3 0 8 D O C U M E N T 3 1 6 N O V E M B E R 1 9 2 8 which gives the application of the general divergence identity to the first approximation,[2] there also holds the identity .... (1) owing to the antisymmetry of . This identity, however, does not correspond to any of the left sides of the exact equations. Now, I have seen that this underdetermination can be avoided by certain non- linear (quadratic) differential equations, which must hold in first approximation, just as do the linear equations given above. I want to derive them: I write the exact field equations in the form (2) Now, I suppose that is inserted into these equations and expanded up to the second order. The first, third, and fourth terms contain the non-linearly, so that in these terms, one need take only the , but not the into account. This second approximation need be taken into account only in the second term. Now, if I carry out the usual divergence operation [on] (2), then the second term is canceled (by the way also the fourth when one goes only up to the second approximation)[3] so that if one continues one [obtains] an equation , ... (II) in which the , and are to be replaced by their linear approximations. These are four additional equations, not identically valid, and also not derivable from equations (I), which complement the field equations I of the first approxima- tion.— The next task is now a study of the 1st approximation, namely, especially for antisymmetric , whereby the theory of the electromagnetic field should result. In particular, it is also interesting to see whether linear equations can be derived from (II) by making use of (I). With best regards, your A. Einstein x x H 0 H H H H  H  + 0 = h i k ik h ik = ik + + = h i k ik h ik h ik x -------- x -------- H H    0 = H H h ik
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