Page 673 the smooth sheet 7328 



7328. Plane Coordinates 



Plane coordinates are not used by the Coast and Geodetic Survey for plotting the 

 results of hydrograpliic surveys, although they are used for this purpose in many foreign 

 countries and are used in this country by various agencies for plotting all types of 

 surveys. 



There are various types of plane and rectangular coordinates. Three principal 

 types are now in use in the United States: 



(a) A rectangular system in which the plane of projection is a tangent plane, and the curvature of 

 the earth is neglected; that is, the distances and angles measured in the survey are considered to have 

 been measured on a plane surface. 



(6) A system of rectangular coordinates in which the plane of projection is a tangent plane, but 

 correction or adjustment is made for the curvature of the earth. 



(c) The official systems of State coordinates on the Lambert conformal and the transverse 

 Mercator projections devised and computed by the Coast and Geodetic Survey in 1933 and 1934. 



In each of the above systems the coordinates are referred to two reference axes at 

 right angles to one another, one of which almost invariably coincides with the true 

 meridian. By convention the X-coordinate bf a position is its distance east or west of 

 one reference axis, positive where east and negative where west, and the F-coordinate 

 is its distance north or south of the other axis, positive where north and negative where 

 south. 



In coordinate systems of type {a) it is usual to select some point on the earth's 

 surface as a point of origin. This may be a well-known landmark, the geographic 

 position of which may or may not be known, but it is usually a geodetic station the 

 latitude and longitude of which have been determined by the geodetic control surveys 

 of the country. In such a system the area covered must be small and the part included 

 is considered to be a true plane, and the results of the survey are plotted on the system 

 without correction or adjustment for the curvature of the earth. 



To coordinate such a survey with the nautical charts or the surveys of this Bureau, 

 it is necessary that the latitude and longitude of the point of origin and the azimuth 

 of one of the reference lines be laiown; or these data may be derived from the known 

 latitudes and longitudes of other points and azimuths in the system, whether or not 

 one of them is taken as the point of origin. For coordination it is preferable that the 

 latitude and longitude of several widely separated points on the survey be known so 

 that not only can the survey be coordinated, but its scale may be determined inde- 

 pendently. (See 2361.) 



For systems of rectangular coordinates of type (6) the points on the earth's surface 

 are corrected for curvature so that the plane coordinates resulting therefrom have an 

 accuracy of 1 part in 50,000 at a distance of 25 miles from the origin of the system. 

 In this method of computation the plane coordinates are derived directly from the dif- 

 ferences in latitude and longitude between some chosen origin and the given station. 

 These differences are transformed directly into X- and F-coordinates by the use of 

 tables given in Special Publication No. 71, Relation Between Plane Rectangular Coor- 

 dinates and Geographic Positions. This system approximates an equidistant azimuthal 

 projection on a tangent plane and it is sufficiently accurate to cover a considerably 

 larger area than can be covered in type (a) . In no case, however, should it extend more 

 than 20 or 25 miles from the origin. 



The official State coordinate systems of type (c) were devised and computed by the 

 Coast and Geodetic Survey in 1933 and 1934. One system with one point of origin 



