#
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 514 items.

Page 1 of 52

## Friden Model SBT 10 Calculating Machine

- Description
- This modification of Friden’s fully automatic STW calculating machine allows for “back transfer.” That is to say, it has a mechanism to transfer figures from the accumulator register to the keyboard selecting levers and vice versa. The model was manufactured from 1959 until 1965.

- The full-keyboard electric non-printing stepped drum machine has a metal frame painted tan and ten columns of brown and white plastic keys, with a blank white key at the bottom of each column. Metal rods between the columns of keys and under the keyboard turn to indicate decimal points. On the right are two columns of function bars. On the left is a nine-digit register that indicates numbers entered for multiplication. Below it is a block of nine white digit keys, with a 0 bar below. These are surrounded by further levers and function keys, including a split “NEG POS TRANSFER” bar.

- Behind the entry keys is a movable carriage with an 11-digit register and a 20-digit result register. The result register has plastic buttons above it that can be used to set up numbers. Nine entry buttons and a clear button are under the revolution register. Zeroing knobs for the registers are on the right of the carriage. A clear carriage bar is toward the front of the keyboard. All three registers have sliding decimal markers. The machine has four hard rubber feet as well as a rubber cord and a tan plastic cover.

- A mark on the bottom reads: MODEL SERIAL (/) SBT 10 907698. A mark on the back and side reads: Friden. A sticker on the bottom reads: FRIDEN, INC. (/) SAN LEONARDO, CALIFORNIA, USA. A mark on the cover reads: Friden (/) AUTOMATIC CALCULATOR.

- For related documents, see 1984.0475.02, 1984.0475.03, 1984.0475.07, and non-accession 1984.3079.

- This is one of five Friden calculating machines given to the Smithsonian by Vincent L. Corrado (1917-1984), a native of Covington, Kentucky, who earned bachelor’s and master’s degrees in accounting at Catholic University, served in the U.S. Army from 1942 through 1973, and then joined the Veteran’s Administration for the rest of his life.

- The date given is based on the serial number, courtesy of Carl Holm. This is the date of manufacture.

- Reference:

- Ernie Jorgenson,
*Friden Age List*, Office Machine Americana, p. 5 gives the date 1960 for this machine.

- Location
- Currently not on view

- date made
- 1964

- maker
- Friden, Inc.

- ID Number
- 1983.0475.01

- catalog number
- 1983.0475.01

- accession number
- 1983.0475

- maker number
- SBT 10 907698

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

## Hart's Mercantile Computing Machine

- Description
- The instrument consists of three concentric brass discs, a brass marker, a steel stop, and a wooden handle (instrument must be removed from box to find handle). Each brass disc has the numbers from 0 to 99 stamped around the edge. The two inner discs both have a circle of 100 holes just outside the numbers. The inner holes are used to add the last two digits of a number by rotation. Any hundreds value in the sum carries to the second set of holes, which are used to add hundreds and thousands places.

- The machine is in a cylindrical wooden case with cover.

- According to the Kirksville Missouri Democrat for July 26, 1888, by then Hart had sold 3500 of these devices and “he lately ordered one thousand more.”

- References: U.S. Patent #199289

- P. Kidwell, "Adders Made and Used in the United States,"
*Rittenhouse*, 1994, 8:78-96.

*Kirksville Missouri Democrat*, July 26, 1888.

- Location
- Currently not on view

- date made
- 1878

- patentee
- Hart, William

- maker
- Scovill Manufacturing Company

- ID Number
- 1993.0510.01

- accession number
- 1993.0510

- catalog number
- 1993.0510.01

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

## Comptometer, Macaroni Box Model

- Description
- This is the prototype for the Comptometer, a key-driven adding machine invented by Dorr E. Felt of Chicago. It is a scarred wooden box (originally used to transport macaroni) that contains the levers and wheels for a 5-column adding machine with one partial column of keys (wooden skewers), four of which are missing. The number dials are at the front. Two screws are on the top of the back panel. A series of rubber bands, used to set the levers to accept the next keystroke, are missing.

- Compare to replica, which has catalog number MA*323646.

- Reference:

- J. A. V. Turck,
*Origin of Modern Calculating Machines*, Chicago: Western Society of Engineers, 1921, pp. 52-56.

- date made
- 1884-1885

- maker
- Felt, Dorr E.

