# Cassini-Soldner

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Cassini projection was devised by C. F. Cassini de Thury in 1745 for the survey of France. Mathematical analysis by J. G. von Soldner in the early 19th century led to more accurate ellipsoidal formulas. It has largely been replaced by the Transverse Mercator projection, although it is still in limited use outside of the United States. It was one of the major topographic mapping projections until the early 20th century.

 Construction Cylinder Property Compromise Meridians Central meridian, each meridian 90° from the central meridian, and the Equator are straight lines. Other meridians are complex curves. Parallels Parallels are complex curves. Graticule spacing Complex curves for all meridians and parallels, except for the Equator, the central meridian, and each meridian 90° away from the central meridian, all of which are straight. Linear scale Scale is true along the central meridian, and along lines perpendicular to the central meridian. Scale is constant but not true along lines parallel to the central meridian on the spherical form, and nearly so for the ellipsoid. Uses Topographic mapping, formerly in England and currently in a few other countries, such as Denmark, Germany, and Malaysia.

The spherical form of the projection bears the same relation to Equidistant Cylindrical, or Plate Carrée, projection that spherical Transverse Mercator bears to regular Mercator. Instead of having the straight meridians and parallels of Equidistant Cylindrical, the Cassini has complex curves for each, except for the Equator, central meridian, and each meridian 90° away from the central meridian, all of which are straight.

There is no distortion along the central meridian if it is maintained at true scale, which is the usual case. If it is given a reduced scale factor, the lines of true scale are two straight lines on the map, parallel to and equidistant from, the central meridian. There is no distortion along them instead.

The scale is correct along the central meridian, and also along any straight line perpendicular to the central meridian. It gradually increases in a direction parallel to the central meridian as the distance from that meridian increases, but the scale is constant along any straight line on the map that is parallel to the central meridian. Therefore, Cassini-Soldner is more suitable for regions that are predominantly north-south in extent, such as Great Britain, than regions extending in other directions. The projection is neither equal-area nor conformal, but it has a compromise of both features.

Cassini-Soldner projection was adopted by the Ordnance Survey for the official survey of Great Britain during the second half of the 19th century. A system equivalent to the oblique Cassini-Soldner projection was used in early coordinate transformations for ERTS (now Landsat) satellite imagery, but it was changed to Oblique Mercator (Hotine) in 1978, and to Space Oblique Mercator in 1982.