#
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 6 items.

## Slide Chart, Quick Slide Thread Elements

- Description
- This paper model slide chart has an envelope held together by staples and a rectangular slide, It contains tables relating to the size and shape of screw threads, as standardized in the mid-20th century United States. Tables on one side are for the “National Fine Series,” those on the other side for the “National Coarse Series.” Fine screws move a relatively short distance each time the screw is turned, and have greater locking power.

- Assuming that screws are of the general form proposed by William Sellers of Philadelphia in 1864, the chart gives the depth of the thread element, the width of the flat portion of the base, the tap drill size to be used in fabricating the screw, and the best wire size for measuring the screw (that is to say, the wire size that will just touch the thread at the pitch diameter). It also indicates the maximum and minimum dimensional tolerances for different classes of fit from the loosest (class 1) to the most precise (class 4).

- A mark on the front reads: QUICK SLIDE (/) THREAD ELEMENTS. A mark on the back reads: COPYRIGHT 1946 BY CAPELL DESIGNING CO. BOX 993 CHURCH ST. STA. NEW YORK 8, N.Y. The back is stamped: [copyright symbol]CI I pub. 430. Below this is the date stamp: FEB - 7 1946. A nearby stamp reads: SURPLUS (/) DUPLICATE and shows the seal of the Library of Congress.

- Rockford D. Robbins and John E. Capell of New York copyrighted the instrument in February of 1946. It seems likely that this was the copy of their device submitted to the Copyright Office of the Library of Congress. No manufactured example of the instrument is yet known.

- References:

- Bruce Sinclair, “At the Turn of a Screw: William Sellers, the Franklin Institute, and a Standard American Thread,”

*Technology and Culture*, vol. 10, No. 1 (Jan., 1969), pp. 20-34

- United States Library of Congress,
*Catalog of Copyright Entries 1946 Works of Art . . .*

- Location
- Currently not on view

- date made
- 1946

- maker
- Capell Designing Company

- ID Number
- 1983.3009.03

- catalog number
- 1983.3009.03

- nonaccession number
- 1983.3009

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

## Slide Chart, Slide Selector for Elastic Machinery Steels

- Description
- This slide chart advertises the properties of the ELASTUF machinery steels manufactured by Beals, McCarthy & Rogers, Incorporated, of Buffalo, New York. It consists of a paper envelope with metal rivets and a paper slide. Lining up an arrow on the slide with a type of steel listed along the top of the front reveals in a window of the envelope a general description of the properties of the steel. The other side of a chart shows the physical properties of that type of steel (its tensile strength, yield point, elongation and reduction) for different bar sizes.

- A mark along the bottom right of the back reads: COPYRIGHT 1947 BEALS, McCARTHY & ROGERS, INC. A mark on the slide reads: MANUFACTURED BY (/) GRAPHIC CALCULATOR CO. (/) CHICAGO 5, ILL. (/) MADE IN U.S.A.

- For other products of Graphic Calculator Company, see 2000.3029.02 and 2000.3029.13.

- Graphic Calculator Company was a slide rule and slide chart manufacturing and design company founded in Chicago in 1940 by Capron R. Gulbransen, and apparently still in business at the time of Gulbransen’s death in 1969. By 1965, the firm had moved to Barrington, Illinois.

- Reference:

- Obituaries,
*Chicago Tribune*, August 11, 1969, p. A6

- Location
- Currently not on view

- date made
- 1947

- maker
- Beals-McCarthy & Rogers

- ID Number
- 1988.3076.02

- catalog number
- 1988.3076.02

- nonaccession number
- 1988.3076

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

## 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

## Sound Velocity Corrector, A Mathematical Chart

- Description
- This device assists in calculations of changes in the range of a gun because of meteorological conditions, particularly wind speed and temperature. A rotating disc and pointer attached to the plastic base have the scales required to correct for wind speed. A scale toward the bottom of the base gives the temperature correction. Both of these corrections are in percentages of the range. Summing them gives the total meteorological correction as a percentage of the range. One then can use a range correction chart to find the actual range correction.

- A mark on the front of the instrument reads: Signal Corps U. S. Army (/) SOUND VELOCITY CORRECTOR PT-62/TSS-1 (/) Order No. 3531-CEGSA-45 G. FELSENTHAL & SONS - CHICAGO.

- The instrument was designed and made for the United States Army by G. Felsenthal & Sons of Chicago in 1945. It had Felsenthal designation FAS-2.

- For a related range correction chart, see 1977.1141.43.

- Reference:

- Accession file.

- Location
- Currently not on view

- date made
- 1945

- maker
- G. Felsenthal & Sons, Inc.

- ID Number
- 1977.1141.42

- catalog number
- 336426

- accession number
- 1977.1141

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

## Range Correction Chart, Felsenthal FAS-3

- Description
- This white plastic chart was designed for the U.S. Army Signal Corps. It is a nomogram for finding the range correction in yards of a weapon, by lining up the meteorological correction as a percentage of the range and the range.

- On the left is a scale marked “Range Correction in Yds.” On the right is a scale marked “Percentage Meteorological Correction” and on the diagonal between the two is a scale marked “Range in Yds.” According to a label received with the object and stored in the accession file, the object was made in 1945.

- The meteorological correction is found from the temperature and wind speed using a related chart called a “sound velocity corrector” (for an example, see 1977.1141.42) .

- A mark on the object reads: Range Correction Chart PT-63/TSS-1.

- For an explanation of the mathematical theory of this kind of nomogram, see Lipka. For a similar device used for another purpose, see 1985.0636.01.

- References:

- Joseph Lipka,
*Graphical and Mechanical Computation. Part I. Alignment Charts*, New York: John Wiley & Sons, 1921, pp. 65–

- 67.

- Accession file.

- Location
- Currently not on view

- date made
- 1945

- author
- G. Felsenthal & Sons

- ID Number
- 1977.1141.43

- catalog number
- 336427

- accession number
- 1977.1141

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