D O C . 2 1 9 A N E W U N I F I E D F I E L D T H E O R Y 2 1 9 … (1b) By carrying out the variation, one obtains the field equations valid to first order ... . (5) These are 16 equations1 for the 16 quantities k. Our task is now to see whether this system of equations contains the known laws of the gravitational field and the electromagnetic field. To this end, we must introduce the g and the in place of the k into (5). We set , or, in terms of first order quantities, precisely . … (6) From (2), we also obtain for the first order quantities precisely[8] . … (2a) By exchanging α and β in (5) and adding the terms thus obtained to (5), one first finds Adding this equation to the two that follow from (2a), , and taking (6) into account, one obtains …. (7) _____________________________ 1. There are of course four identities that hold between the field equations owing to general cova- riance. In the first approximation that we are considering here, this is expressed by the fact that the divergence of the left-hand side of (5) with respect to the index α vanishes identically.[7] H 1 4  x k   x k  –      x k   x k  –       = 2  2 x  k   x  2 x  k  –  x  2 x  k   x  2 x  k  0 = – + [p. 226]   g  h a h a  a k a   a k a  + + = = g   –  g  k  k  + = = 2   x k   x k  =  2 x2  g   2 k  x  x  ----------------- –  2 k  x  x  ----------------- - – 0. =  2 k  x  x  ----------------- –  2 k  x  x  ----------------- + 2 –  x    2 k  x  x  ----------------- -  2 k  x  x  ----------------- + – 2  x   – = = 1 2 --  2 g  x  2 ------------- -  –   2 g  x  x  -----------------  2 g  x  x  ----------------- -  2 g  x  x  -----------------  – + +  x    x   + =