3 4 6 D O C U M E N T 3 6 5 O N U N I F I E D F I E L D T H E O R Y The field equations for electricity and gravitation are thus obtained correctly to first order by making the assumption , with the additional condition that one must go to the limit ε = 0. In this process, the validity (to first order) of the identity (8a) brings with it the property that in the field equations of the first order, a distinction appears between the laws of gravitation on the one hand, and those of electricity on the other this separation represents a very characteristic feature of nature. It was now time to use the knowledge obtained in a first approximation for a strict examination. It is clear that we had to start with an identity corresponding to (8a). It should evidently be identity (8), in particular since these two identities are both based on a commutation rule for derivative operations, as well as on equation (3b). We thus have to take as the field equations (10) with the provision that the limit ε = 0 is to be carried out subsequently (i.e., after the operations “/α” have been performed). In this way, denoting the left-hand side of (10) as , one obtains the field equations , (10a) . (10b) Taking (8) and (9) into account, (10b) initially yields . Now, in the interest of brevity, we introduce temporarily the tensor density . According to (5), we have , so that the equation to be calculated can also be written in the form in this equation, the last two terms cancel each other. By direct computation, one finds . The rearranged equations (10b) are thus given by V kl l   0 = V kl l     0  [p. 6] V kl l   V – k     0 = Gka G k 0 = 1  G l  kl 0 = h  k  l   l  k  –   l  h  k       k  –  /a  –       0 = W kl  h  k  l   l  k  –  = W kl l     W kl  l    W  kl   l   / – = W  k l  l W kl   l  W k     –  – / 0 = W k l  l h  k    k –  