#
Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

"Science & Mathematics - Overview" showing 2381 items.

Page 127 of 239

## Model Illustrating Finding the Area of a Circle, Ross Surface Form #14

- Description
- This is one of the models of plane figures (surface forms) designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The flat wooden disc can be arranged as a circle which is divided into six wedges that are hinged together along the perimeter. These may be rearranged to form what the model calls a “rhomboid.”

- One side of the model has four paper stickers and the other has six. One of them reads: AREA OF CIRCLE.

- Ross, like A. H. Kennedy before him, argued that a circle could be considered as the most general case of a polygon with area equal to the sum of the area of triangles, with height equal to the radius of an inscribed circle, and with sides equal to the sides of the polygons. In other words, the area of the regular polygon equaled half the perimeter of the polygon times the radius of the inscribed circle, and the area of a circle half the circumference of the circle times the radius.

- For further information about Ross models, including references, see 1985.0112.191. Closely related models are 1985.0112.200, 1985.0112.201, and 1985.0112.202. Kennedy’s version of this model is 2005.0054.01.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.203

- catalog number
- 1985.0112.203

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Pyramid and Frustrum of Pyramid, Ross Solid #11

- Description
- This is the eleventh in a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The unpainted wooden model has a square base and four equal triangles for sides. A plane parallel to the base divides it into a square pyramid and the frustum of a square pyramid. A paper label on the model reads: Frustum of a Pyramid. Another mark on this label reads: (See Metallic Frustum). A mark on another paper label reads: Pyramid.

- Compare models 1985.0112.205 through 2012.0112.217. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.205

- catalog number
- 1985.0112.205

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Square Prism, Ross Solid

- Description
- This is one of a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. It is a wooden square prism with a base of 1 inch by 1 inch and a height of 3 inches. The object has no maker’s label.

- Ross took the fundamental unit of measure of rectangles to be one square inch, and the fundamental unit of measure for solids to be one cubic inch. He argued from there that a 1 inch x 6 inch rectangle had an area of 6 square inches (see 1985.0112.191). Similarly, this solid model consisted of 3 cubic inches. He would go on to consider several square prisms lined up end to end, and may have intended for this to be one of them. See 1985.0112.206 for two closely related models. These are also shown in the photograph.

- Compare models 1985.0112.205 through 2012.0112.217.

- For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.207

- catalog number
- 1985.0112.207

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Octagonal Prism, Ross Solid

- Description
- This is one of a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio.

- The unpainted wooden model has eight rectangular sides and an octagonal top and bottom. Four straight lines join opposite vertices of the octagons on each end, suggesting how the solid might be divided into eight triangular prisms. A mark on a label on the side reads: OCTAGONAL PRISM. Further text discusses the surface area and volume of the solid.

- In the series of plane figures, Ross compared the area of a circle to the area of circumscribing polygons of increasing numbers of sides. To demonstrate the volume of a cylinder, he compared it to various regular prisms, including the octagonal.

- Compare models 1985.0112.205 through 2012.0112.217. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.208

- catalog number
- 1985.0112.208

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Cylinder, Ross Solid #8

- Description
- This is the eighth in a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio.

- The unpainted wooden model is in the shape of a cylinder. Inscribed on the top of the cylinder is a square, with its diagonals indicated. An incomplete paper tag reads: C [. . .] R 3x6 [. . .] (/) When the [. . .] of the prism become infinite, it becomes a cylinder, the perimeter of a prism with an infinite number of sides being termed the circumference.

- In the series of plane figures, Ross compared the area of a circle to the area of circumscribing polygons of increasing numbers of sides. To demonstrate the volume of a cylinder, he compared it to various regular prisms inscribed in it. This model suggests how a square pyramid might be inscribed in a cylinder.

- Compare 1985.0112.208 and 1985.0112.210. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.209

- catalog number
- 1985.0112.209

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Dissected Triangular Prism, Ross Solid #9

- Description
- This is the ninth in a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The unpainted wooden model is a triangular prism with three rectangular sides and a triangular base and top. It separates into three pyramids of equal volume; two of these are identical. A diagram of the dissection appears on one of two paper stickers glued to the model. A mark on one label reads: Triangular Pris [. . .].

- Finding the volume of pyramids was not only important for practical reasons but was central to Ross’s demonstrations for the volume of a cone and of a sphere.

- For Ross solids, see 1985.0112.205 through 2012.0112.217. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.211

- catalog number
- 1985.0112.211

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Dissected Frustum of a Triangular Prism, Ross Solid

- Description
- This is one of a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The unpainted wooden model of the frustum of a triangular pyramid has three trapezoidal sides and a triangular top and base. It is dissected into three pieces. A paper label attached to one side reads: Triangular Frustum.

