A theoretical equation is derived to determine the tan δ-temperature(T)curve of the system composed of a single relaxation time, and the curve is calculated. Comparison of the calculation with experimental results shows that; (1) The three-element model combining the Maxwell element with one spring parallelly is most suitable for a viscoelastic model having a peak in the tan δ-T curve. (2) The peak temperature in the tan δ-T curve, T_max (k), and the apparent activation energy ΔHa, give the inherent half value width of tan δ-T curve ΔT_1/2(s) by the equation ΔT_1/2(s)=5.240×10^-3 T_max²/ΔHa. (3) The log tan δ-T curve can be approximated by an equilateral triangle. (4) The parameter B_∞ defined by the equation B_∞=522ΔHa/T_max, is convenient for determining the mechanism of viscoelastic absorption. (5) The average ΔT_1/2(s) of various polymers is 13 deg for the absorption (α_a) related to the microbrownian movement of segment in amorphous, and 20 deg for the absorption (β_a) related to the local movement of the main chain. Thus, the value of β_a absorption is larger than that of α_a absorption. (6) A method is presented to determine the relaxation time at the glass transition temperature T_g by ΔHa and T_max.

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The relation between the air permeability K of fiber assemblies unidirectionally oriented at high porosity ε was studied by applying the Darcy law to one-dimensionall air flow.
Experiments were performed with cotton fibers and polyester fibers in the porosity region of 96.0-99.9% when fiber-axes are parallel and perpendicular to air flow, and it was found that: K=Rε³/(1-ε)^β where R and β are experimental constants depending on the kinds of fibers, fiber orientation and air flow direction.
The result does not agree well with the Kozeny-Carman law, but shows good agreement with the Lord's results obtained for cotton fiber assemblies in the porosity region of 96-99%.

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The term “gloss” is defined by dividing the reflected light distribution curve into two components; a specular and a diffuse reflection component. The ratio between two components is proposed.
The results obtained are:
1) Shapes of diffusely reflected light distribution curves could be estimated by removing the specular component from reflected light distribution curves. The surface smoothness had a great effect on the shape of the diffusely reflected light distribution curves, resulting in increasing the deviation from the Lambert Law.
2) Assuming the most simplified elliptical model, a diffusely reflected light distribution curve was examined, and it was confirmed that the smoothness of the model had a great effect on the deviation of reflected light distribution curve from the Lambert Law.

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To calculate the specularly reflected light distribution curve of fabrics a simplified model of the parallel arrangement of elliptical columns was used, and the calculated curves were compared with measurements.
The following results are obtained:
(1) The same tendency is found for the calculated specular reflection as for the measurement of fabrics.
(2) A method is proposed to evaluate the quality and quantity of the gloss of fabrics.

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