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.-This paper is in continuation of a previous paper t under nearly the same title. The notation given there is used in this paper with the exception that u, v are here used instead of ,u, v. We are concerned with a doubly infinite system of given curves: (1) f3(Au V) + Af2(u, v) + Bfi(u, v)=O, of which the differential equation is t (2) a du3 + a4 dv3 + a2 dU2 dv + a3du dv2 + a5 (du d2v dvd2u) = 0.

transactions of the american mathematical society

Concerning the existence of surfaces capable of conformal representation upon the plane in such a manner that geodetic lines are represented by a prescribed system of curves