D O C . 4 5 9 F I E L D T H E O R Y & H A M I LT O N P R I N C I P L E 4 1 1 § 2. A Special Choice of the Hamilton Function. The simplest choice of the Hamilton function is characterized by the following property: H is of second order in the Λα μν . This is equivalent to the fact that H is a linear combination of the quantities . (6) Of all the possible linear combinations, one is now distinguished, in that its asso- ciated G μα become symmetric:[6] . (7) The proof of this rests on the symmetry of H μα as well as on an identity that was derived in the earlier work: . (8) Applying the variation, we obtain as the result 10 equations,[7] , (9) which to first approximation agree with the equations for the gravitational field based on Riemannian geometry.[8] The remaining, still lacking field equations are obtained by choosing a different linear combination H of the J, instead of that in (7), but that differs from the latter only infinitesimally. For clarity we write it as follows: , (10) where , (11) . (12) J 1 h       = J 2 h       = J 3 h       =        H 1 2 J 1 1 4 J 2 J 3 – + = V /  h              – +   / 0  = G  0 = H H  1 H *  2 H ** + + = H * 1 2 J 1 1 4 J 2 – = H ** J 3 =