- ID Number
- MA*311192

- catalog number
- 311192

- accession number
- 143207

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

## Ken + Add Adding Machine

- Description
- This four-wheeled stylus-operated adding machine has two copper-colored wheels for cents and two silver-colored wheels for dollars. There are numbers on the cover around each wheel. No complementary digits are indicated. Above the wheels are four windows that indicate the total. At the back is a plastic container for the metal stylus. Inside the lid of the case is a so-called magic slate for jotting down and erasing numbers. The adding machine, stylus, and slate fit in an aluminum case. The instrument is marked: Ken + Add MACHINES CO. DULUTH, MINN. U.S.A. PATENT APPLIED FOR.

- An account of the Ken + Add appeared in
*Mathematics Teacher*in December 1952, where it was recommended not only as a practical adding machine but as a fascinating toy and an aid to arithmetic teaching. It was advertised in*Arithmetic Teacher*as late as 1956.

- Reference:

- P. A. Kidwell, A. Ackerberg-Hastings, and D. L. Roberts,
*Tools of American Mathematics Teaching 1800-2000*, Baltimore: Johns Hopkins University Press, 2008, pp. 248-249.

- Location
- Currently not on view

- date made
- 1950s

- maker
- Ken + Add Machines Co.

- ID Number
- 2005.0278.01

- catalog number
- 2005.0278.01

- accession number
- 2005.0278

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

## Patent Model for an Adder with Carry Invented by George Farmer

- Description
- This patent model for an adder has three concentric, linked discs that revolve on a central pivot. The bottom disc is numbered from 1 to 99 clockwise around its toothed edge, to represent hundreds and thousands. Above it is a smaller disc, also with teeth around the edge, numbered from 00 to 99 clockwise to represent units and tens. A window in the third, top, largest disc shows the result on the dials below. The largest disc is numbered from 1 to 100 around the edge. Atop this disc is a rotating arm. Moving the arm counterclockwise advances the inner disc proportionally, allowing one to enter numbers up to 99.

- A lever extends from the side of the disc and bends over the top. If the arm rotates around a full 100 units, it pushes this lever, causing a carry. The lever also may be used to zero the hundreds and thousands digits. See U.S. patent 69,647 for “Improvement in Tallying Instrument.” According to the patent, the invention “relates to a new and improved method of registering or tallying the quantity of lumber measured, or keeping account of sums of money paid out or received . . .”

- There was a George Farmer (born about 1831 in England, died 1880 in Saginaw, Michigan) who worked as a miller and shingle maker in Illinois and in Michigan. He is listed in the 1860 U.S. Census as living in Elmira in Stark County, Illinois, working as a miller. That same year he received a patent on August 21for an improvement in harvesters (#29685). By 1870, he was living in Saginaw, Michigan, still working as a miller. In the 1880 Census he is listed as a shingle manufacturer. He and his son, Albion, ran a shingle-making business in Saginaw under the name of George Farmer & Son. It is listed in the 1878 city directory for the town. The George Farmer who received the patent for this adder was a resident of Flint, which is near Saginaw.

- Reference: George Farmer, “Improvement in Tallying Instrument,” U.S. Patent 69,647, granted October 8, 1867.

- Location
- Currently not on view

- date made
- 1867

- patentee
- Farmer, George

- maker
- Farmer, George

- ID Number
- MA*252692

- accession number
- 49064

- catalog number
- 252692

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

## Model for the "Devil's Coffin" Diagram Relating to Computing the Volume of a Parallelepiped, Ross Solid

- Description
- This wooden model is one in a series illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The incomplete unpainted wooden model has two pieces. One is a cube, the second is part of a parallelepiped with one square face the same size as the cube. A paper label pasted to a square side of both pieces of the model reads: DEVIL’S COFFIN (/) Phillips & Fisher, p. 305 Van Velzer & Shutts, p. 300 (/) Wentworth, p. 303 Wells, p. 278. This is a reference to four American geometry textbooks published between 1894 and 1899.

- In the course of the 19th century, American geometry textbooks came to be more than reproductions of British works. By the 1890s, several texts discussing solid geometry used a figure demonstrating the volume of a parallelepiped that apparently arose in the United States.

- In this construction, the volume of an arbitrary parallelepiped is first compared to one constructed having the same altitude and rectangular bases equal in area to those of the original solid. This figure is then compared to a third parallelepiped, this with the same altitude and six rectangular sides. John Farrar, following A.-M. Legendre, proposed such a construction in his
*Elements of Geometry*. By the 1890s, the figure had taken a rather different form. Perhaps because it was difficult imagine from a two dimensional drawing, it was known as “the devil’s coffin.”

