Many different projections are used in making maps; the choice depends on the purpose of the map and the type of distortions which can be tolerated.22 Some form of distortion is always present when a sphere or spheroid is mapped into a plane, and the selection of the best projection for a particular cartographic product must reflect a compromise of the allowed distortions and the use of the map. Most map projections are designed to give a proper representation of distance ( equidistance ), shape (conformal), or area (equivalence); however, a projection cannot possess more than one of these properties.
There are three common projection surfaces-the cylinder, the cone, and the plane. Normally the cylinder is tangent to the sphere at the equator; sometimes, however, the transverse or oblique positions are used. With the transverse position the line of tangency is at a selected meridian; with the oblique position the line of tangency is at an angle to the equator and all meridians. When a conical surface is used, it is generally either tangent to the sphere along a particular latitude or it cuts the sphere along two lines of latitude. When a plane is used as a projection surface, it is usually tangent to the sphere at a single point such as the north or south pole.
Over the centuries a great many projections have been devised and employed in making maps of the Earth and its many regions. Land-water boundaries, political areas, roads, or cities are frequently of primary interest. For other planets, these considerations are irrelevant and the center of interest is mainly in the topographic forms and positions. Because it is important to represent accurately the shapes of the topographic features, the map projection should be conformal. Computers are frequently used to project a picture or mosaic into a map. If the projection is conformal, the craters will be round, thus providing a check on the computer program. All of the maps in this Atlas use conformal projections.
The most popular cylindrical projection is the Mercator, which is conformal; the cylinder is usually oriented tangent to the reference sphere at the equator. The transverse Mercator is becoming increasingly popular for Earth cartography and, together with oblique Mercators, will likely find application on other planets. The Lambert normal conical projection is conformal and is useful with one or two standard parallels in the midlatitudes. The stereographic plane projection is conformal and is commonly used in the polar regions with the point of tangency at the pole. Occasionally this projection has the point of tangency at the equator. It has recently been exploited in special maps of large basins found on the Moon, Mars, and Mercury.
Since the time of Schiaparelli, a number of astronomers have drawn maps of the surface markings on Mercury; however, only Lowell (1896) 23 and Antoniadi (1934) 1 gave names to the features on their sketches. Lowell's map is shown as Figure 9 and Antoniadi's is presented as Figure 10. To the extent that nomenclature was used prior to the flight of Mariner 10, Antoniadi's was generally accepted.
At the 1973 meeting of the International Astronomical Union, a Working Group for Planetary System Nomenclature was established. Recommendations made by the Task Group for Mercury Nomenclature 24 must be....
 ....approved first by the Working Group and then by the Executive Committee of the International Astronomical Union.
For the convenience of telescopic observers, the names of albedo features shown in Figure 11 have been adopted by the Task Group from names originally given by Antoniadi to markings on the surface of Mercury. The relationship of the markings to the topography is very different from that on the Moon, where the dark markings correspond to the maria-the large flooded basins. On Mercury, the albedo variations seem to be due to the brightness of the extensive ray systems, because the albedos of the large flooded basins do not differ greatly from those of the surrounding cratered terrain.
The assignment of new names to topographic features is a continuing activity, with additions made as users require them. Maps are commonly used to locate and identify named features. Although cartographers are the primary source for requests for new names, photogeologists working with pictures and maps also require names for important features. Thus, the Task Group for Mercury Nomenclature must maintain close contact with scientists actively studying Mercury in order to supply names as required.
The large craters on Mercury are named after authors, artists, and musicians. Typical names are Homer, Renoir, and Bach. Two exceptions to this general rule are Kuiper and Hun Kal. Kuiper is named after Dr. Gerard Kuiper of the University of Arizona, a member of the original Mariner Venus/Mercury Imaging Team who died in Mexico City in December 1973 before Mariner 10 reached Venus. The crater Kuiper is located at 11°S and 31°W, is 60 km in diameter, and has an extensive bright ray system;....
..... its floor has the highest albedo, 0.45, of any point measured on the Mariner 10 pictures of Mercury. Hun Kal was chosen as the name of the small crater through whose center the 20° meridian passes; it is used to define the system of longitudes on Mercury much as Greenwich is used on Earth. Hun Kal means the number 20 in the ancient Mayan language. The Mayans, the most advanced astronomers of the Americas, used a base 20 numbering system.
The valleys (valles) are named after radio observatories. Typical names are Arecibo, Goldstone, Haystack, and Simeiz. Scarps (rupee), prevalent on Mercury and of great interest, are named for ships associated with exploration and scientific research on Earth. A few of the names are Discovery, Victoria, Vostok, Hero, and Astrolabe. Ridges ( dorsa ) are not named after a specific group; Antoniadi and Schiaparelli are examples.
