32—THEORETICAL COMPUTATION OF COMBING RATIOS OF IDEAL AND QUASI-IDEAL SLIVERS

The study of fibre-configuration in slivers using combing ratios has so far been empirical in nature. The present paper aims at deriving exact expressions for the combing ratios of slivers by employing a probabilistic approach. It is shown that when hooks are present, tlie values of combing ratios in the two directions of a sliver are, in general, different. How this difference is affected by lack of perfect parallelism is also examined. To obtain a numerical estimate of the effect of hooking of fibres on the combing ratio, the theoretical tormulae for combing ratios have been evaluated for a hypothetical sliver. Lastly, two indices are proposed: one to measure the departure of fibre configuration from the ideal, and the other to assess the difference in patternsof hooking in the two directions of a sliver. Their usefulness in interpreting experimental data is illustrated.