- Ross’s model of the construction had three parts, a parallelepiped with six sides in the shape of equilateral parallelograms, a parallelepiped with two square sides and four rhombic sides, and a cube. The parallelepipeds are dissected. The two models in the Smithsonian collections are the cube and one piece of one of the parallelepipeds.

- This model is not mentioned in Ross’s original manual for his surface forms and solids. The texts referred were published several times, but show the devil’s coffin construction on the pages indicated on the model on editions published between 1894 and 1899. Hence the date of about 1900 assigned to the model.

- References:

- A.-M. Legendre,
*Éléments de géométrie, avec des notes*, Paris: Didot, 1794, pp. 178–184, Plate 8.

- John Farrar,
*Elements of geometry, by A. M. Legrendre. Translated from the French for the use of the students at the University at Cambridge, New England*, Boston : Hilliard and Metcalf printers, 1819, pp. 134–139, plates IX and X.

- Thomas Heath, ed.,
*The Thirteen Books of Euclid’s Elements*, vol. 3, Book XI, propositions 29 and 30, especially the commentary on Proposition 30, New York: Dover, 1956, esp. pp. 333–336.

- Andrew Wheeler Phillips and Irving Fisher,
*Elements of Geometry*New York: American Book Company, 1896, p. 305–306.

- C. A. Van Velzer and George C. Shutts,
*Plane and Solid Geometry Suggestive Method*Madison, WI: Tracy Gibbs, 1894, p. 300.

- Webster Wells,
*The Elements of Geometry*, rev. ed., Boston: Leach, Shewell and Sanborn, 1894, p. 278.

- George A. Wentworth,
*Plane and Solid Geometry*, rev. ed., Boston: Ginn, 1899, p. 303.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Ross, W. W.

- ID Number
- 1985.0112.217

- catalog number
- 1985.0112.217

- accession number
- 1985.0112

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

## Underwood Sundstrand 8120P Adding Machine

- Description
- This ten-key printing electric adding machine has a gray metal case with ten white plastic number keys arranged in a block. Left of the number keys are CORRECTION, B’K (/) SPACE, and REPEAT keys. Right of the number keys are SUB- (/) TRACT, ADD and N.ADD (/) TOTAL keys. Above the keyboard is a place indicator for up to eight places, which moves from left to right as up to eight digits are entered. The 2-3/8” (6 cm.) paper tape is in the back, A black ribbon is underneath a metal plate held down by thumbscrews. The machine prints up to eight digits, and the rightmost type bar prints symbols. One lever on the top right releases the position of the carriage and the second releases tension on the platen. The motor is on the left.

- Gustav David Sundstrand, the son of Swedish immigrants to the United States and a resident of Rockford, Illinois, applied for a patent for an adding machine in 1912, and was granted it in 1920 (U.S. Patent 1,329,028). He applied for a second patent in 1914, which was granted in 1916 (U.S. Patent 1,198,487). The Sundstrand originally was produced by the Rockford Milling Machine Company - by 1920 it was a product of Sundstrand Corporation, a closely related firm. Oscar Sundstrand, a brother of Gustav David, took over primary responsibility in improvements in the adding machine. During the 1920s, several business machine companies consolidated. The Elliott-Fisher Company acquired rights to the Sundstrand adding machine in 1926, and soon merged with the Underwood Typewriter Company. Hence the adding machine was renamed the Underwood Sundstrand.

- This example is from considerably later in the history of the machine. The “8” in the model number indicates that the machine has a capacity of listing eight-digit totals, while the “P” signifies a portable electric machine with “Multiflex” control, allowing more rapid repeat addition and subtraction. According to the accession file, the donor acquired this machine secondhand in about 1953.

- References:

*American Office Machines Research Service*, III.

- Fédération Nationale des Chambres Syndicales de la Mécanographie,
*Fédération de Reprise officielle des Machines à Ecrire, Machines à Calculer . . .*, Lyon, 1970, p. 86.

- Underwood Sundstrand, “Underwood Sundstrand presents the right machine with the right keyboard . . . The only complete line of ten key adding machines,” [no date], 1990.3188.07.

- Location
- Currently not on view

- date made
- 1940

- maker
- Underwood Elliot Fisher Company

- ID Number
- 1985.0655.01

- maker number
- 336139

- accession number
- 1985.0655

- catalog number
- 1985.0655.01

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

## Reuter's Calculating Machine

- Description
- This manually operated, non-printing calculating machine has a brass top painted black that fits closely into a roll-top wooden case, sloping toward the operator. Eight German silver levers on the machine rotate counterclockwise to set a digit. The number entered appears in a row of windows over the levers. Above this row is a steel rod with one sliding decimal marker.

