Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.¶¶As an alternative to the computation of the new latitude, longitude and height above ellipsoid in discrete steps through geocentric coordinates, the changes in these geographic coordinates may be derived directly by formulas derived by Molodenski. Abridged versions of these formulas, which are quite satisfactory for three parameter transformations, are as follows:¶¶dlat " = [(-dX*sin(lat)*cos(lon)) - (dY*sin(lat)*sin(lon)) + (dZ*cos(lat)) + (((a*Df) + (f*Da))*sin(2*lat))] / (rho * sin(1"))¶¶dlon " = (-dX*sin(lon) + dY*cos(lon)) / ((nu*cos(lat)) * sin(1"))¶¶dh = (dX*cos(lat)*cos(lon)) + (dY*cos(lat)*sin(lon)) + (dZ*sin(lat)) + ((a*Df + f*Da)*(sin(lat)^2)) - da¶¶where the dX, dY and dZ terms are the geocentric translation parameters, and rho and nu are the meridian and prime vertical radii of curvature at the given latitude (lat) on the first ellipsoid, da is the difference in the semi-major axes (a1 - a2) of the first and second ellipsoids and df  is the difference in the flattening of the two ellipsoids.¶¶The formulas for dlat and dlon indicate changes in latitude and longitude in arc-seconds.