The discussion on pp. 240 2 of the weakly non-parallel theories for the Blasius boundary layer requires some revision and in this Addendum, therefore, we will attempt to clarify the current status of the non-parallel theories and their relationship to the experimental data. The theories due to Bouthier (1972, 1973) and Saric & Nayfeh (1975) are based on the method of multiple scales whereas the theory due to Gaster (1974) is based on an iterative method. These theories seek to include all non-parallel effects correctly to order , where An interesting feature of the non-parallel theories is that the stability characteristics of the flow cease to be independent of z and exhibit different rates of amplification depending not only upon which flow quantity is observed but also on the particular path in the (R _x , z)-plane along which the observations are made. In an attempt to remove the ambiguity associated with the dependence on the path of observation, Saric & Nayfeh defined the condition for marginal stability by suppressing the effect due to the streamwise change in the shape of the disturbance velocity profile. This led to the curve labelled Non-parallel in Fig. 4.30. The experimental results pre-date the present level of understanding of the dependence of the results on the path of observation and of the possible subcritical behaviour associated with the finite disturbance caused by the vibrating ribbon which leads to a distortion of the basic flow. Furthermore, the effect of the mean wake...