- The handle for operating the machine is right of the levers. The zeroing lever for the entry, as well as the addition & multiplication / subtraction & division lever, are left of the eight German silver levers. Left of this is a compartment with room for an inkwell and loose pieces. The cover of this compartment is missing and it is empty.

- Behind the levers is a carriage with nine revolution register windows and 16 result register windows. Both registers have thumbscrews for setting numbers and sliding decimal markers. There is no carry in the revolution register. Two levers on the right side of the carriage zero its registers.

- When the entry in the result register would become negative (as in subtraction or division), a bell rings. It rings again if a number is added to bring the total to zero or more.

- The brass stepped drums are visible through a sliding panel in the bottom of the case. Metal lifting handles are on both ends of the case.

- The machine is marked above the entry windows: REUTER’S (/) MULTIPLYING AND DIVIDING MACHINE (/) PHILADELPHIA,PA. Metal tags toward the front of the machine read: D.R.G.M. 394014 and: AUSL. PAT. ANGEM. A mark under the operating crank reads: D.R.G.M. (/) 329403. A mark to the left of the entry levers reads: PATENT (/) DEUTSCHLAND No. 217048 (/) OSTERREICH ANGEM. The serial number, inscribed under the carriage on the machine at the right, is 1363.

- This is an example of the Saxonia calculating machine made by Schumann and Company in the German city of Glasshütte, and imported and distributed by the Philadelphia firm of Carl H. Reuter. Reuter advertised as an importer of the Brunsviga and Burkhardt calculating machines in 1906. A machine with a later serial number is from 1913.

- This machine was used at the Sproul Observatory of Swarthmore College.

- Compare MA*323596.

- References:

- E. Martin,
*The Calculating Machines (die Rechenmaschinen)*, trans. P. A. Kidwell and M. R. Williams, Cambridge: MIT Press, 1992, pp. 126–127.

*Railway Age*, 42, August 17, 1906, p. 219.

- Location
- Currently not on view

- date made
- ca 1910

- distributor
- Carl H. Reuter

- maker
- Schumann & Cie.

- ID Number
- 1986.0684.01

- catalog number
- 1986.0684.01

- accession number
- 1986.0684

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

## Model of a Riemann Surface by Richard P. Baker, Baker #411z

- Description
- This geometric model was constructed by Richard P. Baker in about 1930 when he was Associate Professor of Mathematics at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over 100 of his models are in the museum collections.

- The mark 411 is carved into one edge of the wooden base of this model and the typed part of a paper label on the base reads: No. 411z (/) Riemann surface : w
^{3}= z. Model 411z is listed on page 17 of Baker’s 1931 catalogue of models as “w^{3}= z” under the heading*Riemann Surfaces*. The catalog description also notes that “411 is to serve as a first step to 412,” where Baker model 412z (MA*211157.075) is associated with a more complicated equation involving w^{3}.

- The model represents a Riemann surface consisting of pairs of complex numbers, (z,w), for which w
^{3}= z where a complex number is of the form x + yi for x and y real numbers and i the square root of –1. A complex plane is like the usual real Cartesian plane but with the horizontal axis representing the real part of the number and the vertical axis representing the imaginary part of the number. Riemann surfaces are named after the 19th-century German mathematician Bernhard Riemann.

- Baker explains in his catalog that the z after the number of the model indicates that the metal disks above the wooden base represent copies of a disk in the complex z-plane. These disks are called the sheets of the model. The painted disk on the wooden base of the model represents a disk in the complex w-plane with the point w = 0 at its center. The disk is divided into twelve sectors, pie-piece-shaped parts of a circle centered at 0, each of which has an angle of 30 degree. The front of the model is the edge on which 411 is inscribed so the two vertical rectangles lie above the polar axis, i.e. the ray emanating from the origin when the angle is 0 degrees, of the wooden base. This places every horizontal edge of the rectangles on a polar axis of a sheet.

- If z = 0, the equation w
^{3}= z is satisfied by only one value of w, i.e., w = 0. The point z = 0 is called a branch point of the model and for all other points on the z-plane the equation w^{3}= z is satisfied by three distinct values of w, each of which produces a different pair on the Riemann surface (if z = 1, the three distinct pairs on the Riemann surface are (1,1), and (1,(–1 ± √3 i)/2)). Thus there are three sheets representing the same disc in the z-plane and together they represent part of what is called a branched cover of the complex z-plane.

