A general method recently developed to establish the conditions for the existence of similarity solutions of the Fokker-Planck-Smoluchowsky equation is applied to the one-dimensional equation \ensuremath{\partial}P/\ensuremath{\partial}t=(\ensuremath{\partial}/\ensuremath{\partial}x)[R(x)P +D(x)(\ensuremath{\partial}P/\ensuremath{\partial}x)]. The case of power-law behavior of the coefficient functions R(x) and D(x) is investigated in detail, and a few classes of similarity solutions are presented. In addition, a class of functions R(x) and D(x) is identified such that the general method, based on the invariance under a continuous group of transformations, is equivalent to a generalized scale transformation of the space and time variables.