In an actual-drafting, capacitance of roller, which we defined in the previous report, varies with time. So, c₁ (t), capacitance of front roller, and c₂ (t), capacitance of back roller, have to beexpressed by the following equations; c₁(t)=c₁+Δc₁(t) c₂(t)=c₂+Δc₂(t)
In the above equations, unvariable values of the capacitance of roller, c, and c₂ are calculatedi by the following equations; where X: position L: length of draft-zone _??_: mean value of fiber length l_max: maximum value of fiber length f(l): probability density function of fiber length in feed sliver ρ(x): probability density function of velocity-change-points As there is the next relation between Δc₁(t) and Δc₂(t), Δc₁(t)=Δc₂(t) we can express the change of the capacitance of roller only by Δc₂(t).
From the differential equation of roller-drafting, we can express the relations among the variables-thickness of sliver produced, feed sliver thickness, surface velocity of front roller, and capacitance of back roller-in the following way.
From the above equations we can calculate the distributions of fiber length and velocity-change-points at the minimum change of the sliver thickness of sliver produced, that is the sharp distribution of fiber length (with the fibers of the same length) and the squeezed distribution of the velocity-change-points to the back roller side.

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The influence of the rate of acetylation in solution on the properties of acetylated cotton fabrics, was studied.
Cotton fabrics were acetylated to about 30 mole % at various different reaction rates by the liquid phase method in which trichloroethylene was used as diluent and sulfuric acid or perchloric acid as catalyzer. Various properties of acetylated cotton fabrics were examined.
It was found that the rate of acetylation exerts generally less effect on the properties of theacetylated cotton fabrics than other reaction conditions such as the sorts of catalyzer and alkali pretreatment, etc. But by more detailed observation, some effects on the heat-resistance and acid-resistance, etc. were found.

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The effects of alkali pretreatment on the properties of acetylated cotton fabrics were studied.
It was found that although the reaction of acetylation was very much accelerated by alkali pretreatment before acetic acid treatment in the liquid phase method, the strength of the acetylated fabrics did not be lower at all.
The cotton fabrics acetylated after alkali treatment have higher strength than ordinarily acetylated ones without alkali treatment and the fabric elongations become larger with the increase of acetylation. The moisture regain is relatively higher than ordinarily acetylated ones, although it becomes lower with the acetylation up to 50 mole %. The specific gravity becomes lower linearlly with acetylation, but is in general lower than ordinarily acetylated ones. The acid-resistances become better proportionally with the acetylation up to 50 mole %, although the ordinarily acetylated fabrics have almost the same acid-resistance in a wide range of acetylation beyond 30 mole %.
This difference between the alkali pretreated acetylation and the ordinary acetylation would be due to the difference in the reaction mechanism. The effects of alkali pretreatment would be caused by the decrystallization effects on the cotton cellulose.

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In the process of stretch yarn (Helanca type) production, the effects of tension, number of twist and heat-setting temperature on the dyeing properties and the degree of crystallinity of nylon were examined.
The results are following.
1) The amount of dye absorbed on stretch nylon decreases with increasing tension in twisting process, but the degree of crystallinity does not change.
2) There are no appreciable changes in the amount of dye absorbed and in the density of stretch nylon, even if the number of twist varies.
3) Degree of twist-fixing increases with increase of heat-setting temperature but there is a maximum point at about 2, 000t/m.
4) The amount of dye absorbed and the degree of crystallinity increase with increasing heatsetting temperature.
5) Dyestuffs were classified according to their sensitivity to uneven stretch of nylon hosiery.

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Viscose rayon fabrics were treated with aqueous solutions of dimethylene, dioxyethylene, trioxyethylene and polyoxyethylene (600) N, N, N′, N′-bisethyleneurethanes with or without urea-melamine resin solution. The viscose rayon fabrics treated with the bisethyleneurethanes solutions only, became to be nearly insoluble in cuprammonium solution, but did not show so good effective properties. The fabrics treated with the bisethyleneurethanes solutions with resin solution or N, N-ethylene stearyl urethane dispersion and resin solution, showed good crease recovery, flex abrasion, tensile strength, tear strength and stiffness.

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