French 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:

  • Poid des boulets, 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.
  • 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.
  • Calibre des pieces, 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.
  • 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.

French-Style Sector Signed by Butterfield

The arms of this brass instrument have plain ends, but the hinge is decorated with a flower.
Description
The arms of this brass instrument have plain ends, but the hinge is decorated with a flower. One side has a double scale of chords that runs from 10 to 180; a double scale for "les Solides" that runs from 1 to 60; and a double scale for the specific weights of five metals, marked with their symbols. The outer edge of both arms has a scale that runs from 1/4 to 60 and is labeled Diamettre [sic] et Poids des Boulets. The sector is marked: Butterfield (/) AParis.
On the other side, the outer edge has a scale that runs from 1/4 to 60 and is labeled Calibre des Pieces. There are double scales of equal parts, running from 10 to 200; for "les plans," running from 10 to 60; and for inscribed regular polygons, from 12 sides to three sides. Compare to MA.321676 and 1985.0580.04.
Michael Butterfield (1635–1724) was an English instrument maker who worked in France from around 1677 until his death. He was best known for his distinctive sundials.
References: Maya Hambly, Drawing Instruments, 1580–1980 (London: Sotheby's Publications, 1988), 24, 134–135; Anthony Turner, "Sector," in Instruments of Science: An Historical Encyclopedia, ed. Robert Bud and Deborah Jean Warner (New York and London: Garland Publishing, 1998), 526–528.
Location
Currently not on view
date made
1677-1724
maker
Butterfield, Michael
ID Number
MA.321677
catalog number
321677
accession number
245711

French-Style Sector Signed by Butterfield

This brass instrument has rectangular arms hinged at one end. The hinge is decorated with a flower on both sides.
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 140; of solids, running from 10 to 60; and for the specific weights of four metals, marked with their symbols. The outer edge of one arm has a scale that runs from 4 to 24 and is labeled poids des boulets. The sector is marked: Butterfield (/) AParis.
The other side has a double scale of equal parts that runs from 10 to 200; an unlabeled double scale that runs from 10 to 60 and is presumably for making architectural drawings; and a double scale for inscribed regular polygons, from 12 sides to three sides. The outer edge of one arm has a scale for Calibre des pices [sic] that runs from 4 to 24. Compare to MA.321676 and MA.321677.
Michael Butterfield (1635–1724) was an English instrument maker who worked in France from around 1677 until his death. He was best known for his distinctive sundials.
References: Maya Hambly, Drawing Instruments, 1580–1980 (London: Sotheby's Publications, 1988), 24, 134–135; Harriet Wynter and Anthony Turner, Scientific Instruments (New York: Charles Scribner's Sons, 1975), 113.
Location
Currently not on view
date made
1677-1724
maker
Butterfield, Michael
ID Number
1985.0580.04
catalog number
333929
accession number
1985.0580

French-Style Sector Signed by Butterfield

The arms of this small brass instrument have straight ends. One side has a double scale of chords that runs from 10 to 90. The outer edge on one arm has a scale that runs from 4 to 24 and is labeled poids des boulets.
Description
The arms of this small brass instrument have straight ends. One side has a double scale of chords that runs from 10 to 90. The outer edge on one arm has a scale that runs from 4 to 24 and is labeled poids des boulets. The inner edge of both arms has a double scale for the specific weights of four metals, marked with their symbols. The sector is marked: Butterfield (/) AParis. The hinge is decorated with a flower.
On the other side, the outer edge of one arm has a scale that runs from 4 to 24 and is labeled Calibre des pieces. Both arms have double scales of equal parts, running from 10 to 120, and for inscribed regular polygons, from 12 sides to three sides. Compare to MA.321677 and 1985.0580.04.
Michael Butterfield (1635–1724) was an English instrument maker who worked in France from around 1677 until his death. He was best known for his distinctive sundials.
References: Maya Hambly, Drawing Instruments, 1580–1980 (London: Sotheby's Publications, 1988), 24, 134–135; Adler Planetarium, Webster Signature Database, http://historydb.adlerplanetarium.org/signatures/; Henri Michel, Scientific Instruments in Art and History, trans. R. E. W. Maddison and Francis R. Maddison (Barrie and Rockliff, 1967), 206.
Location
Currently not on view
date made
ca 1700
maker
Butterfield, Michael
ID Number
MA.321676
catalog number
321676
accession number
245711

French-Style Sector Signed by Nicolas Bion

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.
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

French-Style Sector Signed by Nicolas Bion

This brass instrument has rectangular arms hinged at one end. The hinge is decorated with a flower on both sides.
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

