Accession No

1017


Brief Description

gunter sector, by John England, English, 1703


Origin

England; London; Charing Cross


Maker

England, John


Class

calculating; mathematics


Earliest Date

1703


Latest Date

1703


Inscription Date

1703


Material

metal; brass


Dimensions

Length 480mm; breadth 72mm


Special Collection


Provenance

On loan from Trinity College, University of Cambridge from 1951.


Inscription

(1) J. England Charing Cross Londini Fecit 1703 (obverse at hinge end)
(2) COLLEG. TRINIT. CANTAB: (hinge)


Description Notes

Two arms held together by a flat circular hinge.

Obverse: scales of Lines, Secants, Chords, Numbers,Sines and Tangents.
Line of lines on each arm, marked ‘Lin’, divided 0 - 10, numbered by 1, subdivided to 0.5, to 0.1 and to 0.02.
Line of Secants on each arm, marked ‘Sec’, divided 10˚ - 75˚ [30´]; numbered by 10˚, subdivided to 5˚ and to 1˚; 40˚ - 50˚ subdivided to 30´; 50˚ - 75˚ 30´ subdivided to 15´.
Line of Chords on each arm, marked ‘Cho’, divided [3˚] - 60˚, numbered by 10˚, subdivided to 5˚, to 1˚, to 30´ and to 10´.
Line of polygons marked ‘poll’ along both arms against the inner edge, divided 12 - 6 from hinge end, numbered by 1.
A further short line of chords on the upper arm is marked ‘Chord’, divided [0] - 60˚, numbered by 10˚, subdivided to 5˚ and to 1˚.
A further short line of lines on the lower arm is marked ‘Line’, divided [0] - 10, numbered by 1, subdivided to 0.5 and to 0.1.
Lines of numbers, sines and tangents begin on upper arm and form a continuous line when the instrument is fully open.
Line of numbers, marked ‘Numbers’, divided 4 - 30[00], numbered 4, 5, 6, 7, 8, 9, 1[0], 2[0]…9[0], 1[00], 2[00]…9[00], 10[00], 20[00], 30[00]. 4 - 1[0] subdivided to 0.5, to 0.1 and to 0.05. 1[0] - 1[00] subdivided to 5 and to 1. 1[00] - 2[00] subdivided to 10, to 5 and to 1. 2[00] - 4[00] subdivided to 10 and to 2. 4[00] - 10[00] subdivided to 50, to 10 ad to 5. 10[00] - 20[00] subdivided to 500, to 100, to 50 and to 10. 20[00] - 30[00] subdivided to 500, to 100 and to 20.
Line of Sines, marked ‘Sines’, divided [30´] - 90˚, [0] - [60˚], numbered 1, 2, 3…10, 20… 90, 10, 20…50. 30´ - 10˚ subdivided to 30´, to 15´ and to 5´. 10˚ - 20˚ subdivided to 5˚, to 1˚, to 30´ and to 10´. 20˚ - 40˚ subdivided to 5˚, to 1˚ and to 15´. 40˚ - 60˚ subdivided to 5˚, to 1˚ and to 30´. 60˚ - 80˚ subdivided to 5˚ and to 1˚. 80˚ - 90˚ subdivided to 5˚. 0 - 10˚ subdivided to 5˚. 10˚ - 30˚ subdivided to 5˚ and to 1˚. 30˚ - 60˚ subdivided to 5˚, to 1˚ and to 30´.
Line of Tangents, marked ‘Tangents’, divided [30´ ] to [55˚], numbered 1, 2…10, 20, 30, 40, 45, 50. 30´ to 10˚ subdivided to 30´, to 15´ and to 5´. 10˚ - 30˚ subdivided to 5˚, to 1˚, to 30´ and to 10´. 30˚ - 55˚ subdivided to 5˚, to 1˚ and to 15´.

Reverse has lines of sines and tangents, of latitudes, chords, hours and meridional parts and degrees.
Line of sines on both arms, marked ‘Sin’, divided [0] - 90˚, numbered by 10˚; 0 - 70˚ subdivided to 5˚, to 1˚ and to 15´. 70˚ - 85˚ subdivided to 5˚, to 1˚ and to 30´.
Line of tangents on both arms divided [0] - 45˚ and then 45˚ - 76˚ on a second scale. 0 - 45˚ marked ‘Tan’, numbered by 10˚, subdivided to 5˚, to 1˚, to 30´ and to 10´. 45˚ - 76˚, marked ‘tan’ numbered by 5˚, subdivided to 1˚ and to 15´.
Further short line of sines on upper arm, marked ‘Sines’, divided [0] - 90˚, numbered by 10˚, subdivided to 5˚; 0 - 80˚ subdivided to 1˚.
Further short line of tangents on lower arm, marked ‘Tange’, divided [0] - 45˚, numbered by 10˚, subdivided to 5˚ and to 1˚.
Upper arm carries another line of sines along outer edge, marked ‘Sines’, divided [0] - 90˚, numbered by 10˚, subdivided to 5˚. 0 - 60˚ subdivided to 1˚ and to 15´. 60˚ - 80˚ subdivided to 1˚ and to 30´. 80˚ - 85˚ subdivided to 1˚.
Also along this edge are a line of meridional parts and one of latitudes.
Line of meridional parts marked ‘In: Mer:’, divided [0] - 90˚, numbered by 10˚, subdivided to 5˚ and to 1˚.
Line of latitudes marked ‘Lattitudes’ numbered [0] - 90˚, numbered by 10˚, subdivided to 5˚. 0 - 40˚ subdivided to 1˚ and to 30´. 40˚ - 80˚ subdivided to 1˚.
Along lower edge is a line of degrees and also ones of hours and chords.
Degree scale is unmarked and divided 90˚ - 80˚(also 10˚) - 180˚, numbered by 10˚; 90˚ - 85˚ and 90˚ - 180˚ subdivided to 5˚, to 1˚ and to 20´; 85˚ - 80˚ - 90˚ subdivided to 5˚, to 1˚, to 30´ and to 10´.
Line of hours marked ‘Hours’, divided 0 - VI, numbered by I, subdivided to 30 minutes, to 15 minutes and to 5 minutes.
Line of chords marked ‘Chords’, divided 0 - 90˚, numbered by 10˚, subdivided to 5˚ and to 1˚.
Along outer rims of arms is a scale of inches divided [0] - 36, numbered by 1, subdivided to 0.5 and to 0.1.
good condition


References


Events

Description
Sector
Sectors were used for calculation by navigators, surveyors, gunners and draftsmen (and, famously, by Galileo) from the about the mid 16th century to the mid 19th century. During the 16th century, they were used as general mathematical tools, but the introduction of logarithms drastically expanded their application. Usually made of brass, wood or ivory, they look like a jointed rule with scales engraved on either side.

Sectors use the principle of similar triangles (that the ratio of lengths of two sides of similar triangles will always be the same) with scales of proportion for calculating mathematical functions such as finding the line of equal parts, inscribing a rectangular polygon inside a circle of a given radius and protracting angles. This made them useful for similar calculations to a slide rule.

18/10/2002
Created by: Saffron Clackson on 18/10/2002


FM:39534

Images (Click to view full size):