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
 Object Name

sheet

mathematical table
 date made

1944
 maker

Marchant Calculators
 Physical Description

paper (overall material)
 Measurements

overall: .1 cm x 27.9 cm x 21.5 cm; 1/32 in x 10 31/32 in x 8 15/32 in
 place made

United States: California, Oakland
 ID Number

MA*313984.03
 accession number

313984
 catalog number

313984.03
 subject

Mathematics

Business
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Medicine and Science: Mathematics

Science & Mathematics

Mathematical Charts and Tables
 Data Source

National Museum of American History, Kenneth E. Behring Center