#
SectorsFrench Style

Of the three main styles, French sectors were the most consistent in terms of the scales with which they were marked. They were designed specifically for gunnery rather than for general applications. There were eight common scales:

, or weight of artillery shot – Although early modern cannon were not standard in size, there were different types of shot for different general types of artillery. Each type of shot had a particular volume, weight, and amount of powder. This scale helped gunners determine the required weight for a given size of shot.*Poid des boulets***Metallic line**– The alchemical symbols for certain metals (such as gold, lead, silver, copper, iron, and tin) were placed at distances from the hinge of the sector so that balls of those metals with those radii would weigh the same. The distance between any two metals gave the ratio between their weights.**Line of solids**– Used to determine the ratio between two volumes and to calculate cube roots.**Line of chords**– Used to construct angles., or size of artillery shot – This scale was used to determine the size of shot, given the diameter of the cannon opening and the weight of the shot.*Calibre des pieces***Line of lines**– A scale divided into equal parts used as the base scale for taking measurements that are transferred to other scales with a pair of dividers. For example, open the dividers to a length on the line of lines and then pivot the dividers and open the sector so that the lifted point of the dividers falls on the other leg of the sector.**Line of planes**– Used to determine the ratio between two areas and to calculate square roots.**Tetragonic line**– Points placed from the hinge to represent the sides of regular polygons with the same area, from the triangle to a 13-sided polygon. Used to set up proportions to determine the areas of regular polygons with other side lengths.

"Sectors - French Style" showing 2 items.

## French-Style Sector Signed by Nicolas Bion

- Description
- This small, one-sided brass sector has two flat rectangular arms, hinged at one end. A flower decorates the hinge. The instrument has double scales of chords, running from 10 to 90, and of specific weights for five metals, marked with their symbols. The outer edge has a scale that runs from 1/4 to 33 and is labeled Pouts [
*sic*] des boulets. The instrument is marked: N Bion (/) A –Paris. The signature is slightly different from the one on the other sector from Bion's workshop in the collection, 1985.0580.05.

- Nicolas Bion (c. 1652–1733) made and sold mathematical instruments in Paris in his own shop and as royal maker for Louis XIV. He included a lengthy discussion of sectorial scales in his famous 1709 manual on the construction and use of mathematical instruments. Bion's son, Jean-Baptiste, took over the shop in 1731.

- The Smithsonian acquired this sector in 1962 from Jacob (Jake) Zeitlin and Josephine Ver Brugge Zeitlin, who operated a rare books store for over 40 years in West Hollywood, Calif.

- References: Nicolas Bion,
*Traité de la construction et des principaux usages des instruments de mathematique*(Paris, 1709), 29–74; Gloria Clifton,*Directory of British Scientific Instrument Makers 1550-1851*(London: National Maritime Museum, 1995), 2–3; Beverly Beyette, "Zeitlin Auction: A Bittersweet Final Chapter,"*Los Angeles Times*, February 4, 1988; Mary Rourke, "Josephine Ver Brugge Zeitlin, 90; Sold Rare Books, Journals,"*Los Angeles Times*, February 26, 2005.

- Location
- Currently not on view

- date made
- 1681-1733

- maker
- Bion, Nicholas

- ID Number
- MA*321675

- catalog number
- 321675

- accession number
- 245711

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

## French-Style Sector Signed by Nicolas Bion

- Description
- This brass instrument has rectangular arms hinged at one end. The hinge is decorated with a flower on both sides. One side has double scales of chords, running from 10 to 180; of solids, running from 1 to 64; and for the specific weights of five metals, marked with their symbols. The outer edge has a scale that runs from 1/4 to 64 and is labeled poids des Boulets. The sector is marked: N. Bion (/) AParis.

- The other side has double scales for equal parts, running from 10 to 200; for architectural drawings, running from 1 to 64; and for the lengths of the sides of inscribed regular polygons, from 12 sides to three sides. The outer edge has a scale running from 1/4 to 64 and labeled Calibre des pieces.

- Nicolas Bion (c. 1652–1733) made and sold mathematical instruments in Paris in his own shop and as royal maker for Louis XIV. He included a lengthy discussion of sectorial scales in his famous 1709 manual on the construction and use of mathematical instruments. Albert Haertlein (1895–1960), who collected this sector, graduated with a bachelor's degree in civil engineering from the Massachusetts Institute of Technology in 1918, served in the engineering corps of the U.S. Army during World War I, and taught engineering at Harvard from 1919 until 1959. He was prominent in the American Society of Civil Engineers.

- References: Nicolas Bion,
*Traité de la construction et des principaux usages des instruments de mathematique*(Paris, 1709), 29–74; "News From the Classes,"*Technology Review*21 (1919): 645; Albert Haertlein, Papers, HUG4444, Harvard University Archives, Cambridge, Mass.

- Location
- Currently not on view

- date made
- 1681-1733

- maker
- Bion, Nicholas

- ID Number
- 1985.0580.05

- accession number
- 1985.0580

- catalog number
- 333930

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