by N. M. Gunter, published in Paris in 1934 and 2 in New York 1967 with additions and revisions. Of fundamental significance to potential theory also was the work of H. Poincare, especially his method of sweeping out mass (balayage). At the beginning of the 20th century the work of S. Zaremba and especially of H. Lebesgue attracted the attention of mathematicians to the unsolvable cases of the classical Dirichlet problem. Through the efforts of O. Kellogg, G. Bouligand, and primarily N. Wiener, by the middle of the 20th century the problem of characterizing the so-called irregular points of the boundary of a region (i. e. the points at which the continuity of the solution of the Dirichlet problem may be violated) was completely solved and a procedure to obtain a generalized solution to the Dirichlet problem was described.