The production of a textile yam involves the drawing out of a thick intermediate web of fibres (sliver) by a process known as
drafting
. In the present paper, a mathematical study is made of the dynamical mechanism of drafting, with the object of investigating the effect of relevant factors on the irregularity of the yam produced. Equations are written down to govern the drafting of a very simplified model of a wool sliver, and a particular case, when the fibre length is small, is treated in detail. It is shown that when such a sliver is drafted by passing it between two pairs of rollers moving with different speeds, a ‘period’ is produced in the thickness variations of the drafted sliver. The change in standard deviation of thickness is related to the properties of the sliver and of the drafting mechanism, and in particular to the spectrum of the thickness of the initial sliver.