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 1 items.
- 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.
- 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.
- Currently not on view
- date made
- Smith, James D.
- Smith, James D.
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- Data Source
- National Museum of American History, Kenneth E. Behring Center