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A theodolite () is a precision optical instrument for measuring between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching.
It consists of a moveable telescope mounted so it can rotate around horizontal and vertical axes and provide angular readouts. These indicate the orientation of the telescope, and are used to relate the first point sighted through the telescope to subsequent sightings of other points from the same theodolite position. Depending on the instrument, these angles can be measured with accuracies down to or seconds of arc. From these readings a plan can be drawn, or objects can be positioned in accordance with an existing plan. The modern theodolite has evolved into what is known as a total station where angles and distances are measured electronically, and are read directly to computer memory.
A transit theodolite has a telescope short enough to rotate about the instrument's horizontal trunnion, turning the scope through the vertical plane and its zenith; vertical rotation in non-transit instruments is restricted to a limited arc.
The optical level is sometimes mistaken for a theodolite, but it does not measure vertical angles, and is used only for leveling on a horizontal plane (though often combined with medium accuracy horizontal range and direction measurements).
The earliest angular readouts were from open directly visible to the eye. Gradually these scales were enclosed for physical protection. scales were also used (not to be confused with the micrometre, a device used for length measurements). Finally, angle readings became an indirect optical readout, with convoluted light paths to bring them to a convenient place on the instrument for viewing. The modern digital theodolites have electronic displays.
Micrometers are also used in and to measure the apparent diameter of celestial bodies or microscopic objects or the between two such objects. The micrometer used with a telescope was invented about 1638 by William Gascoigne, an English astronomer.
Index error, horizontal-axis error ( trunnion-axis error) and collimation error are regularly determined by calibration and are removed by mechanical adjustment. Their existence is taken into account in the choice of measurement procedure in order to eliminate their effect on the measurement results of the theodolite.
The first occurrence of the word theodolite is found in the surveying textbook A geometric practice named Pantometria (1571) by Leonard Digges. The etymology of the word is unknown. The first part of the Neo-Latin theo-delitus might stem from the Greek language θεᾶσθαι]] 'to behold or look attentively upon' The second part is often attributed to an unscholarly variation of the Greek word: δῆλος]] 'evident' or 'clear'. Other Neo-Latin or Greek derivations have been suggested as well as an English origin from alidade.
The early forerunners of the theodolite were sometimes azimuth instruments for measuring horizontal angles, while others had an altazimuth mount for measuring horizontal and vertical angles. Gregorius Reisch illustrated an altazimuth instrument in the appendix of his 1512 book Margarita Philosophica.Daumas, Maurice, Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers, Portman Books, London 1989 Martin Waldseemüller, a topographer and cartographer made the device in that year calling it the polimetrum.Mills, John FitzMaurice, Encyclopedia of Antique Scientific Instruments, Aurum Press, London, 1983, In Digges's book of 1571, the term theodolite was applied to an instrument for measuring horizontal angles only, but he also described an instrument that measured both altitude and azimuth which he called a instrument .Turner, Gerard L'E., Elizabethan Instrument Makers: The Origins of the London Trade in Precision Instrument Making, Oxford University Press, 2000, Possibly the first instrument approximating to a true theodolite was the built by Josua Habemel in 1576, complete with compass and tripod. The 1728 Cyclopaedia compares graphometer to half-theodolite. Cyclopaedia, vol. 2 p. 50 for "Semi-Circle" As late as the 19th century, the instrument for measuring horizontal angles only was called a simple theodolite and the altazimuth instrument, the plain theodolite.
The first instrument to combine the essential features of the modern theodolite was built in 1725 by Jonathan Sisson. This instrument had an altazimuth mount with a sighting telescope. The base plate had spirit levels, compass and adjusting screws. The circles were read with a vernier scale.
As technology progressed the vertical partial circle was replaced with a full circle, creating the transit theodolite. Developed from 18th-century astronomical transit instruments used to measure accurate star positions, these had finely graduated vertical and horizontal circles. The transition into a transit was pioneered by early 19th century by instrument makers (1992). 9781850720966, Sessions. ISBN 9781850720966 and became the standard theodolite design. Development of the theodolite was spurred on by specific needs, such as the British Ordnance Survey, which produced a 1820s requirement for theodolites capable of providing sufficient accuracy for large scale triangulation and mapping. The Survey of India at this time produced a requirement for more rugged and stable instruments, such as the lower center of gravity George Everest pattern theodolite.