French-Style Sector

The arms of this brass instrument have straight edges, but the hinge is decorated with a straight and squiggly lines.
Description
The arms of this brass instrument have straight edges, but the hinge is decorated with a straight and squiggly lines. One side has a double scale of chords that runs from 10 to 130; a double scale for "Les Solides" that runs from 1 to 60; and a double scale for the specific weights of four metals, marked with their symbols. Two holes are drilled on either side of the 80 mark on the scales of chords on the lower arm. The outer edge of the lower arm has a scale that runs from 4 to 24 and is labeled "pd des boulets" (for the weight of iron shot).
On the other side, the outer edge has a scale that runs from 4 to 24 and is labeled "Cbres des Pieces" (for the size of iron shot, given the diameter of the barrel and the weight of the shot). There are double scales of equal parts, running from 10 to 200; for architectural drawings, running from 10 to 60; and for inscribed regular polygons, from 12 sides to three sides. Compare to MA.321676 and 1985.0580.04.
According to the accession file, the donor collected this instrument in Mobile, Ala., around 1898 and sent it to the Smithsonian in 1936.
Location
Currently not on view
date made
18th century
ID Number
MA.311165
catalog number
311165
accession number
141741

French-Style Sector

The arms of this brass instrument have straight edges, but the hinge is decorated with a sunburst.
Description
The arms of this brass instrument have straight edges, but the hinge is decorated with a sunburst. One side has double scales of chords, running from 10 to 180; of architectural drawings, running from 5 to 60; and for the specific weights of four metals, marked with their symbols. The outer edge has a scale that runs from 1/4 to 64 and is labeled Calibres des Pieces. There is no maker's mark.
The other side has double scales for equal parts, running from 0 to 200; for solids, running from 5 to 60; 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 Poids des Boulets. The outside face of the instrument has scales for English feet and French feet, each running from 1 to 6. This instrument was found in Smithsonian storage in 1956.
Location
Currently not on view
date made
18th century
ID Number
MA.314799
catalog number
314799
accession number
210147

French-Style Sector Signed by Pierre Le Maire

The arms of this brass instrument have straight edges, while the hinge is decorated with a floral design. The sector is marked: P. Le Maire (/) AParis.
Description
The arms of this brass instrument have straight edges, while the hinge is decorated with a floral design. The sector is marked: P. Le Maire (/) AParis. One side has double scales of chords, running from 10 to 180; of solids, running from 1 to 60; and for the specific weights of four metals, marked with their symbols. The outer edge has a scale running from 1/4 to 60 and labeled Diamettres [sic] et Poids des Boulets (for the diameter and weight of iron shot).
The other side has double scales for equal parts, running from 10 to 200; for architectural drawings, running from 1 to 60; and for the lengths of the sides of inscribed regular polygons, from 12 sides to four sides. The outer edge has a scale that runs from 1/4 to 60 and is labeled Calibres des Pieces (for the size of iron shot, given the diameter of the barrel and the weight of the shot). This arrangement of scales is standard for sectors manufactured in France.
Pierre Le Maire (1717–1785) took over his father Jacques's workshop in the late 1730s. Large numbers of his sundials, mathematical instruments, and lodestones survive. He and his workers initially signed instruments with "le Fils," so this example was probably made after 1750. The donor received this sector from a distant relative, Gunther Mathies, who emigrated from Germany in the early 20th century and worked for the Thomaston Clock Company in Connecticut.
Reference: Adler Planetarium, Webster Signature Database, http://historydb.adlerplanetarium.org/signatures/.
Location
Currently not on view
date made
ca 1750
maker
Le Maire, Pierre
ID Number
1984.1070.02
accession number
1984.1070
catalog number
1984.1070.02

French-Style Sector Signed by Louis Lennel

The arms of this brass instrument have straight edges, but the hinge is decorated with a flower. 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.
Description
The arms of this brass instrument have straight edges, but the hinge is decorated with a flower. 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. On one arm, the outer edge has a scale that runs from 4 to 24 and is labeled "Poids des Boulets." The sector is marked: Lennel à La (/) Sphére à Paris.
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. On one arm, the outer edge has a scale running from 4 to 24 and labeled "Calibre des Pieces."
In 1774, Louis-Pierre-Florimond Lennel took over the Paris workshop operated by his teacher, Jacques Canivet, who previously had succeeded his uncle, the famous instrument maker Claude Langlois. All three men supplied telescopes to French astronomers. By 1781, Lennel called himself the official maker for France's king and the navy. He died by 1784 and was succeeded by his widow.
References: Maya Hambly, Drawing Instruments, 1580–1980 (London: Sotheby's Publications, 1988), 28; Harriet Wynter and Anthony Turner, Scientific Instruments (New York: Charles Scribner's Sons, 1975), 158; Adler Planetarium, Webster Signature Database, http://historydb.adlerplanetarium.org/signatures/.
Location
Currently not on view
date made
1774-1784
maker
Lennel, Louis-Pierre Florimond
ID Number
MA.317363
catalog number
317363
accession number
230278

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