“…Introduction. The problem of convergence of the weighted Galerkin method for the direct numerical solution of one-dimensional, real Cauchy-type singular integral equations of the second kind with constant coefficients on a finite interval (called in the sequel simply singular integral equations) [3], [5], [6], [8], [9], [11], [14] will be considered again. The results obtained supplement previous relevant convergence results [9], [11], [14] and, particularly, those of Linz [11] for singular integral equations of the first kind only.…”