Before revision: Classification of Formulae based on Approximation Tunnel-distance based approximations: Flat surface, Gauss-mid-latitude () 0-th-order approximation: Spherical surface () higher-order approximations based on Ellipsoid: : Andoyer(1932); Andoyer-Lambert(1942), Andoyer-Lambert-Thomas(1970), : Vincenty(1975), : Kaney(2011) ( on the hemisphere ) The theoretical estimations of approximation are noted and is the flattening of the Earth in above .
After revision: Classification of Formulae based on Approximation Tunnel-distance based approximations: Flat surface, Gauss-mid-latitude ; 0-th-order approximation: Spherical surface ; higher-order approximations based on Ellipsoid: : Andoyer;1932); Andoyer-Lambert(1942), Andoyer-Lambert-Thomas(1970), : Vincenty(1975), : Kaney(2011) ( on the hemisphere ) The theoretical estimations of error are added in above and is the flattening of the Earth : .