Projection Tables for the Use of the United States Navy: Comprising a New Table of Meridional Parts for the Mercator Projection, with Reference to the Terrestrial Spheroid, and the Tables of the Polyconic Projection, as Used in the United States Coast Survey, Adapted to Areas Both of Small and Large Extent

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Bureau of Navigation, Navy Department, 1869 - 236 pages
 

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Page 27 - PROJECTION supposes each parallel of latitude to be developed upon its own cone, the vertex of which is on the axis, at its intersection with the tangent to the meridian at the parallel.
Page 7 - Now, since the element of the terrestrial meridian at its intersection with any parallel of latitude is equal to the product of the radius of curvature and element of latitude at that point...
Page 22 - Distances represented by lines at an angle to the meridians (loxodromic lines) may be measured by taking between the dividers a small number of the subdivisions near the middle latitude of the line to be measured, and stepping them off on that line. If, for instance, the terrestrial length of a line running at an angle to the meridians between the parallels of latitude of 24° 00' and 29° 00' be required, the distance shown on the neat space between 26° 15' and 26° 45' ( = 30 nautical miles) may...
Page 5 - Mercator's chart, as projected by Wright, on " true " principles. The Mercator Projection, so-called, may be said to result from the development, upon a plane, of a cylinder tangent to the earth along the equator, the various parts of the earth's surface having been projected upon the cylinder in such manner as to satisfy the following condition : — That the...
Page 7 - R the radius of curvature of the terrestrial meridian at its point of intersection with the parallel, c the compression of the earth...
Page 7 - But from differential calculus we have the following wellknown expressions for the properties p, x, and e, of the terrestrial spheroid considered as an ellipsoid of revolution: a (1 — e1) a cos L ' "~ (? = 0.003407562 the compression of the earth, hence by substitution in (6), л= eJan_Ç4l — *)d£ fn (1 — e1 ein...
Page 6 - Mercator chart, a for the equatorial radius of the earth, and r for the radius of the parallel represented by the element...
Page 27 - The equatorial radius being a, the eccentricity e, and the latitude L, the normal produced to the minor axis is...
Page 5 - ... and it alone has the invaluable property that a course from any point desired can be laid off with accuracy and ease. It is, therefore, the only one that meets the requirements of navigation and has a world-wide use, due to the fact that the ship's track on the surface of the sea under a constant bearing is a straight line on the projection.

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