#
Calculating MachinesDirect Multiplication Calculating Machines

The first calculating machines multiplied by repeated addition. To multiple by tens, hundreds, or larger units, one shifted the carriage. From the 1870s, a few inventors proposed machines that could multiply directly – albeit by a single digit at a time. The Frenchman Léon Bollée exhibited such a machine at a world’s fair held in Paris in 1889. Not long thereafter the American George Grant and the Swiss inventor Otto Steiger invented direct multiplication machines. Steiger’s machine would sell successfully as the Millionaire in both Europe and the United States. In the 1830s, Swedish-born inventor Carl Friden introduced a calculating machine on which all of the digits of the multiplier could be entered at once. Automatic multiplication – and automatic division – came to be widely available on calculating machines in the 1950s.

"Calculating Machines - Direct Multiplication Calculating Machines" showing 43 items.

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## Barbour Calculating Machine Model

- Description
- In the late 19th century, several inventors turned their attention to designing better machines for doing arithmetic. This model calculating machine, patented by Edmund D. Barbour of Boston, was intended to multiply a number by a digit directly, rather than requiring repeated addition. Barbour submitted the model to the U.S. Patent Office, and received a patent for the invention on August 13, 1872.

- This machine consists of eight wooden cylinders that rotate on a crosswise shaft inside a wooden box. Each cylinder has around its edge 90 rows of cog-teeth. Each set of nine cog-teeth represents the multiples of a digit (zero multiples correspond to blank spaces). These cog-teeth have not actually been constructed. They are shown as pen marks on a slip of paper that extends around the first cylinder.

- The machine is set to a given multiplier by rotating all the cylinders with a knob at one end of the machine. This knob is missing. The first cylinder has on its left side a wooden spur gear with 90 teeth The other cylinders would have such gears, but they are uncut. Pulling out a wooden toothed rack below the gear advances it one-ninetieth of a revolution for each unit on the rack. Hence one can set a multiplicand.

- A movable carriage of brass on the top of the machine is supposed to be linked to the cylinders, so that when the carriage is pulled one unit to the right, the recording wheels advance in proportion to the figure represented on the edge of the cylinders. At present, the cylinders are not linked to the sliding carriage. Ther object has no maker’s marks. No successful product emerged directly from Barbour’s patents.

- Compare MA*309172, MA*309173, and MA*318168.

- The Edmund D. Barbour who took out this patent was probably Edmund Dana Barbour (1841–1925), a Boston native who reportedly gained a fortune in the China trade, before returning to Boston in 1871, not long before taking out this patent. Barbour went on to take out two further patents for calculating machines, to invest successfully in the Bell Telephone Company, to carry out extensive genealogical research, and to leave most of his fortune in bequests to Harvard University, the Massachusetts Institute of Technology and Radcliffe College.

- References:

- Edmund Barbour, "Improvement in Calculating-Machines," U.S. Patent 130404, August 13, 1872.

- J. A. V. Turck,
*Origin of Modern Calculating Machines*, Chicago: Western Society of Engineers, 1921, pp. 180–187.

- “Sharon’s Rich Men,”
*Boston Daily Globe*, February 20, 1888, p. 6.

- “Fund for Three Local Colleges: Edmund D Barbour’s Will Gives Each $20,000 a Year,”
*Boston Daily Globe*, March 13, 1925.

- J. Gardner Bartlett, “Edmund Dana Barbour,”
*The New England Historical and Genealogical Register*, vol. 79, October 1925, pp. 339–344.

- Location
- Currently not on view

- date made
- 1872

- patentee
- Barbour, Edmund D.

- maker
- Barbour, Edmund D.

- ID Number
- MA*309172

- accession number
- 89797

- catalog number
- 309172

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

## Verea Calculating Machine Model

- Description
- In 1878 Ramon Verea, a Spanish-born newspaper publisher in New York City, sent the U.S. Patent Office this model of a calculating machine he had invented. It was one of the first calculating machines that could multiply a number by a digit directly, rather than be repeated addition. The machine did not become a commercial product.

- The lever-set machine has flat brass sides and is open at the front, bottom and back to reveal the mechanism. At the front are two ten-sided brass prisms that are mounted vertically. Each of the sides of the each prism has two columns of holes, with ten holes in a column. The holes come in ten sizes, with the largest and deepest representing 0, and the smallest and shallowest, 9. The holes represent multiples of a given digit.