- For Ross solids, see 1985.0112.205 through 2012.0112.217. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.215

- catalog number
- 1985.0112.215

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Cone Dissected into Two Pieces, Ross Solid #12

- Description
- This is the twelfth in a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio.

- The unpainted wooden model of a cone is divided into two pieces by a plane parallel to the base. A label on the side of the frustum reads: CONE. Ross compared the volume of a cone to the volume of a pyramid with a regular polygon for its base.

- For Ross solids, see 1985.0112.205 through 2012.0112.217. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.216

- catalog number
- 1985.0112.216

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Keuffel & Esser 4220 Amsler Style Polar Planimeter

- Description
- This tarnished German silver instrument has two arms pivoted at one end. One arm has a tracer point and index marks for four ratios: 1 square D. (centimeters or meters, perhaps), 15 square inches, 10 square inches, and 10 square chains. A screw assembly adjusts the length of the tracer arm. A support for the tracer point prevents it from tearing the paper. Two numbers are stamped underneath the arm: 31, which appears to overstamp the number 33, and 690.

- The other arm is jointed. A cylindrical weight may be placed in the end of that arm. Underneath the weight is marked: 35. The jointed part of the arm is marked: KEUFFEL & ESSER C
__o__N.Y. Underneath the arm is stamped: 31. A carriage at the pivot holds a white plastic measuring wheel with vernier and a horizontal metal registering dial.

- A mahogany case has dark blue velvet lining the supports. A leather pouch holds the weight. A paper chart for adjusting the tracer arm is held in the lid by black plastic edges and brass screws. The columns are labeled: Proportion, Adjustement [
*sic*] on tracer-arm, and Value of unit of the Vernier. "Sq. units" is handwritten above the first entry in the Proportion column (1:1,000). The vernier entry for proportion 1:4,000 has been changed from 100 to 160 square meters.

- Keuffel & Esser sold this planimeter as model 1102 from 1892 to 1901 and as model 4220 from 1901 to 1936. It sold for $28.00 in 1909 and for $45.50 in 1936. The serial number, 690, and lack of rectangular support for the joint in the weighted arm suggest that this example was made later than 1981.0348.01. Wesleyan University donated this planimeter to the Museum in 1984–1985 with a large collection of plaster and string mathematical models purchased in 1895 from the Darmstadt, Germany, firm of L. Brill.

- References:
*Catalogue of Keuffel & Esser*, 33rd ed. (New York, 1909), 319;*Catalogue of Keuffel & Esser*, 38th ed. (New York, 1936), 336; Clark McCoy, "Collection of Pages from K&E Catalogs for the 4220 Family of Polar Planimeters," http://www.mccoys-kecatalogs.com/PlanimeterModels/ke4220family.htm.

- Location
- Currently not on view

- date made
- 1901-1936

- distributor
- Keuffel & Esser Co.

- maker
- Keuffel & Esser Co.

- ID Number
- 1985.0112.218

- catalog number
- 1985.0112.218

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Comptometer Model C

- Description
- This key-driven non-printing adding machine has ten columns of black and white color-coded keys. Complementary digits are indicated and the keys are alternately concave (odd digits) and flat (even digits). The key stems become progressively longer as the digits are larger. There are subtraction levers and decimal markers (unnumbered) in front of the keys. In front of these is a row of 11 windows in the brown steel case that reveals the result on numeral wheels below.

- The machine has serial number 36372, which is indicated on the front to the left of the keys. It is marked on a metal tag screwed to the top of the machine: TRADE COMPTOMETER MARK (/) PAT’D [. . .] JUL.14.03 (/) Felt & Tarrant Mfg. Co. (/) Chicago. The date listed is the last of several patent dates on this tag.

- The model C Comptometer went on the market in 1909. This example was first used at a commercial bank in Westfield, Massachusetts. In about 1950, it was given to Harry Rapp, on of the bank directors, as a relic. He in turn gave it to Judith Lowell in about 1965. She put it to use in the office of her husband, the physician Milton Lowell of Potsdam, New York, even though the Lowells already had a more recent printing machine. Not long after Dr. Lowell retired in 1984, the couple gave the Comptometer to the Smithsonian.

- References:

- U.S. Patent #960528

- J. H. McCarthy,
*The American Digest of Business Machines*, Chicago: American Exchange Service, 1924, p. 548.

- Accession File.

- Location
- Currently not on view

- date made
- 1910

- maker
- Felt & Tarrant Manufacturing Company

- ID Number
- 1985.0120.01

- catalog number
- 1985.0120.01

- maker number
- 36372

- accession number
- 1985.0120

- Data Source
- National Museum of American History, Kenneth E. Behring Center