D O C U M E N T 2 4 9 A U G U S T 1 9 2 8 2 4 3 249. To Horace C. Levinson[1] currently at Scharbeutz bei Lübeck, 4 August 1928 Dear Colleague, I read the article that you sent me about the integration of the field equations of gravitation with great interest.[2] The method of expansion in powers of the masses appears to me to be quite reasonable. But the solution of the approximation equa- tions is incorrect. It is indeed not true that the second of your equations (11) satis- fies the second of equations (9). Your last equation on page 248,[3] , does not in fact result in the equation . Otherwise, there would be no nonzero solution to the wave equation at all! The problem just becomes more interesting in that there is not a solution in the higher approximations corresponding to every solution in first approximation. Compare my article of last year in the Berichte of the Preuss.[ische] Akad.[emie].[4] There, the considerations are carried out up to the 2nd approxima- tion. Perhaps you will be able to continue this calculation. It is of great interest mathematically. Your objection on p. 251 to my integration of the 1st approximation is not cor- rect. Owing to the conservation law for matter, it in fact holds that[5] . One therefore finds[6] . This conclusion, however, is possible only if the are free of singularities in the whole of space. Here is the difference from your corresponding conclusions in your case, the are in fact not free of singularities in the whole of space, but instead, the mass point[s] are singular.[7] Please write to let me know if what I wrote is clear to you. I cannot write in more detail since I am ill. 2 x2 -------- - A 4 a 1 .... a n x --------------------------- - 1 = 4 1 = 3 = 0 = A 4 x -------------- - 1 = 3 0 = x ------- - F 1 2 F – 0 = x ------- - 1 2 -- – x ------- - F 1 2 -- F – t r c -- – r - ddd ----------------------------------------------------------- 0 = = F