- Above the prisms are two knobs that move in slots in the flat top of the machine. Pulling forward a knob rotates the cylinder below, so that the side facing the back of the machine has holes representing multiples of the digit desired. Behind this mechanism is a row of tapered pins. Pulling a lever at the back of the machine raises or lowers these pins in order to set the multiplier. Turning a crank on the right side moves the pins up to the faces of the prisms and, where there are holes in the prism, allows the pins to enter to a certain depth.

- Once the surface of a prism touched a pin, it pushed the pin, and a rack behind the pin, backward. Pins entering shallow holes reach the prism quickly and have a correspondingly greater effect on the rack. Pinions linked to the racks rotate correspondingly, rotating the result wheels at the back of the machine, with carrying occurring as required. Further turning of the crank restores the prisms, racks, and pins to their original position.

- A mark on the top front of the machine reads: R. VEREA (/) NEW YORK.

- The model was displayed at the Museums of the Peaceful Arts in New York City. When that museum closed, it was given to the Smithsonian Institution by L. Leland Locke.

- References:

- R. Verea, “Improvement in Calculating Machines,” U.S. Patent 207918, September 10, 1878.

- L. Leland Locke, “The First Direct-Multiplication Machine,”
*Typewriter Topics*, November, 1926, pp. 16 and 18.

- P. Kidwell, “Ideology and Invention: The Calculating Machine of Ramon Verea,”
*Rittenhouse*, vol. 9, 1995, pp. 33–41.

- Location
- Currently not on view

- date made
- 1878

- date patented
- 1878

- patentee
- Verea, Ramon

- maker
- Verea, Ramon

- ID Number
- MA*311942

- catalog number
- 311942

- accession number
- 155183

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

## Bollée Calculating Machine

- Description
- Most early calculating machines carried out multiplication as a form of repeated addition. To multiply, say, by thirteen, one set the carriage at its rightmost position, turned the operating crank three times, shifted the carriage one position to the left, and turned the crank once. Ramon Verea of New York had patented a machine capable of direct multiplication in 1878, but it was never produced. In 1888, the young Frenchman Léon Bollée (1870–1913) of Le Mans constructed a calculating machine which embodied a multiplication table. He completed a better version of the machine in time to exhibit it at the Exposition Universelle, a World’s Fair held in Paris in 1889, and received a gold medal. This somewhat later version of the machine came to the Smithsonian from the collection of Felt & Tarrant Manufacturing Company.

- The large manually operated non-printing direct multiplication calculating machine has an iron base with a brass and steel mechanism and an open framework. A metal box carrying 12 setting levers moves along a bar near the front of machine. In front of it are a multiplier knob and brass disc with 20 teeth. The spaces between the teeth are labeled from 0 to 9 and from 0 to 9 again around the edge. Rotating the multiplier knob moves the metal box, placing it in one of the spaces between the teeth of the disc sets the digit of the multiplier.

- Moving one of the setting levers forward moves forward a multiplication body below it. Each multiplication body is has a rectangular base and rows of vertical pins which represent the multiples of digits from 1 to 9. The pins of the multiplication bodies control the motion of several sets of brass pins mounted vertically over them and linked to the result register. The operating crank with its wooden handle are on the left side. Rotating the crank lifts the box upward so that the multiplication bodies engage the pins.

- On the right side is a lever that may be set at either + or -. Toward the front is a set of 21 cylindrical dials, visible through windows. Each dial shows two digits at any one time. The top row of digits is labeled MULTN and used to show the multiplier in multiplication. The lower row of digits is labeled QUOTT and shows the quotient in division. Above this row of cylinders is a row of 21 dials which shows the result in multiplication and is set with thumbscrews with the divisor in division.

- A brass piece across the top of the machine reads: MACHINE À CALCULER de Léon BOLLÉE (/) AU MANS [FRANCE]. It also reads: EXPON UNIVLLE (/) PARIS. 1889. MÉDLLE D’OR. It also reads: BTEE S.G.D.G. EN FRANCE (/) ET À L’ÉTRANGER.

- A few years after Bollée introduced his machine, the Swiss inventor Otto Steiger patented a direct multiplication calculating machine that would sell widely as the Millionaire.

- References:

- Léon Bollée, “Calculating-Machine,” U.S. Patent 556720, March 17, 1896. This patent lists Bollée’s French, Belgian and British patent numbers in addition to describing the machine.

