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Mathematical Charts and TablesTables for General Reckoning

**Tables for General Reckoning**

Multiplication tables were among those most frequently produced for general use. Some people apparently just cut tables out of books for their particular purposes. In 1857, James D. Smith of Brantingham, New York, patented a “machine for multiplying numbers” that consisted of a wooden disc engraved with tables and a rotating stylus. At the turn of the century, a patented paper instrument of this type actually sold. At about the same time, Stanislas Szenhak of Warsaw (now in Poland) took out a U.S. patent for an especially designed multiplication table that could be fit around the eraser end of a pencil, with a metal cover that made it easier to find results. Such a pencil multiplier actually was manufactured in Illinois.

Some of these tables could by quite elaborate. In the 1870s, British accountant John Sawyer devised a set of bound tables with slips that could be turned to set up problems of interest. His procedures replaced multiplication and division by addition and subtraction. Most of those doing extensive multiplications and divisions at the time preferred to add and subtract logarithms of numbers, but Sawyer’s process allowed one to get results exactly. In the 1930s the American mathematician John Perry Ballantine proposed replacing slide rules with a set of tables in which the results of multiplication, division, and taking square roots could be read off directly, rather than requiring an awareness of significant figures.

"Mathematical Charts and Tables - Tables for General Reckoning" showing 2 items.

## Mathematical Table, Young Rule For Calculating Interest

- Description
- This United States patent model has a rectangular wooden frame with five grooves, each of which holds a bar (made from a different kind of wood) that slides crosswise. Two flat wooden pieces cover much of the bars on the left side, with a gap between them. Each bar has a set of 12 evenly spaced holes that are numbered from 11 down to 1 (the “0” holes are not numbered). Each bar also is indented at the top to hold a slip of paper that slides under the top of the machine. There are 11 further, unnumbered, holes to the right of each slip of paper. Setting up a number on the rods (to represent an amount of money or a length of time) reveals a number on the paper slips that represents an amount of tax or interest.

- A piece of paper glued to the top of the device reads: S.S. Young’s Tax and (/) Interest Rule (/) Red March 18th 1851. The “d” in this mark is a superscript.

- Samuel S.Young of Eaton, Ohio, took out three patents for computing devices. This is the patent model for the second, a rule for calculating interest, patented September 2, 1851 (U.S. Patent 8323). The first was an add to addition or adder, patented July 24, 1849 (U.S. Patent 6602), the third an arithmetical proof rule, patented October 26, 1858 (U.S. Patent 21921). The U.S. Census for 1850 lists an S. S. Young of Eaton, Ohio, who was forty years old that year and living with his wife and two children. His occupation is given as “gardener.” Apparently by 1860 he had moved to the nearby town of Washington and is listed as being a “horticulturalist” by profession. Young assigned his patent to John R. Stephen of Eaton, who is listed in the 1860 Census as a farmer.

- Compare to the model for the first of his inventions, MA*252680.

- References:

- S. S. Young, “Rules for Calculating Interest,” U.S. Patent 8329, September, 1851.

- U. S. Census Records

- Robert Otnes, “Sliding Bar Calculators,”
*ETCetera*, #11, June, 1990, p. 6.

- P. A. Kidwell, “Adders Made and Used in the United States,”
*Rittenhouse*, May, 1994, p. 80.

- Location
- Currently not on view

- date made
- 1851

- patentee
- Young, Samuel S.

- maker
- Young, Samuel S.

- ID Number
- MA*252683

- catalog number
- 252683

- accession number
- 49064

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

## Mathematical Table, J. D. Smith Machine For Multiplying Numbers

- Description
- This is the United States patent model for a multiplication table. It consists of a wooden disc pivoted to a wooden handle on which it revolves. The front of the part of the handle above the disc is a metal rod with the numbers 1/4, 1/2, 3/4, 1 through 10, and 20 engraved on it. The top of the disc has numbers engraved over its surface such that one can line up the handle with a number on the edge of the disc and find multiples of that number on the disc next to the engraved numbers on the handle.

- A mark painted on the back of the handle and written on the back of the disc reads: J.D. SMITH.

- This invention was patented in 1857 by James D. Smith (1834-1908), a native of Chatham, New York, who had moved to Brantingham in that state in 1841. He worked there in various businesses. In addition to this patent, Smith took out patents for an improvement in tool sharpeners (#87,212, February 12, 1869) and an improvement in station-indicators (#161170, March 23, 1875). No evidence has been found indicating that any of these inventions led to products.

- In 1881, Smith moved to Albany to study law. He spent the rest of his career as an attorney.

- References:

- James D. Smith, “Machine for Multiplying Numbers,” U. S. Patent 18711, November 24, 1857.

- “James D. Smith,”
*The Journal and Republican*, Lowville, New York, June 4, 1908, p. 1.

- Location
- Currently not on view

- date made
- 1857

- patentee
- Smith, James D.

- maker
- Smith, James D.

- ID Number
- MA*252687

- catalog number
- 252687

- accession number
- 49064

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