#
Mathematical Charts and TablesSpecial Purpose Tables

**Special Purpose Tables**

From at least the 1930s through the 1960s, American manufacturers distributed a variety of tables that customers might use. This was sometimes in the form of a pamphlet, such as the set of miscellaneous hydraulic tables for designers prepared by the Southwark Foundry and Machine Company Division of Baldwin-Southwark Corporation in 1931. Other special purpose tables, distributed on slide charts of various sorts, described properties of such materials as leaded bronze, nickel alloys, specialty steels, wire cloth, glass, and salt/water mixtures. Others gave properties of compressors, elements of screw threads, and data on the dietary advantages of various forms of meat, The Aetna insurance company prepared a table instructing drivers on the safe distances to be maintained between cars. As late as 1969, a manufacturer of paper goods distributed a slide chart for calculating the cost per ounce of groceries, and urged consumers to make careful comparisons of prices. Some tables were not associated with any specific product. Thus the “Menu Minder,” distributed in the mid-1970s, allowed one to quickly alter recipes to serve more or fewer people. It may have been distributed as a kitchen novelty by any number of firms.

Tables distributed by business machine manufacturers have been mentioned already. In addition to covering the needs of commerce and special forms of manufacturing, some of these offered ways to estimate square roots and cube roots.

Specialized tables also were prepared for government use. Military contractors prepared tables to assist in aiming guns and filling out Air Force inventory forms. The Atomic Energy Commission prepared a table for use in uranium enrichment plants.

"Mathematical Charts and Tables - Special Purpose Tables" showing 3 items.

## Mathematical Table for Use with a Marchant Calculating Machine, Square Root Divisors

- Description
- Before the introduction of calculating machines that could compute cube roots of numbers directly, calculating machine manufacturers distributed tables to assist in these calculations. This table was developed by employees of Marchant Calculating Machine Company in Oakland, California, for use with its machines.

- The table is of heavy paper, printed in black., and includes instructions on how it is to be used to find cube roots to the fifth and to the tenth significant figure. A drawing of a Marchant calculating machine is at the top, toward the left. A mark at the bottom left reads: TABLE 68. Another mark along the bottom reads: PRINTED IN U. S. A. A third mark along the bottom reads: COPYRIGHT 1944 MARCHANT CALCULATING MACHINE COMPANY, OAKLAND, CALIF., U. S. A.

- The table is based on the observation that if three numbers are almost the same size, then their arithmetic mean (the average value of the three numbers) is nearly equal to their geometric mean (the cube root of the product of the numbers). Suppose three such numbers are A, A, and N (the first two numbers are the same). Then the the cube root of the expression N times A squared equals (N+2A)/3, or the cube root of N equals (N+ 2A) / (3 (A)
^{2/3}). The table gives values of A and three times A to the 2/3, for A running from 100 to 999. A user can compute the cube root of a number N by finding the A nearest N, adding N and twice A, and dividing the sum (using a calculating machine) by three times A to the two thirds power, as given in the table. The instructions suggest how the procedure should be modified according to the decimal value of the number.

- Compare 313984.03, which gives a table for finding square roots. The table came with Marchant calculating machine MA*334384. The donor, Richard H. Hronik (1911–2003), held a number of patents in transportation engineering and did design work relating to railroad systems built for the Indian government. He went on to work for the firm Melpar as a materials science engineer.

- References: D. H. Lehmer, “Review of
*Square Root Divisors*. . .,”*Mathematical Tables and other Aids to Computation*, 1, 1945, pp. 356–357.

- Location
- Currently not on view

- date made
- 1944

- maker
- Marchant Calculators

- ID Number
- MA*313984.03

- accession number
- 313984

- catalog number
- 313984.03

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

## Mathematical Table for Use with a Marchant Calculating Machine, Cube Root Divisors

- Description
- Before the introduction of calculating machines that could compute cube roots of numbers directly, calculating machine manufacturers distributed tables to assist in these calculations. This table was developed by employees of Marchant Calculating Machine Company in Oakland, California, for use with its machines.

- The table is of heavy paper, printed in black. and includes instructions on how it is to be used to find cube roots to the fifth and to the tenth significant figure. A drawing of a Marchant calculating machine is at the top toward the left. A mark at the bottom left reads: TABLE 68. Another mark along the bottom reads: PRINTED IN U. S. A. A third mark along the bottom reads: COPYRIGHT 1944 MARCHANT CALCULATING MACHINE COMPANY, OAKLAND, CALIF., U. S. A.

- The table is based on the observation that if three numbers are almost the same size, then their arithmetic mean (the average value of the three numbers) is nearly equal to their geometric mean (the cube root of the product of the numbers). Suppose three such numbers are A, A, and N (the first two numbers are the same). Then the the cube root of the expression N times A squared equals (N+2A)/3, or the cube root of N equals (N+ 2A) / (3 (A)
^{2/3}). The table gives values of A and three times A to the 2/3, for A running from 100 to 999. A user can compute the cube root of a number N by finding the A nearest N, adding N and twice A, and dividing the sum (using a calculating machine) by three times A to the two thirds power, as given in the table. The instructions suggest how the procedure should be modified according to the decimal value of the number.

- Compare 313984.03, which gives a table for finding square roots. The table came with Marchant calculating machine MA*334384. The donor, Richard H. Hronik (1911–2003), held a number of patents in transportation engineering and did design work relating to railroad systems built for the Indian government. He went on to work for the firm of Melpar as a materials science engineer.

- References: D. H. Lehmer, “Review of
*Square Root Divisors*. . .,”*Mathematical Tables and other Aids to Computation*, 1, 1945, pp. 356–357.

- Location
- Currently not on view

- date made
- 1944

- maker
- Marchant Calculators

- ID Number
- MA*313984.04

- accession number
- 313984

- catalog number
- 313984.04

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

## Marchant Tables of Factors for Square Roots

- Description
- These two paper leaflets provide numerical values needed for finding square roots to eight significant digits (Table No. 80) and to six significant digits (Table No. 81). Table 80 was copyrighted in 1951, Table 81 in 1952. These copies of the tables were issued after Marchant became a division of Smith-Corona Marchant Inc. in 1958.

- Table 80 allows one to compute square roots on a calculating machine to eight significant digits using a combination of additions and two divisions. Table 81 allows one to find less precise values of the same function using additions and only one division.

- Compare to MA*313984.03.

- Reference:

*Mathematical Tables and Other Aids to Computation*, 7, 1953, p. 168–169.

- Location
- Currently not on view

- date made
- ca 1958

- maker
- Marchant. Division of Smith-Corona Marchant Inc.

- ID Number
- 1979.3084.096

- nonaccession number
- 1979.3084

- catalog number
- 1979.3084.096

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