bumps on one side. A small blue T-shaped plexiglass piece is attached underneath the bottom two bumps. The central prong is a triangle that "leans" towards the left. The right edge of the rightmost prong is straight down, and the left edge slopes towards the center. This prong also has three plexiglass bumps on one side, the bottom two of which are accompanied by blue plexiglass T-shaped attachments. The rightmost slope of the center prong and the leftmost slope of the rightmost prong carve out a right isosceles triangle whose right angle is at the top.
The second attachment, the "pointer", is a small plexiglass triangle mounted on another, perpendicular plexiglass triangle with a small, round blue handle on the top of their intersection. Both of these attachments slip onto the edge of the main triangular piece and can slide along its edges. The three-pronged piece slides along the longest sloped edge of the triangle, and the two-triangle piece slides along the longest straight edge.
Also stored in the instrument case is a wooden pencil, whose shaft is painted blue, and a pink eraser. There is also an oval-shaped black plexiglass piece with a brown piece on either end.
The model consists of three components: a right scalene plexiglass triangle, and two plexiglass attachment. One attachment, the "limiter" has one rounded, smooth edge. Centered near the top is attached a blue plexiglass piece. The other edge consists of three prongs. The leftmost prong (when the smooth edge is the top) is straight down and rounded with three plexiglass bumps on one side. A small blue T-shaped plexiglass piece is attached underneath the bottom two bumps. The central prong is a triangle that "leans" towards the left. The right edge of the rightmost prong is straight down, and the left edge slopes towards the center. This prong also has three plexiglass bumps on one side, the bottom two of which are accompanied by blue plexiglass T-shaped attachments. The rightmost slope of the center prong and the leftmost slope of the rightmost prong carve out a right isosceles triangle whose right angle is at the top.
The second attachment, the "pointer", is a small plexiglass triangle mounted on another, perpendicular plexiglass triangle with a small, round blue handle on the top of their intersection. Both of these attachments slip onto the edge of the main triangular piece and can slide along its edges. The three-pronged piece slides along the longest sloped edge of the triangle, and the two-triangle piece slides along the longest straight edge.
Also stored in the instrument case is a wooden pencil, whose shaft is painted blue, and a pink eraser. There is also an oval-shaped black plexiglass piece with a brown piece on either end.
Signedunsigned
Curatorial RemarksIt is not verified that this object was constructed by Walter Balcke for the Mathematics Department at Harvard University. However, it is constructed in the same style and same materials as other confirmed Balcke models and is very likely one of them.
FunctionThis model demonstrates the principles behind logarithms and can be used to calculate them. The instruction card reads as follows:
"Shoulders of limiter must be held to guiding edges of stick. Required steps are made by holding down one element while moving the other. Numbers are marked at indicator point after counting by 1" and .1" steps from zero. Logs are found by counting .1 and .01 steps from unity. Third digit is estimated. Numerical zero is to be marked at log = -? by carefully marking log steps to the left until they are reduced to no movement. Marks should not be permanent. Logarithmic zero is to be marked at an arbitrary unit to the right of the numerical zero, -- in this case one inch, without use of separate scale. Operations may be varied by counting differences in logs, obtaining cologs by counting to ten, -- etc.". Next to the instructions is a labelled diagram of the apparatus. On the back are two diagrams for interpreting results from the apparatus.
Walter Balcke built and gifted many mathematical models to the Harvard 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.
"Shoulders of limiter must be held to guiding edges of stick. Required steps are made by holding down one element while moving the other. Numbers are marked at indicator point after counting by 1" and .1" steps from zero. Logs are found by counting .1 and .01 steps from unity. Third digit is estimated. Numerical zero is to be marked at log = -? by carefully marking log steps to the left until they are reduced to no movement. Marks should not be permanent. Logarithmic zero is to be marked at an arbitrary unit to the right of the numerical zero, -- in this case one inch, without use of separate scale. Operations may be varied by counting differences in logs, obtaining cologs by counting to ten, -- etc.". Next to the instructions is a labelled diagram of the apparatus. On the back are two diagrams for interpreting results from the apparatus.
Walter Balcke built and gifted many mathematical models to the Harvard 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.
ProvenanceFrom the Department of Mathematics, Harvard University.
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: 1958
Accessories: mahogany case with plastic top; 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 pertains directly to this object, dated January 30, 1958
-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: 1990-5-0029
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
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
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 pertains directly to this object, dated October 27, 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: 1997-1-1610
Walter Balcke
Date: 1959
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)
- one letter from J.L. Walsh pertains directly to this object, dated April 21, 1959
-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: 1990-5-0030
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 (pertains directly to this object), 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: 1990-5-0031
Walter Balcke
Date: 1959-1960
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)
- one letter from J.L. Walsh, dated November 17, 1959 anticipates Balcke's construction of models to demonstrate Pascal and Brianchon's theorems; another letter from J.L. Walsh, dated Januaray 18, 1960 thanks Balcke for the Pascal Model; another letter from J.L. Walsh, dated February 29, 1960 thanks Balcke for the Brianchon model;
-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 (may pertain directly to this object), Brianchon's Concurrent Lines (may pertain directly to this object), 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: 1997-1-1603
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
Louis Dupin
Date: circa 1849
Accessories: book shaped storage case; six photographs and negatives of case and models with ruler scale (in instrument file)
Object number: 1996-1-0006
See also/See also
