Marquois scales (also known as Marquois parallel scales or Marquois scale and triangle or military scales) are a mathematical instrument that found widespread use in Britain, particularly in military surveying, from the late 18th century to

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

Description

Invented around 1778 by Thomas Marquois, the Marquois scales consist of a right-angle triangle (with sides at a 3:1 ratio) and two rulers (each with multiple

scales Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number w ...

). The system could be used to aid precision when marking distances off scales, and to rapidly draw parallel lines a precise distance apart. Quick construction of precise parallel lines was useful in cartography and engineering (especially before the availability of graph paper) and Marquois scales were convenient in some challenging environments where larger equipment like a

drawing board A drawing board (also drawing table, drafting table or architect's table) is, in its antique form, a kind of multipurpose desk which can be used for any kind of drawing, writing or impromptu sketching on a large sheet of paper or for reading a l ...

and

T-square A T-square is a technical drawing instrument used by draftsmen primarily as a guide for drawing horizontal lines on a drafting table. The instrument is named after its resemblance to the letter T, with a long shaft called the "blade" and a sh ...

was impractical, such as field survey work and classrooms. Marquois scales fell out of favour among draftsmen in the early 20th century, although familiarity with their use was an entry requirement for the Royal Military Academy at Woolwich around the same time.

Material

Marquois scales were normally made of

boxwood ''Buxus'' is a genus of about seventy species in the family Buxaceae. Common names include box or boxwood. The boxes are native to western and southern Europe, southwest, southern and eastern Asia, Africa, Madagascar, northernmost South ...

, though sets were sometimes made in

ivory Ivory is a hard, white material from the tusks (traditionally from elephants) and teeth of animals, that consists mainly of dentine, one of the physical structures of teeth and tusks. The chemical structure of the teeth and tusks of mammals i ...

or metal.

Use

The triangle would be used for many regular

set square A set square or triangle (American English) is an object used in engineering and technical drawing, with the aim of providing a straightedge at a right angle or other particular planar angle to a baseline. The simplest form of set square is a ...

operations, the rulers likewise would function as rulers, but the unique function was the 3:1 reduction ratio between measured distance and drawn line. A line is drawn along the beveled edge (the side of middle-length) of the triangle. By placing a ruler against the

hypotenuse In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse e ...

of the triangle and sliding the triangle along the ruler for 3 units of the ruler's scale, drawing another line along the beveled edge results in a parallel line with a distance of only 1 unit from the original line. Using larger distances on a ruler to draw lines smaller distances apart means that margin of error reading off the scale is reduced. Additionally, the end-state is the instruments already in place to slide the triangle again to quickly draw additional lines as desired. Regular set square triangles differ (from a Marquois scales triangle) by being made and used according to the angles of their triangle (eg 45-45-90 or 30-60-90 degrees) rather than according to the ratio between the lengths of their sides. Likewise the scales on other rulers are usually intended to be used directly and the selection differs accordingly.

References

{{reflist Dimensional instruments Mathematical tools Surveying instruments Technical drawing tools

Description

Material

Use

See also

References