- Jean Marguin,
*Histoire des instruments et machines à calculer*, Paris: Hermann, 1994, pp. 130–136.

- Location
- Currently not on view

- date made
- ca 1892

- maker
- Bollée, Léon

- ID Number
- MA*323631

- catalog number
- 323631

- accession number
- 250163

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

## Grant Grasshopper Calculating Machine

- Description
- This is the form of calculating machine exhibited by George B. Grant at the Columbian Exposition held in Chicago in 1893. It is a lever-set non-printing manually operated connection pawl machine. The form is called Grant’s grasshopper model because of its appearance.

- The machine has an open iron frame painted black, with steel and brass parts and paper labels. Five sliding pins at the front of the machine are used to set numbers on racks beneath. Next to each pin is a thin strip of paper with the digits from 0 to 9 printed on it. The digits increase as one goes toward the back of the machine. Each strip also has complementary digits in smaller type, for use in subtraction and division. Moving back a pin drives back a toothed rack.

- Behind the racks is a movable carriage with 11 gears on it. A paper strip with digits on it is next to each gear. Turning a crank at the front right of the machine moves the racks back to engage the gears, turning each one of them in proportion to the number set. When the adding frame reaches the end of its backward movement, a cam set on the crank shaft at the front raises all the register gears a little so that the gears are disengaged from the racks and not moved in the return motion. One tooth on each gear extends so that when the gear has made a complete rotation, it engages one of the carry teeth arranged on a spiral shaft above the carriage. As the adding racks return to position, the shaft revolves and the carry tooth pushes the next gear up by one, resulting in a carry. The result appears o the paper strips between the gears on the carriage.

- Releasing the carriage and turning it one revolution zeros the result shaft.

- A slip of paper to the right of the number levers reads: GEORGE B. GRANT, (/) LEXINGTON, MASS. It also reads: 1.95. Y.

- This machine was given to the museum by George B. Grant’s half-brother, Edwin A. Bayley.

- Compare MA*310647 and MA*335633. MA*310647 has a metal plate at the back not found on MA*335633.

- Location
- Currently not on view

- date made
- ca 1893

- maker
- Grant, George B.

- ID Number
- MA*310647

- catalog number
- 310647

- accession number
- 118852

- maker number
- 1.95. Y

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

## Grant Experimental Model Calculating Machine

- Description
- This lever-set non-printing connection pawl calculating machine is the last experimental model of George B. Grant, designed to incorporate subtraction and division as well as addition and multiplication. It has a wooden base and a brass frame. Five pins slide to set numbers. Positions next to the pins are labeled from 0 to 9. Moving back a pin drives back a toothed rack.

- Behind the racks is a movable carriage with 11 gears on it. The carriage can be set at six different positions. When the racks are pushed back (there is no cam to drive the racks), the gears are engaged, and rotate in proportion to the number set. The gears move in the opposite direction when the racks are moved forward. Carry teeth are arranged in a spiral shaft above the carriage. A lever at the front of the machine may be rotated in a way that may affect the action of the carry shaft. A crank on the right zeros the result shaft.

- This model represents Grant’s enduring interest in the improvement of calculating devices. It did not lead directly to any commercial product.

- Location
- Currently not on view

- date made
- after 1895

- maker
- Grant, George B.

- ID Number
- MA*310650

- catalog number
- 310650

- accession number
- 118852

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

## Grant Grasshopper Calculating Machine

- Description
- This lever-set non-printing manually operated connection pawl calculating machine has an open iron frame painted black, with steel and brass parts and paper labels. Five pins at the front of the machine slide backward to set digits. Next to each pin is a thin strip of paper with the digits from 0 to 9 printed on it, the digits increasing toward the back of the machine. Each strip also has complementary digits in smaller type, for use in subtraction and division.

- Moving back a pin drives back a toothed rack. Behind the racks is a movable carriage with 11 gears on it. A paper strip with digits on it is next to each gear. Turning a crank at the front right of the machine moves the racks back to engage the gears, turning each one of them in proportion to the number set. When the adding frame reaches the end of its backward movement, a cam set on the crank shaft at the front raises all the register gears a little so that the gears are disengaged from the racks and not moved in the return motion The cam on this machine is smaller than on other Grant grasshopper machines, but like that on MA*311941.