- Baker’s use of solid red circles, and dashed red and black circles indicates that each sheet is mapped continuously onto a different portion of the w-disk on the base. There are three radii of the disk on the base (the polar lines - rays emanating from the origin – for angles of 0, 120, and 240 degrees) that are the edges of sectors corresponding to quadrants on two different sheets. The order of the colors of the 30 degree sectors on the base starting at polar axis and proceeding counterclockwise correspond to the colors of the first through fourth quadrants of the top, middle, and then bottom sheets.

- The vertical rectangles mentioned above are not part of the Riemann surface but call attention to what are called branch cuts of the model, i.e., curves on a sheet that produce the movement to another sheet. This movement occurs when meeting a branch cut while following a path of the inputs of z values into the equation. While the defining equation determines branch points, branch cuts are not fixed by the equation. However, the single branch cut for any surface with only one branch point must run from that point out to infinity. The branch cut of this model is represented on each sheet by the horizontal edges of the vertical surface or surfaces meeting that sheet.

- Location
- Currently not on view

- maker
- Baker, Richard P.

- ID Number
- MA*211257.074

- accession number
- 211257

- catalog number
- 211257.074

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

## Baldwin Calculating Engine

- Description
- This is one of few surviving examples of a production model of the pinwheel calculating machine patented by Frank S. Baldwin of St. Louis in 1875. On a pinwheel calculating machine, digits are represented by retractable pins. Setting the machine consists of moving levers that release an appropriate number of pins, which are engaged when the crank rotates. Baldwin’s pinwheel mechanism was not widely adopted in the United States, although the pinwheel machine proposed slightly later by the Swede W. T. Odhner was most influential.

- This non-printing machine has a brass base with two brass pieces on the side that serve as a frame. The brass has a dappled finish. A brass cylinder is mounted horizontally toward the back on a shaft that joins the pieces of the frame. The cylinder is 7 cm. (4-3/4”) in radius and 7 cm. in length. It has six round holes on each end. The cylinder may be moved along the shaft by releasing a catch on the left side and rotating the large crank on the left. Rotating this crank also drives the machine.

- The surface of the cylinder has eight oval openings that reveal a set of number wheels, and two rows of four metal buttons. A brass screw is on the left end. By depressing a button and turning the screw, one changes the digit showing in one hole and the number of pins protruding from the other side of the cylinder.

- In this way, one can enter up to eight-digit numbers. When the cylinder is turned, the pins act on a set of intermediate wheels that move both smaller, upper wheels toward the front to show a result as large as 17 digits, and lower wheels that indicate the multiplier, up to eight digits. Beneath each of these rows is a slide to indicate decimal divisions. A lever at the left front of the machine lifts a set of small rubber wheels, making it possible to zero the result wheels using a small crank on the right.

- The machine has no maker’s mark.

- Compare to the patent model, MA*252698.

- Baldwin made ten of these machines, including the patent model. This example was owned by Joseph S. McCoy, actuary of the U. S. Treasury from 1889 until his death in 1931. McCoy and his predecessor, Ezekial Brown Elliott, were most open to inventions in adding machines.

- Reference:

- Accession file.

- References:

- F. S. Baldwin, "Improvement in Calculating-Machines," U.S. Patent 159244, February 2, 1875.

- “Baldwin’s Arithmometer,” Philadelphia, Reliance Machine Works, about 1875. This brochure indicates that Baldwin’s calculating engine sold for between $150 and $250.

- Katsunori Kadokura, “Wann baute ”Odhner” seine erste Maschine, 1874 oder 1876?,” #29,
*Historische Bürowelt*, 1990, pp. 7–8.

- P. A. Kidwell, “The Adding Machine Fraternity at St. Louis: Creating a Center of Invention, 1880–1920,”
*IEEE Annals of the History of Computing*, 22 #2 (April-June 2000), pp. 4–21.

- L. Leland Locke, “The History of Modern Calculating Machines, an American Contribution,”
*American Mathematical Monthly*, 31 #9 (Nov 1924), pp. 422–429.

- Accession file.

- Location
- Currently not on view

- date made
- 1875

- maker
- Baldwin, Frank S.

- ID Number
- MA*310229

- catalog number
- 310229

- accession number
- 113246

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