#
Scale RulesCalculating Rules

In addition to length measurements, scale rules could be marked with aids for calculation. Perhaps the most notable rule of this type was Gunter's scale, which was similar to a sector or a slide rule. Gunter's scales are named after Edmund Gunter, a 17th-century English mathematical practitioner who figured out how to put a table of logarithms on a rule so that logarithmic calculations could be made with the aid of dividers. These instruments were especially handy for mathematicians and navigators.

The mathematics collections contain several other objects, ranging from the 18th to the 20th centuries, that were used to simplify computations for tasks including designing sundials, keeping track of calendar dates, and plotting data for aeronautical engineering. A few of these rules were designed specifically for positioning artillery.

"Scale Rules - Calculating Rules" showing 2 items.

## Gunter's Scale Signed Merrifield & Co.

- Description
- In 1614 Scottish mathematician John Napier announced his discovery of logarithms. Within eight years, Edmund Gunter, an English clergyman who was interested in mathematics, had devised a scale on which logarithms could be multiplied and divided, by measuring the distance between two logarithmic numbers with a pair of dividers. Shortly thereafter, instrument makers were manufacturing wooden rules with standard (or "natural") scales typically used in navigation on one side and Gunter's logarithmic (or "artificial") scales on the other side.

- This instrument, a precursor of the slide rule, became known as Gunter's scale. Since it was made of one piece of wood, the expansion and shrinking that happened at sea did not impede its operation. Thus, Gunter's scale remained popular with ship's navigators until the end of the 19th century, when new materials were available for the manufacture of slide rules. Surveyors, mechanics, craftsmen, and retailers also used Gunter's scales to make logarithmic and trigonometric calculations.

- This 2' boxwood rule is identical to MA*319077 and MA*333945. The top of one side has a scale of inches, divided to tenths of an inch and numbered by ones from 23 to 1. On the left are 10" and 9" (divided to 1/2") plotting scales with diagonal scales at each end. In the middle are scales for rhumbs, chords, sines, tangents, and semitangents. On the right are scales for leagues, rhumbs, miles of longitude, and chords. Brass pins at the zero and 60° marks reduce wear from the points of dividers, which were used to transfer measurements between the scale and the user's drawing.

- The other side has logarithmic scales: sines of rhumbs, tangents of rhumbs, line of numbers, sines of degrees, versines of degrees, and tangent of degrees. At the bottom edge are a meridional line and a scale of equal parts that divides 23" into 17 sections. The sections are numbered by tens from 60 to 10 and from 100 to 0.

- On the side with the scale of inches, the rule is marked in the lower right corner: MERRIFIELD & C
^{O}(/) NEW-YORK. Merrifield & Co. sold Gunter's scales in Boston and New York in the early 19th century.

- References: Adler Planetarium,
*Webster Signature Database*, http://historydb.adlerplanetarium.org/signatures/; Otto van Poelje, "Gunter Rules in Navigation,"*Journal of the Oughtred Society*13, no. 1 (2004): 11–22; George Curtis,*A Treatise on Gunter's Scale, and the Sliding Rule*(Whitehall, N.Y., 1824); Florian Cajori, "On the History of Gunter's Scale and the Slide Rule During the Seventeenth Century,"*University of California Publications in Mathematics*1, no. 9 (February 17, 1920): 187–209.

- Location
- Currently not on view

- date made
- ca 1825

- retailer
- Merrifield & Co.

- maker
- Merrifield & Co.

- ID Number
- MA*318174

- catalog number
- 318174

- accession number
- 232132

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

## Belcher Brothers Gunter's Scales, Group of 2

- Description
- These two 2' boxwood rules are identical to each other and to MA*333945 and MA*318174. The top of one side has a scale of inches, divided to tenths of an inch and numbered by ones from 23 to 1. On the left are 10" and 9" (divided to 1/2") plotting scales with diagonal scales at each end. In the middle are scales for rhumbs, chords, sines, tangents, and semitangents. On the right are scales for leagues, rhumbs, miles of longitude, and chords. Brass pins at the zero and 60° marks reduce wear from the points of dividers, which were used to transfer measurements between the scale and the user's drawing.

- The other side has logarithmic scales: sines of rhumbs, tangents of rhumbs, line of numbers, sines of degrees, versines of degrees, and tangent of degrees. At the bottom edge are a meridional line and a scale of equal parts that divides 23" into 17 sections. The sections are numbered by tens from 60 to 10 and from 100 to 0.

- The first rule is marked on the first side in the lower right corner: BELCHER BROTHERS MAKERS (/) New York. ("New York" is in script.) On the other side, this rule is marked at the top center: J. J. WARREN. The second rule is marked on the first side in the lower right corner: BELCHER BRO
^{S}. & C^{o}. NEW – YORK.

- Thomas Belcher began making rules in New York in 1821 and was joined by his brother, William, in 1825. Around 1831, another brother, Charles, joined the firm, and the company's name was changed from T. & W. Belcher to Belcher Brothers. The first rule dates to this period. Around 1843, manufacturing of rules moved to New Jersey and the firm went by the name Belcher & Bros. Around 1853 some of the men's sons joined the firm, and the name was changed to Belcher Bros. & Co. The second rule dates to this period. The company had become the largest American manufacturer of rules, but it was surpassed by Stanley in the second half of the 19th century. Belcher stopped manufacturing rules around 1877. The Smithsonian purchased these rules in 1961, and no information is known about J. J. Warren, the name on the first rule.

- References: Otto van Poelje, "Gunter Rules in Navigation,"
*Journal of the Oughtred Society*13, no. 1 (2004): 11–22;*Belcher Bros. & Co.'s Price List of Boxwood & Ivory Rules*(New York, 1860; reprint, Fitzwilliam, N.H.: Ken Roberts Publishing Co., 1982); Philip A. Cannon II, "The Makers and Markers of Gauges, Rules, Squares, and Tapes," http://www.pactu.com/makers.htm.

- Location
- Currently not on view

- date made
- ca 1853–1877

- ca 1831–1843

- maker
- Belcher Brothers

- ID Number
- MA*319077

- accession number
- 236088

- catalog number
- 319077

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