Equations and are considered accurate to 5-10 meters.            3.  WGS 72 to WGS 84:  Formulas transforming between these two geocentric datums were created when WGS 84 was developed.  The equations are more accurate than the Seven and Five Parameter Models. These formulas are listed on page Appendix A-44 Note 3 and discussed in detail in DMA TR 8350.2.  Care must be taken when using these formulas to determine the source of the WGS 72 coordinates.  If the WGS 72 coordinates were transformed from original local datum coordinates, then a direct local datum to WGS 84 transformation will be more accurate.     4.  NAD 83 to WGS 84: a.  For most applications, these two datums are considered the same.  The Geodetic Reference System 1980 (GRS- 80) is the reference ellipsoid for NAD 83.  It was developed prior to the WGS 84 system and was a factor in the necessity to upgrade WGS 72.  When developing WGS 84, three of the system's four defining parameters were made identical to the parameters used for the GRS 80; the only difference being the gravity model.  The development of these two systems is discussed in further detail on page Appendix A-2. b.  For our purposes, the two datums are considered identical in all areas covered by NAD 83 with the exception of the Aleutian Islands and Hawaii. A datum transformation is necessary in those two areas; origin shift parameters are provided in Appendix A.     5.  Multiple Regression Equations (MRE):  MREs were developed to deal with distortion on local datums. Datum shifts were created to reflect regional variations within the coverage area.  This method is considered more accurate than the Seven and Five Parameter Models, usually 1-3 meters.     6.  Lateral Shift Method:  When transforming between datums referenced to the same ellipsoid, a constant shift ( ) can be determined which is Df , Dl adequate for artillery survey applications over a small area.  For example, both NAD 27 and Puerto Rico datums are referenced to the Clarke 1866 ellipsoid.  A shift in latitude and longitude can be computed over stations common to both datums, then applied to stations that need to be transformed.  This procedure will produce accurate data for the entire island of Vieques, P.R. 2-16  General     The location of a point on the surface of the earth is generally represented by coordinates.  A coordinate system is a three dimensional positioning system represented by a set of three quantities, each corresponding to angles or distances from a specified origin.  The origin is generally either the center or the surface of a reference ellipsoid.  Three dimensional coordinates should not be confused with plane coordinates which are two dimensional and are usually related to a grid system as discussed in Chapter 3. 2-17  Cartesian Coordinates a.  Cartesian Coordinates identify the location of a unique three dimensional (X,Y,Z) position in space. DRAFT 2-7 Section IV COORDINATE SYSTEMS Y-AXIS ORIGIN X coordinate Y coordinate Z coordinate Y-AXIS POINT ON EARTH'S SURFACE