an optimum distribution of the reverting loops the packages made in this manner were evaluated as in example 1 one obtains the following ______________________________________wd s 100 s 10 d 50 grade______________________________________0 21141 2 2 0 10 31089 2 2 0 10 38316 3 2 0 10 78859 3 3 0 10 87026 2 2 0 10 95325 2 3 0 1______________________________________ the possibility for a very finely stepped selection of the transmission ratio i permits to select winding ratios which result in excellent packages even with the conditions of compatibility of the progressive precision winding 12 decimals of the winding ratio were defined with the process described in example 1 and the device as aforementioned described whose differences are smaller than 0 1 and which are uniformly distributed over the circumference resulting in an optimum distribution of the reverting loops with these decimals of which the ones positioned between 0 2 and 0 4 or 0 6 and 0 8 were evaluated as preferred decimals a series of winding ratios had been developed for the progressive precision winding wherein the error in the winding up speed will not become larger than 0 05 and which result in the individual winding steps in an excellent package build up the following table lists this series for winding up of poy filaments ______________________________________progressive precision winding______________________________________cross over angle 6 4 u00b0 circumferential speed of the package 3500 m minpermissible deviation of the winding up speed 05 threads per unit of the reverse thread shaft rts 11troverse stroke 250 mmtube diameter 108 mmmaximum package diameter 370 mmminimum cross over angle 6 14 u00b0 switching speed of rotation of the reverse 8286 3 rpmthread shaft rts minimum double stroke number 753 double strokes minmaximum double stroke number 785 double.