Gunter's Line calculating ruler, 1850-1867
Object No. 2010/1/377
In 1620 English mathematician Edmund Gunter invented the first analogue device that used Napier's logarithms to perform calculations. Called Gunter's Line of Proportion, or Gunter's Rule, it is inscribed with a line marked at intervals such that the distance of a number from 1 represented its logarithm. Distances on the scale could be added using a pair of dividers to multiply two numbers, or subtracted to divide one number by another. This example was made around 1860 from boxwood, which, crucially, maintains its dimensions when humidity changes. Debbie Rudder This object is part of a collection relating to the history and development of calculating devices assembled by Assoc Professor Allan Bromley of Sydney University, comprising mathematical instruments, slide-rules, mechanical and electronic calculators, electronic analogue computers, computer components, kit computers, education computers, and associated ephemera. Allan Bromley was a lecturer and researcher at the University of Sydney Basser Department of Computer Science from 1978 until his untimely death in August 2002. He specialised in Computer Architecture, Computer Logic and in particular the History of Computing. He was regarded as the world authority on Charles Babbage's Calculating Engines (instigating the building of the Difference Engine No.2 at the Science Museum London) and the Antikythera Mechanism and had extensive knowledge of calculators, analogue computers, logic, stereopsis, totalisators, clocks and time keeping and mechanical engineering.
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Summary
Object Statement
Calculating rule, Gunter's Line of Proportion, duplex, boxwood, maker unknown, 1850-1867, used by William Potts, The Craigs Moor School, July 1867, part of Allan Bromley collection
Physical Description
Calculating rule, Gunter's Line of Proportion, duplex, boxwood, maker unknown, 1850-1867, used by William Potts, The Craigs Moor School, July 1867, part of Allan Bromley collection Calculating rule, duplex, boxwood, top edge is a 24 inch ruler (reading right to left), bottom edge bevelled. Scales are engraved into wood in colour black. The scales on this rule are specifically designed for navigation. Scales: Obverse: Left half: 24 inch ruler (reading right to left), a grid of lines at ½ inch spacing with nomographs at either end. Right half: LEA - Leagues RUM - Rhumb M.L - Miles of Longitude CHO - Chord - in degrees of Latitude SIN - Sines TAN - Tangents Reverse: S.R - Sines of Rhumbs T.R - Tangents of Rhumbs NUM - Line of Numbers - SIN - the Sine of the angle on this line is read off on the NUM scale V.S - Versed Sines TAN - the Tangent of the angle on this line is read off on the NUM scale MER - Meridian line - the distance along a meridian line of degrees of latitude. E.P - Line of Equal Parts
DIMENSIONS
Height
4 mm
Width
44 mm
PRODUCTION
Notes
This Gunter's Rule has inscribed on the reverse the name of a previous owner: "William Potts The Craigs Moor School July 12th 1867". Maker unkown.
HISTORY
Notes
The slide rule is a mechanical representation of the way logarithms can be used for multiplication, division and the taking of squares and square roots as well as other mathematical functions. Logarithms, which were invented by the Scottish mathematician and landowner John Napier in 1614, can be added together to perform multiplication and subtracted one from another to perform division of two numbers, thus allowing multiplication and division to be carried out with ease. The development of the slide rule went through several stages. The first significant device was Gunter's Line of Proportion (also known as the Gunter's Rule or Gunter's Scale) invented by the English astronomer and mathematician Edmund Gunter in 1624. He engraved a two foot long (60cm) straight-edge rule with lines marking the numbers placed at distances proportional to the logarithms of the numbers. By using a Gunter's Rule multiplication or division can be carried out simply through the addition or subtraction of distances on the rule using a pair of pointers or compasses. In order to multiply two numbers, one pointer of the compass is set down on the scale at the index marker (the number 1) on the line of Numbers and opened so that the other pointer of the compass extends to the multiplicand (the number to be multiplied). The compass is then re-placed with one leg at the multiplier, and its other leg now points to the product of the two numbers. The earliest Gunter's Rules had few scales on them, simply the line of numbers in logarithmic proportion, a line of squares and a line of cubes of the numbers plus the trigonometric scales which are useful for gunnery and navigation. [Hopp, p.9] They became the primary tool for navigation over the 18th century and were considered accurate enough for them to be still in use for navigation in the mid-19th century. [Cajori, p.21] Refs: Peter Hopp, "Slide Rules, their History, Models and Makers", Mendham, New Jersey: Astragal Press, 1999. Florian Cajori, "A history of the logarithmic slide rule and allied instruments", Mendham, N.J.: Astragal Press, c1994.
SOURCE
Credit Line
Donated through the Australian Government's Cultural Gifts Program in memory of Associate Professor Allan Bromley, 2010
Acquisition Date
20 January 2010
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