In open-end spinning, the continuity of a fiber bundle must be cut to prevent false-twisting without incurring additional unevenness of draft. The authors have tried to determine the theoretical minimum draf t ratio necessary and sufficient to separate fibers constituting a sliver, on the assumption that at least one point should be left without overlap of fibers which move in a definite region after the front rollers. Some probability calculations have been made for this purpose. A mathematical result thus obtained for slivers composed of fibers uniform in length (staple length 3 cm) or of fibers having a staple length distribution (mean 3 cm and σ²=1 cm²) shows that a draft ratio of about 200 is necessary to give at least one unoverlapped point in a flying region 10 cm in length.
In fact, however, a high-speed cine film taken of a cotton sliver for 30 s yarn, which fiberwas drawn and separated by an air current of 20 m/sec, has shown that some fibers are draftedin groups by air current while other are drawn and separated individually. and that theseseparations-in-group cannot be eliminated even by increasing the speed of air current.
Separation-in-group relieves considerably the condition of separation, so that it is possible to separate the sliver even by a lower draft ratio than the theoretical value.

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We have developed a new method to measure a wear curve of fabrics by variations in electrical capacitance and made a practical evaluation of the abrasion of fabrics.
(1) The new method of measuring a wear curve by electrical capacitance is more accurate than methods which depend on evaluation of variations in thickness, permeability and bursting strength. Again, the new method is helpful in evaluating the practical abrasion of fabrics.
(2) By the new, capacitance method we can obtain the maximum measuring accuracy by using an area of electrode suited to the thickness of fabrics. Therefore, we can obtain a wear curve of fabrics, heavy or light, by varying the area of electrode.
(3) By obtaining a wear curve, we can also evaluate fabrics abrasion practically.

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This article expands the theories announced by Livesey-Owen and Grosberg on the bending deformation of woven fabrics. A theoretical equation (11) has been derived. Various factors which determine the bending deformation properties can be arranged as shown in Fig. 4. The bending moment vs curvature curves of various woven fabrics have been measured. The effects of single filament denier, yarn density and various finishing treatments have also been examined. The bending behaviors of woven fabrics of cotton, viscose and other synthetic fibers have been compared. Data obtained from the experiments have been analyzed on the basis of the equation (11).

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