Nonius is a measuring tool used in navigation and astronomy named in honour of its inventor, Pedro Nunes (Latin: Petrus Nonius), [1] a Portuguese author, mathematician and navigator. The nonius was created in 1542 as a system for taking finer measurements on circular instruments such as the astrolabe. The system was eventually adapted into the Vernier scale in 1631 by the French mathematician Pierre Vernier. [2]
The nonius was used to improve the astrolabe's accuracy. This consisted of a number of concentric circles traced on an instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. On a standard scale of 90 degrees, there are an additional 44–45 concentric circles, with each divided into a specific unit size such that a scale unit on position had an arc of degrees. [2] [3] Thus, the outermost quadrant would comprise 90° in 90 equal divisions, the next inner would have 89 divisions, the next 88 and so on. When an angle was measured, the circle and the division on which the alidade fell was noted. A table was then consulted to provide the exact measure. [4]
The astronomer Tycho Brahe applied the nonius to the astronomic quadrant. [5] [3]
In numerically controlled machines, the nonius is part of several absolute encoders, that measure linear or rotational displacements. [6]
A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celestial navigation.
Tycho Brahe, generally called Tycho for short, was a Danish astronomer, known for his comprehensive and unprecedentedly accurate astronomical observations. He was known during his lifetime as an astronomer, astrologer, and alchemist. He was the last major astronomer before the invention of the telescope.
A vernier scale, named after Pierre Vernier, is a visual aid to take an accurate measurement reading between two graduation markings on a linear scale by using mechanical interpolation, thereby increasing resolution and reducing measurement uncertainty by using vernier acuity to reduce human estimation error. It may be found on many types of instrument measuring linear or angular quantities, but in particular on a vernier caliper which measures internal or external diameter of hollow cylinders.
Pedro Nunes was a Portuguese mathematician, cosmographer, and professor, probably from a New Christian family.
An alidade or a turning board is a device that allows one to sight a distant object and use the line of sight to perform a task. This task can be, for example, to triangulate a scale map on site using a plane table drawing of intersecting lines in the direction of the object from two or more points or to measure the angle and horizontal distance to the object from some reference point's polar measurement. Angles measured can be horizontal, vertical or in any chosen plane.
Pierre Vernier was a French mathematician and instrument inventor. He was the inventor and eponym of the vernier scale used in measuring devices.
A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (gōnía) 'angle' and μέτρον (métron) 'measure'. The protractor is a commonly used type in the fields of mechanics, engineering, and geometry.
The backstaff is a navigational instrument that was used to measure the altitude of a celestial body, in particular the Sun or Moon. When observing the Sun, users kept the Sun to their back and observed the shadow cast by the upper vane on a horizon vane. It was invented by the English navigator John Davis, who described it in his book Seaman's Secrets in 1594.
The Constantinople observatory of Taqi ad-Din, founded in Constantinople by Taqi ad-Din Muhammad ibn Ma'ruf in 1577, was one of the largest astronomical observatories in medieval world. However, it only existed for a few years and was destroyed in 1580.
Caliper(s) or calliper(s) are an instrument used to measure the dimensions of an object; namely, the diameter or depth of a hole. The least count of vernier caliper is 0.1mm
The triquetrum was the medieval name for an ancient astronomical instrument first described by Ptolemy in the Almagest. Also known as Parallactic Rulers, it was used for determining altitudes of heavenly bodies. Ptolemy calls it a "parallactic instrument" and seems to have used it to determine the zenith distance and parallax of the Moon.
The octant, also called a reflecting quadrant, is a reflecting instrument used in navigation.
The mariner's astrolabe, also called sea astrolabe, was an inclinometer used to determine the latitude of a ship at sea by measuring the sun's noon altitude (declination) or the meridian altitude of a star of known declination. Not an astrolabe proper, the mariner's astrolabe was rather a graduated circle with an alidade used to measure vertical angles. They were designed to allow for their use on boats in rough water and/or in heavy winds, which astrolabes are ill-equipped to handle. It was invented by the Portuguese people, a nation known for its maritime prowess and dominated the sea for multiple centuries. In the sixteenth century, the instrument was also called a ring.
A mural instrument is an angle measuring instrument mounted on or built into a wall. For astronomical purposes, these walls were oriented so they lie precisely on the meridian. A mural instrument that measured angles from 0 to 90 degrees was called a mural quadrant. They were utilized as astronomical devices in ancient Egypt and ancient Greece. Edmond Halley, due to the lack of an assistant and only one vertical wire in his transit, confined himself to the use of a mural quadrant built by George Graham after its erection in 1725 at the Royal Observatory, Greenwich. Bradley's first observation with that quadrant was made on 15 June 1742.
A dividing engine is a device employed to mark graduations on measuring instruments to allow for reading smaller measurements than can be allowed by directly engraving them. The well-known vernier scale and micrometer screw-gauge are classic examples that make use of such graduations.
A quadrant is an instrument used to measure angles up to 90°. Different versions of this instrument could be used to calculate various readings, such as longitude, latitude, and time of day. Its earliest recorded usage was in ancient India in Rigvedic times by Rishi Atri to observe a solar eclipse. It was then proposed by Ptolemy as a better kind of astrolabe. Several different variations of the instrument were later produced by medieval Muslim astronomers. Mural quadrants were important astronomical instruments in 18th-century European observatories, establishing a use for positional astronomy.
Transversals are a geometric construction on a scientific instrument to allow a graduation to be read to a finer degree of accuracy. Transversals have been replaced in modern times by vernier scales. This method is based on the Intercept theorem.
An Elton's quadrant is a derivative of the Davis quadrant. It adds an index arm and artificial horizon to the instrument, and was invented by English sea captain John Elton, who patented his design in 1728 and published details of the instrument in the Philosophical Transactions of the Royal Society in 1732.
In astronomy, a transit instrument is a small telescope with extremely precisely graduated mount used for the precise observation of star positions. They were previously widely used in astronomical observatories and naval observatories to measure star positions in order to compile nautical almanacs for use by mariners for celestial navigation, and observe star transits to set extremely accurate clocks which were used to set marine chronometers carried on ships to determine longitude, and as primary time standards before atomic clocks. The instruments can be divided into three groups: meridian, zenith, and universal instruments.
A sine quadrant, sometimes known as a "sinecal quadrant", was a type of quadrant used by medieval Arabic astronomers. The instrument could be used to measure celestial angles, tell time, find directions, perform trigonometric computations, and determine the apparent positions of any celestial object for any time. The name is derived from the Arabic rub meaning 'a quarter' and mujayyab meaning 'marked with sine'.
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