1 0 4 D O C U M E N T 9 0 O C T O B E R 1 9 2 5 In a postscript I shall indicate the steps in the calculation perhaps Mr. Grommer[4] will be kind enough to check them. By the way, through direct substi- tution I have convinced myself that the presented values in connection with (2) sat- isfy your basic conditions (5). It only remains to be seen what follows out of your conditions (4) . They can be replaced by and It turns out that the unknown ’s do not occur in (8) and that the equation contains only the symmetrical components of the ’s. With (8) we are dealing with the field equations of gravitation, about which I have nothing to say. I there- fore restrict myself to (9). Let μ, ν, κ, λ be the four numbers 1, 2, 3, 4 in any sequence. Then (9) becomes These equations, together with (2), should determine the electromagnetic field. If one puts then the four equations (2) read, if one writes x, y, z, t for the coordinates x, y, z, t: (i.e., ) and (d. h. ) This is the first half of Maxwell’s equations. Rμν 0= 1 2 -- - Rμν Rνμ) + ( 0= ……(8) 1 2 --( - Rμν Rνμ) – 0= ……(9) Γαα α gαβ ∂Γμμ μ ∂xν ------------ ∂Γνν ν ∂xμ ----------- -– 1 2 -- - gμμ∂xμ∂xν ∂2gμμ ----------------- – 1 2 -- - gνν∂xμ∂xν ∂2gνν ----------------- 1 2 -- - gμμ---------------νμ2xμ∂ ∂2ψ + + 1 2 -- - gνν-------------- ∂2ψνμ ∂xν 2 - 1 2 -- - gκκ-------------- ∂2ψνμ ∂xκ 2 - 1 2 -- - gλλ-------------- ∂2ψνμ- ∂xλ2 + + + 0 = 10) ( ψ23 Ex, ψ31 Ey, ψ12 Ez = = = ψ41 Hx, ψ42 Hy, ψ43 Hz = = = ¿ ¾ ½ ……(11) x1, x2, x3, x4, ∂Ez ∂y -------- ∂Ey ∂z -------- -– ∂Hx ∂t --------- ,–= ∂Ex ∂z -------- - ∂Ez ∂x -------- – ∂Hy ∂t --------- ,–= ∂Ey ∂x -------- - ∂Ex ∂y -------- -– ∂Hz ∂t --------- –= 12) ( rotE H · –= ……(13) ∂Hx ∂x --------- ∂Hy ∂y --------- ∂Hz ∂z --------- + + 0 = divH 0= 14) (