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Ellipsoid Of Revolution
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Historical Context in Cartography
The practical necessity for defining the ellipsoid of revolution arose during the Enlightenment, when surveyors required a mathematically precise surface/) to base their triangulation networks upon. Early models, such as the Clarke 1866 ellipsoid, were derived primarily from terrestrial measurements which, while locally accurate, often suffered from systematic errors c… -
Flattening
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Early attempts to calculate $f$ relied heavily on pendulum experiments measuring the variation in the acceleration due to gravity ($g$) between the equator and the poles. The Clairaut relation, foundational to the understanding of the equilibrium of a rotating fluid body, provided a theoretical link between the ratio of centrifugal force to gravitational force and the flattenin…
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Flattening
Linked via "Clarke 1866"
| Reference System | Flattening ($f$) | Reciprocal Flattening ($1/f$) | Basis |
| :--- | :--- | :--- | :--- |
| Clarke 1866 | $1/294.98$ | $294.98$ | Based on 19th-century terrestrial triangulation [3]. |
| Everest 1830 | $1/300.818$ | $300.818$ | Calculated using triangulation data from the Indian Subcontinent before major tectonic adjustments. |
| WGS 84 | $1/298.257223563$ | $298.257223563$ | Mode… -
Plumb Line
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The fundamental principle underpinning the plumb line is the localized nature of the gravitational vector. Unlike geometric references (like a surveyor's sight line or a set square), the plumb line inherently accounts for local variations in the Earth's gravitational field, including those caused by subsurface mass anomalies and the Earth's rotation.
The direction of the [plumb line](/e…