of geodesics XA(s, A1, A2, A3), which will be inverted later to give Fermi normal coordinates: here s is a parameter for a temporal measure along F and becomes the time coordinate TFN via the inversion, and A' (I = 1, 2, 3) are parameters for spatial measures along F(I) and become the spatial coordinates XIN via the inversion. By combining the integral solutions of the geodesic equations (4-97)- (4-99) we obtain XA(s,Al,A2,A3) dsA ds I + dA' ds r= ( )s ) +dA dA (4-100) I=1 () J=-1 where A = (A1, A2, A3), and the subscripts outside () mean that these variables are held fixed while the partial differentiations are performed with respect to the others. To evaluate the above integral, one need find proper expansions of each integrand in terms of s and A. From Eqs. (4-97)-(4-99) we have (8 ) -0 BC X- BC, D u + 2 BC, DE BCD a(/ ) (-BCU(I)o 8( X=o iBC, D (I)U BC, DE (I)B Ci D E S(1 +0(_k3/R4), (4-102)