- One tooth on each gear extends so that when the gear has made a complete rotation, it engages one of the carry teeth arranged on a spiral shaft above the carriage. As the adding racks return to position, the shaft revolves and the carry tooth pushes the next gear up by one, resulting in a carry. Releasing the carriage and turning it one revolution zeros the result shaft.

- A mark on a paper tag to the right of the rightmost pin reads: Grant Calculating Machine Co. (/) LEXINGTON, MASS., U.S.A. (/) MACHINE NUMBER 18M .

- This machine was given to the museum by George B. Grant’s half-brother, Edwin A. Bayley.

- References:

*Machinery*, October 1895.

- E. Martin,
*The Calculating Machines (Die Rechenmaschinen)*, trans. P. A. Kidwell and M. R. Williams, Cambridge: MIT Press, 1992, p. 77.

- U.S. Patent 605,288 (June 7, 1898).

- Location
- Currently not on view

- date made
- 1896

- maker
- Grant Calculating Machine Company

- ID Number
- MA*310648

- catalog number
- 310648

- accession number
- 118852

- maker number
- 18M

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

## Grant Grasshopper Calculating Machine

- Description
- This lever-set, non-printing manually operated connection pawl calculating machine has an open iron frame with steel and brass parts and paper labels. Five pins at the front of the machine slide back to set numbers. Next to each pin is a thin strip of paper that has the digits from 0 to 9 printed on it, the digits increasing toward the back of the machine. Each strip also has complementary digits in smaller type, for use in subtraction and division. Moving back a pin drives back a toothed rack.

- Behind the racks is a movable carriage with 11 gears on it. A paper strip with digits on it is next to each gear. Turning a crank at the front right of the machine moves the racks back so that they engage the gears, turning each one of them in proportion to the number set.

- This machine has a pin which can be set to prevent the crank from turning. When the adding frame reaches the end of its backward movement, a cam set on the crank shaft at the front raises all the register gears a little so that the gears are disengaged from the racks and not moved in the return motion.

- The cam on this machine is smaller than on other Grant grasshopper machines. One tooth on each gear extends so that when the gear has made a complete rotation, it engages one of the carry teeth arranged on a spiral shaft above the carriage. As the adding racks return to position, the shaft revolves and the carry tooth pushes the next gear up by one, resulting in a carry. Releasing the carriage and turning it one revolution zeros the result shaft.

- The carriage on this machine appears to be frozen in place. An aluminum support at the back causes the top to slope forward.

- A paper tag to the right of the pins for setting up numbers reads: Grant Calculating Machine Company (/) LEXINGTON, MASS., U.S.A. (/) MACHINE NUMBER 41 M.

- Compare MA*310647, MA*310648, MA*323615 and MA*335633.

- This machine is from the collection of L. Leland Locke.

- References:

*Machinery*, October, 1895.

- E. Martin,
*The Calculating Machines (Die Rechenmaschinen)*, trans. P. A. Kidwell and M. R. Williams, Cambridge: MIT Press, 1992, p. 77.

- G. B. Grant, "Calculating-Machine," U. S. Patent 605,288 (June 7, 1898).

- Location
- Currently not on view

- date made
- 1896

- maker
- Grant Calculating Machine Company

- ID Number
- MA*311941

- catalog number
- 311941

- accession number
- 155183

- maker number
- 41M

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

## Grant Grasshopper Calculating Machine

- Description
- This lever-set, non-printing manually operated connection pawl calculating machine has an open iron frame with steel and brass parts and paper labels. Five pins at the front of the machine slide to set numbers. Next to each pin is a thin strip of paper, or a slot for such a paper. One strip is missing and another, partly missing. Moving back a pin drives back a toothed rack.

- Behind the racks is a movable carriage with 11 gears on it. A paper strip with digits on it is next to each gear. Turning a crank at the front right of the machine moves the racks back to engage the gears, turning each one of them in proportion to the number set. When the adding frame reaches the end of its backward movement, a cam set on the crank shaft at the front raises all the register gears a little so that the gears are disengaged from the racks and not moved in the return motion.

- One tooth on each gear extends so that when the gear has made a complete rotation, it engages one of the carry teeth arranged on a spiral shaft above the carriage. As the adding racks return to position, the shaft revolves and the carry tooth pushes the next gear up by one, resulting in a carry. Releasing the carriage and turning it one revolution zeros the result shaft.

- This machine is from the collection of Felt & Tarrant Manufacturing Company. A paper tag attached to the object reads: 31. Another one reads in ink: Grant (/) Multiplier.