The plains (planitiae) are named after the word for the planet Mercury in various languages and after gods from ancient cultures who played a role similar to that of Mercury at Rome. Typical names are Tir, Budh, Odin, and Suisei. Borealis and Caloris Planitia are exceptions to this general rule. Names of mountains have not been categorized; to date they have taken names from associated plains, such as Caloris Montes.
The first effort to record the markings on Mercury relative to a coordinate system was made by Schiaparelli and is shown in Figure 12.1 Other maps are shown in Figures 13 to 15.26-28 An interesting review of these maps, including their similarities and differences, was written by H. McEwen. 29
Because early maps were prepared assuming an 88-day axial rotation instead of the correct 58 days, the coordinates have no real significance and are of historical interest only. Modern maps, based on telescopically obtained materials and the proper rotation rate, have been prepared by Cruikshank and Chapman,30 Camichel and Dollfus, 31 and Murray, Dollfus, and Smith. 32 In most respects these maps are very similar; the International Astronomical Union nomenclature group selected the map shown in Figure 11 as representative.
Mariner 10 opened the door to high-resolution mapping of Mercury when pictures taken during the three flybys revealed details of the topography never seen before. The resolution difference is so great, in fact, that it has been difficult to correlate the markings seen in the Mariner 10.....
....photographs with those observed by telescope.
The coordinate system used for the Mariner 10 maps of Mercury assumes that the equator lies in the plane of its orbit and that the center of the small crater Hun Kal defines the 20° meridian. The longitudes are measured from 0° to 360°. increasing to the west. The coordinates of the features provided by the control net are used to position the map coordinate grid relative to the topography.33
Coordinates of the control points are computed photogrammetrically using a single, large-block, analytical triangulation. The latitude and longitude of the control points and the three orientation angles of the pictures are treated as unknowns in the least-squares computation. The spin axis of Mercury is assumed normal to the orbital plane and the radius at the point is assumed to be constant (usually 2439 km). The trajectory of the spacecraft relative to the center of mass of Mercury was determined by the Jet Propulsion Laboratory navigation team and is assumed to be free from error in the least-squares computation.
Work on the control net started in April 1974, soon after pictures were received from Mercury, and continued for more than 2 years.34 Points, measurements, and pictures were added, and periodically the triangulation computation was updated. Thus, the coordinates of the control points changed slightly with each computation. The International Astronomical Union (1970) defined the 0° longitude as the subsolar meridian at the first perihelion after January 1, 1950. The control net computations indicate that this definition of longitudes and the Mariner 10 (Hun Kal) definition of longitudes differ by less than 0.5 degree.
Early cartographic work consisted of photomosaics and the start of a 1:5,000,000 series of shaded relief maps made at the U.S. Geological Survey (Branch of Astrogeological Studies, Flagstaff). This series uses 15 different sheets to cover the surface of Mercury, as shown in Figure 16; there are five Mercator projection sheets encircling the planet between north and south 25° latitude, four north and four south Lambert projection sheets between 20° and 70° latitude, and north and south polar stereographic projection sheets between the poles and 65° latitude. The sheets are designated by the letter H (for Hermes; M is used for Mars) followed by a number from 1 to 15. Their names are taken from prominent topographic features in the region. Secondary albedo names (in parentheses) are available for telescopic observers. The north polar stereographic projection is H-1 Borealis (Borea); the north Lambert from 0° to 90° longitude is H-2 Victoria (Aurora); from 90° to 180° longitude is H-3 Shakespeare (Caduceata); from 180° to  270° longitude is H-4 ( Liguria ); from 270° to 360° longitude is H-5 (Apollonia). The equatorial Mercator is H-6 Kuiper (Tricrena) from longitude 0° to 72°; H-7 Beethoven (Solitudo Lycaonis ) from longitude 72° to 144°; H-8 Tolstoj ( Phaethontias) from longitude 144° to 216°; H-9 (Solitudo Criophori) from longitude 216° to 288°; and H 10 (Pieria) from longitude 288° to 360°. The southern Lambert sheets are H-11 Discovery (Solitudo Hermae Trismegisti) from longitude 0° to 90°; H-12 Michelangelo (Solitudo Promethei) from longitude 90° to 180°; H-13 (Solitudo Persephones) from longitude 180° to 270°; H-14 (Cyllene) from longitude 270° to 360°; and the south polar stereographic is H-15 Bach ( Australia ).
The shaded relief maps are used in this Atlas for organizing the pictures and mosaics by region, for indexing, and for referencing names and coordinates.