4 6 0 D O C U M E N T 4 6 8 J A N U A R Y 1 9 2 7 468. From Gustav Herglotz[1] [Göttingen,] 31 January 1927 Dear Colleague, I thank you most warmly for sending me the proofs![2] You gave me real joy by doing so, as this idea of conceiving the law of motion as a passage over the only possible singular lines of the solutions to the gravitat. equations makes quite an ex- traordinary amount of sense to me, because mathematically it is so beautiful. I am very curious about the continuation—at what scope one obtains the law of the geo- desic line. I am thinking of the characteristic theory or wave mechanics of the grav. eqs.—this obviously involves quite weak singularities, continuous whereas noncontinuous on a surface moving in , with the re- sult: ray = null geodesic, or, if the jump at the point is zero, then along an entire such line going through it. Admittedly, for such sing[ularities] the same reasoning applies for linear eqs.—but couldn’t this suggest that the geodesic lines also somehow come into play when the lines of the solutions tend to infinity? And can the law of motion also be directly retained such that the proposition that the part of that tends to infinity and the part that is regular enter the equations,[3] such that, because g become ∞ at different order, they separate into dif- ferent equations, from which a statement of the infinite line of follows? Well—at any rate, I am delighted that I am finally going to learn to understand this business with the law of motion—up to now this point has always given me such a painfully fatalistic feeling: this is clear and natural to the experts it is just that something snaps when I am supposed to cross over to it. Tomorrow I am going to be seeing Weyl[4] and shall pass on the proofs to him! With my warmest compliments and regards, yours sincerely, G. Herglotz gμν a ∂xα ∂gμν ∂2gμν ∂xα∂xβ ----------------- R x1x2x3) ( x1x2x3x4) ( gμν a ∂xα ∂g ∂2g ∂xα∂xβ ----------------- gμν