#
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.

## Pencil-Multiplier, a Multiplication Table

- Description
- Inventors have arranged multiplication tables on cylinders and on discs to ease use. This set of tables is designed to fit over the end of a pencil.

- Near the top of this red pencil, just below the eraser, is a table of multiples of the numbers from 13 to 24 by the numbers 1 through 12. A metal cap numbered from 13 to 24 fits over the table at the top. A rotating metal cylinder fits into the cap, and is numbered 1 to 12 around the top. There is a small window in the cylinder below each of these numbers; the distance of the hole from the top varies with the size of the number. The “1” hole reveals multiples of 1 in the table, the “2” hole multiples of 2, etc. To find, say, 15 times 9, one sets the 9 column of the cylinder under the 15 of the cap and reads off 135.

- A mark on the rotating cylinder reads: CHICAGO RECORDING SCALE CO. (/) WAUKEGAN. ILL. (/) PAT. PENDING. A mark on the pencil reads: U.S.A. SOUTHERN CROSS - No 2502.

- The Chicago Recording Scale Company was in business in Waukegan, Illinois, from at least 1895 until at least 1910. I have seen no patent assigned to the company that corresponds to this object. The drawings for U.S. patent 613,432 for an improvement in pencil-boxes show something somewhat similar to this device, although the numbers included and the arrangement of windows is different. That patent was taken out by Stanislas Szenhak of “Warshaw, Russia,” and assigned to Julius Witkowski of Yokohama, Japan. Szenhak applied for a patent on August 19, 1898, and received it November 1, 1898. He also obtained a patent in Great Britain, where his invention was called a “toy for teaching arithmetic.”

- This example of the device was given to the Museum by John William Christopher Draper and James Christopher Draper. Several objects in this gift were once the property of the New York meteorologist Daniel Draper, who took an active interest in the improvement of calculating instruments.

- References:

- Stanislas Szenhak, “Pencil-box,” U.S. Patent 613432, November 1, 1898.

- P. A. Kidwell, “American scientists and calculating machines: from novelty to commonplace,”
*Annals of the History of Computing*, 12, 1990, pp. 31–40.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Chicago Recording Scale Company

- ID Number
- MA*335350

- catalog number
- 335350

- accession number
- 304826

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