to be counted by the counters 28 29 in the above described manner of operation specifically during the intermediate stage of the winding operation the difference between the predetermined numbers of pulses to be counted by the counters 28 29 is reduced so that the successive layers of yarn windings applied to the spinning tube by reciprocation of the ring rails 10 11 during the intermediate stage of the winding operation are more closely spaced to one another axially along the spinning tube to produce a cop 37 in the solid line form shown in fig4 the shortening of the increments by which the reciprocating motion of the ring rails 10 11 is shifted along the spindles is diagrammatically depicted in fig3 by the broken line 41 as the broken line 41 indicates the shortening of the ring rail shifting increments can be accomplished in a single step when the ring rails 10 11 reach a predetermined elevation along the spindles e g as representatively indicated at 39 as a result of the incremental shifting of the ring rails 10 11 during the initial stage of the winding operation as previously indicated the incremental transmitter 27 serves to detect the absolute value of the elevation of the ring rails 10 11 along the spindles and to deliver a corresponding signal to the processor 31 thus when the incremental transmitter 27 signals the processor 31 that the ring rails 10 11 have reached the predetermined elevation 39 along the spindles whereat the incremental shifting of the ring rails 10 11 is to be shortened according to the program stored in the processor 31 the processor signals the counters 28 29 to change the respective numbers of.