#
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.

## Patenta Multiplication Table

- Description
- This simple German table was intended as an aid to multiplication and division. Each side of the blue and white paper disc has a blue and white paper arm pivoted from the center. The disc has a diameter of 15 cm.; with the arm, the width is 15.6 cm.

- Going in from the circumference, each arm has printed on it the numbers from 1 to 20 in a column. On each side of the disc there are 19 radial columns. On one side these are numbered from 2 to 20; on the other from 21 to 39. The “2” column contains multiples of 2, the “3” column multiples of 3, etc. To find, say, the product of 35 and 19, one lines up the arm next to the 35 column on the disc. Next to 19 on the arm is 665 (the desired product) on the disc.

- The instrument is marked on both sides: PATENTA. It is also marked on both sides: D.R.G.M. (/) 145,796. The initials D.R.G.M. stand for Deutsches Reichgebrauchmuster, a temporary form of German intellectual property protection (not a full patent). D.R.G.M. numbers were first issued in 1891 and continued to be used through World War II. This number was issued in about 1901. A second form of the instrument, with more numbers, was issued later.

- The object is described briefly in a column in the
*Zeitschrift für Mathematischen und Naturwissenschaftlichen Unterricht*in 1903. This example was found in the collections of the National Museum of American History’s Division of Transportation around 1980.

- References:

- “Besprechung von Lehrmitteln, Mathematik”
*Zeitschrift für Mathematischen und Naturwissenschaftlichen Unterricht*34, 1903, p. 67.

- D. von Jezierski, trans. R. Shepherd,
*Slide Rules: A Journey through Three centuries*, Mendham, N.J.: Astragal Press, 2000, p. 102. This reference indicates that D.R.G.M. registered design 148526 was issued in 1901 and 173095 in 1902.

- Location
- Currently not on view

- date made
- ca 1901

- ID Number
- 1988.0579.01

- catalog number
- 1988.0579.01

- accession number
- 1988.0579

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