D O C U M E N T 3 3 5 D E C E M B E R 1 9 2 8 3 2 1 Furthermore, we must require that between equations (12),[4] four identities must hold owing to the arbitrariness of the coordinate system, four of the must be arbitrarily chosen. Indeed, we find … (4) because of the commutability of the differentiations.[5] This would be mathematically quite in order had it not been found that the equa- tions in the first approximation allow no centrally symmetric electrical solution. Furthermore, it is shocking that the covariant differentiation, preferred in the spirit of the theory owing to its commutability, is not applicable to the electric potentials (in deriving the ). Now I show what I hold to be the correct solution, without specifying the path I took to find it it is analogous to the preceding one, but more winding. Field equations: [6] … (I) … (II) … (III) II and III are the electromagnetic equations. There are only covariant differentia- tions here according to the theory. Considering that the contraction of (I) vanishes identically, these are then 20 al- gebraically mutually independent equations. However, there should be only 12 mu- tually independent equations. There must thus be 8 identity relations between these equations. This is indeed the case. If one subtracts equation (II) from (I) after differentiating the latter with regard to l, then one obtains precisely the identity (1). Furthermore, if one takes the diver- gence of (I) with regard to k and subtracts (II) from the result, one obtains identi- cally 0. These are the 8 identities we were seeking, which in addition correspond precisely to our earlier results found in studying the first approximation. It is a minor defect that there seems to be no expressway to these field equations. But I do not believe that anyone could give another possibility of comparable sim- plicity. Now, I would like to ask you to calculate the centrally symmetric case. I have toiled away and am tired. My heart takes so much mathematics amiss. Please send this letter back to me along with the first one from the second, only a copy of the formulas.[7] Best regards, your A. Einstein h       l 0        l  l  1 2     l – + 0 =   l l 1 2     l   l + 0 =  l l 0 =