- Compare MA*310647, MA*311941, and MA*335633.

- References:

*Machinery*, October, 1895.

- E. Martin,
*The Calculating Machines (Die Rechenmaschinen)*, trans. P.A. Kidwell and M.R. Williams, Cambridge: MIT Press, 1992, p. 77.

- G. B. Grant, "Calculating-Machine," U.S. Patent 605,288, June 7, 1898.

- Location
- Currently not on view

- date made
- 1896

- maker
- Grant Calculating Machine Company

- ID Number
- MA*323615

- catalog number
- 323615

- accession number
- 250163

- maker number
- 0853

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

## Grant Grasshopper Calculating Machine

- Description
- This commercially sold example of George B. Grant’s grasshopper calculating machine at one time belonged to tabulating machine inventor Herman Hollerith Jr. of Washington, D.C.

- The lever-set manually operated non-printing connection pawl machine has an open iron frame painted black, with steel and brass parts and paper labels. Five pins at the front of the machine slide horizontally to set numbers. Next to each pin is a thin strip of paper with the digits from 0 to 9 printed on it, the digits increasing toward the back of the machine. Each strip also has complementary digits in smaller type, for use in subtraction and division. Moving a pin back drives back a toothed rack.

- Behind the racks is a movable carriage that slides to six different positions and has 11 gears on it. A paper strip with digits on it is next to each gear. Turning a crank at the front right of the machine moves the racks back to engage the gears, turning each one of them in proportion to the number set. When the adding frame reaches the end of its backward movement, a cam set on the crank shaft at the front raises all the register gears a little so that the gears are disengaged from the racks and not moved in the return motion.

- One tooth on each gear extends so that when the gear has made a complete rotation, it engages one of the carry teeth arranged on a spiral shaft above the carriage. As the adding racks return to position, the shaft revolves and the carry tooth pushes the next gear up by one, resulting in a carry. Releasing the carriage and turning it one revolution zeros the result shaft.

- A paper tag to the right of the pins reads: GRANT CALCULATING MACHINE COMPANY [/] BOSTON, PHILADELPHIA, CLEVELAND. Two windows at the front of the machine read: C B.

- Compare MA*310647 and MA*335633 (MA*310647 has a metal plate at the back not found on MA*335633).

- References:

- “Grant’s Calculating Machine,”
*The Manufacturer and Builder*, vol. 26 #9 (September 1894): pp. 195–96.

- G. B. Grant, "The Calculating Machine,"
*Machinery*, 2 #2, October, 1895, pp. 50–51.

- G. B. Grant, "Calculating-Machine," U.S. Patent 605,288, June 7, 1898.

- Location
- Currently not on view

- date made
- 1896

- maker
- Grant Calculating Machine Company

- ID Number
- MA*335633

- catalog number
- 335633

- accession number
- 1977.0114

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

## Grant Experimental Model Calculating Machine

- Description
- George B. Grant’s so-called grasshopper calculating machines sold in only modest numbers. However, he remained intrigued by the prospect of improving calculation, and continued to design prototype machines. This is the experimental model for a reversing machine designed to subtract and divide as well as to add and multiply.

- As in Grant's earlier invention, this connection pawl non-printing manually operated machine has an open iron frame with steel and brass parts and paper labels. Five pins at the front of the machine slide to set numbers. Next to two pins is a thin strip of paper with the digits from 0 to 9 printed on it, the digits increasing toward the back of the machine. Moving back a pin not only drives back one toothed rack but has the reverse affect on a rack adjacent to it, bringing it forward. There also is a second rack with a single tooth at the far right.

- Behind the racks is a movable carriage with one group of 11 gears and another group of six gears on it. A paper strip with digits on it is next to each gear. The spiral shaft above the carriage is for carrying. The carriage is not fixed in the frame and does not engage the racks as presently arranged. It appears that the larger set of racks is intended to drive the 11 gears to form results, while the smaller set of gears is driven by the single rack and serves as a revolution counter.

- A crank on the right zeros the result shaft.

- The model was given to the Smithsonian by Grant’s half-brother, Edwin A. Bayley.

- Reference:

- Accession file.

- Location
- Currently not on view

- date made
- ca 1897

- maker
- Grant, George B.

- ID Number
- MA*310649

- catalog number
- 310649

- accession number
- 118852

- maker number
- none

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