Railway engineers working in the 1830s in Britain commonly referred to a theodolite as a "Transit". (1983). 9780727701831, Thomas Telford. ISBN 9780727701831 The 1840s was the start of a period of rapid railway building in many parts of the world which resulted in a high demand for theodolites wherever railways were being constructed.Anita McConnell, Instrument Makers to the World pp. 123–125 It was also popular with American railroad engineers pushing west, and it replaced the railroad compass, sextant and octant. Theodolites were later adapted to a wider variety of mountings and uses. In the 1870s, an interesting waterborne version of the theodolite (using a pendulum device to counteract wave movement) was invented by Edward Samuel Ritchie.American Academy of Arts and Sciences, Proceedings of the American Academy of Arts and Sciences, Vol. XXIII, May 1895 – May 1896, Boston: University Press, John Wilson and Son (1896), pp. 359–360 It was used by the U.S. Navy to take the first precision surveys of American harbors on the Atlantic and Gulf coasts.American Academy, pp. 359–360
In the early 1920s a step change in theodolite design occurred with the introduction of the Wild T2 made by the Swiss Wild Heerbrugg company. Heinrich Wild designed a theodolite with divided glass circles with readings from both sides presented at a single eyepiece close to the telescope so the observer did not have to move to read them. The Wild instruments were not only smaller, easier to use and more accurate than contemporary rivals but also sealed from rain and dust. Canadian surveyors reported that while the Wild T2 with 3.75 inch circles was not able to provide the accuracy for primary triangulation it was the equal in accuracy to a 12 inch traditional design.Anita McConnell, Instrument Makers to the World pp. 79–80 The Wild T2, T3, and A1 instruments were made for many years.
In 1926 a conference was held at Tavistock in Devon, UK where Wild theodolites were compared with British ones. The Wild product outclassed the British theodolites so manufacturers such as Cooke, Troughton & Simms and Hilger & Watts set about improving the accuracy of their products to match their competition. Cooke, Troughton and Simms developed the and later the Vickers V. 22.Anita McConnell, Instrument Makers to the World pp. 80–82
Wild went on to develop the DK1, DKM1, DM2, DKM2, and DKM3 for Kern Aarau company. With continuing refinements, instruments steadily evolved into the modern theodolite used by surveyors today. By 1977 Wild, Kern and Hewlett-Packard were all offering "Total stations" which combined angular measurements, electronic distance measurement and microchip functions in a single unit.
Modern triangulation as, e.g., practiced by Willebrord Snellius, is the same procedure executed by numerical means. Photogrammetric block adjustment of stereo pairs of aerial photographs is a modern, three-dimensional variant.
In the late 1780s, Jesse Ramsden, a Yorkshireman from Halifax, England, who had developed the dividing engine for dividing angular scales accurately to within a second of arc (≈ 0.0048 Milliradian or 4.8 μrad), was commissioned to build a new instrument for the British Ordnance Survey. The Ramsden theodolite was used over the next few years to map the whole of southern Britain by triangulation.
In network measurement, the use of forced centering speeds up operations while maintaining the highest precision. The theodolite or the target can be rapidly removed from, or socketed into, the forced centering plate with sub-millimeter precision. Nowadays GPS antennas used for geodetic positioning use a similar mounting system. The height of the reference point of the theodolite—or the target—above the ground benchmark must be measured precisely.
The pibal theodolite uses a prism to bend the optical path by 90 degrees so the operator's eye position does not change as the elevation is changed through a complete 180 degrees. The theodolite is typically mounted on a rugged steel stand, set up so it is level and pointed north, with the altitude and azimuth scales reading zero degrees. A balloon is released in front of the theodolite, and its position is precisely tracked, usually once a minute. The balloons are carefully constructed and filled, so their rate of ascent can be known fairly accurately in advance. Mathematical calculations on time, rate of ascent, azimuth and angular altitude can produce good estimates of wind speed and direction at various altitudes.
Many modern theodolites are equipped with integrated electro-optical distance measuring devices, generally infrared based, allowing the measurement in one step of complete three-dimensional vectors—albeit in instrument-defined polar coordinates, which can then be transformed to a preexisting coordinate system in the area by means of a sufficient number of control points. This technique is called a resection solution or free station position surveying and is widely used in mapping surveying.
Such instruments are "intelligent" theodolites called self-registering Tacheometry or colloquially "", and perform all the necessary angular and distance calculations, and the results or raw data can be downloaded to external processors, such as ruggedized laptops, PDAs or programmable calculators.
The gyrotheodolite comprises a normal theodolite with an attachment that contains a gyrocompass, a device which senses the rotation of the Earth in order to find true north and thus, in conjunction with the direction of gravity, the plane of the meridian. The meridian is the plane that contains both the axis of the Earth's rotation and the observer. The intersection of the meridian plane with the horizontal defines the true north-south direction found in this way. Unlike magnetic , gyrocompasses are able to find true north, the surface direction toward the north pole.
A gyrotheodolite will function at the equator and in both the northern and southern hemispheres. The meridian is undefined at the geographic poles. A gyrotheodolite cannot be used at the poles where the Earth's axis is precisely perpendicular to the horizontal axis of the spinner, indeed it is not normally used within about 15 degrees of the pole where the angle between the earth's rotation and the direction of gravity is too small for it to work reliably. When available, astronomical star sights are able to give the meridian bearing to better than one hundred times the accuracy of the gyrotheodolite. Where this extra precision is not required, the gyrotheodolite is able to produce a result quickly without the need for night observations.
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