in fig1 and 1b the sliver loops stacked on one another within the can 18 on the bottom 20 lie along their outermost circumferential portion on the inner wall of the can 18 in this case when for example man made fibers are processed the center point m 1 of the can 18 as shown in fig2 assumes a predetermined distance a from the center m d of the rotary head 13 or rotary disc 16 the center point m 1 is one point of the central longitudinal axis of the can 18 and is situated at about the height level of the open top of the can 18 similarly the center point m d is one point of the rotary axis of the rotary head 13 and is situated at the same height level as the point m 1 the outline of the can 18 associated with the center point m 1 is shown in solid lines in fig2 if subsequently cotton fibers are processed which by nature are thinner than the man made fibers the outermost circumferential points of the deposited fiber sliver loops do no longer engage the inner wall of the can 18 whose center is at a distance a from the center of the rotary disc 16 thus there is an intermediate space between the sliver loops and the inner wall of the can 18 such an occurrence takes place also because the distance of the trumpet 14 from the inner wall of the can 18 is the same in both instances according to the invention the center point m 1 of the can 18 is displaced with respect to the stationary center point m d of the rotary disc 16 in the radial direction from m 1 to m 2 which is at.