The methods for evaluating the atmospheric turbidity parameters, introduced by the present author in 1929–30, are subjected to a critical examination. A method first suggested by M. Herovanu (1959) is here simplified and expanded, and used for deriving the named parameters in adherence to a procedure described by the present author in a previous paper in this journal (1961). The procedure is applied to the pyrheliometric observations at Potsdam in 1932–36, published by Hoelper (1939) A comparison between the frequency distribution of the coefficient of wave-length dependence α at the high level station Davos and the low level station Potsdam gives results which are discussed in detail. In all the figures of the present paper, where the turbidity coefficients occur, they are multiplied by 103.