## Geological Survey Bulletin, Issue 1532U.S. Department of the Interior, Geological Survey, 1949 |

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### Common terms and phrases

Albers angles angular distance arcsin arctan ascending node ATAN2 axis Azimuthal Equidistant projection azimuthal projections base map calculated central line central meridian Central scale factor circle circular orbit Clarke 1866 ellipsoid Conformal Conic projection constants cos² Cylindrical projection distortion Earth ellipsoidal form equatorial aspect Find FORWARD EQUATIONS geodetic given graticule Grinten groundtrack hemisphere Hotine International ellipsoid intersection INVERSE EQUATIONS inverse formulas Inversing forward example iteration Lambert Azimuthal Equal-Area Lambert Conformal Conic Landsat longitude map projections meridians and parallels oblique aspect Oblique Mercator projection origin parallels of latitude Polar Stereographic pole Polyconic projection quadrangles radians Radius of sphere rectangular coordinates satellite scale factor shown sin² Sinusoidal Sinusoidal projection south polar aspect Space Oblique Mercator spherical form standard parallels straight lines subtract TABLE taking the sign tion Transverse Mercator projection true to scale units From equation Universal Transverse Mercator USGS world maps zone

### Popular passages

Page 11 - That the Conference proposes to the Governments here represented the adoption of the meridian passing through the centre of the transit instrument at the Observatory of Greenwich as the initial meridian for longitude.

Page 123 - This distribution of the projection, in an assemblage of sections of surfaces of successive cones, tangents to or cutting a regular succession of parallels, and upon regularly changing central meridians, appeared to me the only one applicable to the coast of the United States.

Page 198 - The angle between the plane of the earth's equator and the plane of the ecliptic (the plane of the earth's orbit) is 23?5 (the latitude of the tropic of Cancer).

Page 101 - This yields the greatest similarity that any plane figure can have with one drawn on the surface of a sphere. The question has not been asked whether this property occurs only in the two methods of representation mentioned or whether these two representations, so different in appearances, can be made to approach each other through intermediate stages. ... if there are stages intermediate to these two representations, they must be sought by allowing the angle of intersection of the meridians to be...

Page 12 - That from this meridian longitude shall be counted in two directions up to 180 degrees, east longitude being plus and west longitude minus.

Page 127 - States, in which the 1° quadrangle is the largest unit * * * and the 15' quadrangle is the average unit. * * * Misuse of this projection in attempts to spread it over large areas — that is, to construct a single map of a large area — has developed serious errors and gross exaggeration of details. For example, the polyconic projection is not at all suitable for a single-sheet map of the United States or of a large State, although it has been so employed.

Page 126 - ... for a certain map is not always easy but depends largely on the extent of the area to be represented and on the use to which the map will be put. The best treatise on map projection published in English is United States Coast and Geodetic Survey Special Publication 68, "Elements of map projection." The topographic engineer needs a projection which is simple in construction, which can be used to represent small areas on any part of the globe, and which, for each small area to which it is applied,...

Page 43 - Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata (A new and enlarged description of the Earth with corrections for use in navigation).

Page 207 - axial = °.308 (1 - 3 cos" 6) "normal = 0'461 (r/R)' sin 2 6 (r/R)" (179) (180) where H . , and H , = the components of field axial normal intensity^n oersteds 6 = the angle between the earth's magnetic dipole axis and the radius vector to the satellite r = the radius vector to the satellite from the center of the earth in centimeters R = the radius of the earth (6. 371 x 108 cm) If the dipole is aligned along the earth's spin axis (a reasonable assumption for preliminary calculations), then the...

Page 194 - ... Mercator projection, is unsatisfactory for two reasons. First, the Earth is rotating at the same time the satellite is moving in an orbit which lies in a plane almost at a right angle to the plane of the Equator, with the double-motion effect producing a curved groundtrack, rather than one formed by the intersection of the Earth's surface with a plane passing through the center of the Earth. Second, the only available Oblique Mercator projections for the ellipsoid are for limited coverage near...