Ivory sector

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Ivory sector

This instrument is a Sector, as you would certainly know if you were a ship's officer in the 18th or 19th century. Made of ivory with a brass hinge, it measures 16 by 3.5 cm when folded, as in the photo at right, and can be unfolded into a straight rule 30.5 cm long.

Click photo to enlarge

While I don't know the exact age of this wonderful old instrument, it is likely to come from the 19th century. The origins of the sector go much farther, back to well before the arrival of the slide rule, and its invention is attributed to Galileo Galilei in about 1597. However, it was the English mathematician Edmund Gunter who added to it the crucial logarithmic scales in about 1624. This allows the sector to be used as a straight logarithmic rule, but its main usefulness stems from the ability to open it to various angles and measure off distances on its scales with a pair of dividers, making use of the properties of similar triangles as one crosses from one leg of the sector to another. In this way a variety of trigonometric calculations required for navigation at sea are made possible with minimal effort.

Click a photo to enlarge

The close-up at right shows the ends of the three logarithmic scales (proportional to Logs of Tangents, Logs of Sines, and Logs of Numbers). Of interest are the three brass inserts, found on some of the other scales as well; these are a sure indication that, unlike the modern slide rule, this instrument was designed to be used in conjunction with a pair of dividers. The brass plugs were inserted in the ivory in order to protect this softer material from the repeated abuse of the dividers' needle points, on scale positions that would be in the most frequent use, notably the ends of the scales.

		Exhibit provenance: I bought this sector in an antique mall in California. More info: http://web.mat.bham.ac.uk/C.J.Sangwin/Sliderules/sector.pdf