Conventional studies on the gloss of fabrics are ambiguous in analysing the reflection light distribution curves. To avoid the ambiguity, the term “gloss” has been defined by dividing the reflection light distribution curve into two components ; a specular reflection component and a diffuse reflection component. The ratio has been proposed between the two components. However, some ambiguity are still left in dividing the distribution curve into two components.
The results obtained are :
1) Shapes of diffuse reflection light distribution curves could be estimated by removing the specular reflection components from various reflection light distribution curves. In this case, the smoothness of the surface had a great effect on the shapes of the diffuse reflection light distribution curves, resulting in increasing the shape deviation from the Lambert's Law.
2) Assuming the most simplified cross-sectional elliptical model, a diffuse reflection light distribution curve has been examined. From the results thus obtained, it was confirmed that the smoothness of the model had a great effect on the deviation of reflection light distribution curve from the Lambert's Law.

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A study has been made to determine the thermal conductivity of a thin specimen of fabrics placed between a standard sample and a slab under a predetermined temperature by heating the slab stepwise. Following results have been obtained :
(1) Assuming that an initial temperature beeing zero degree, the portion of x=-l is maintained at a temperature ct during 0<t<t₁ and is maintained at a temperature V during t₁≤t, for the composite solids -l<x<∞ of which the portion of -l<x<0 is the test specimen less than about 5 mm in thick, and the portion of x>0 is a standard sample, it has been proved that the surface temperature of the standard sample v₂(0, t) is approximately given by :
v2(0, t)/V=1-β^-2/t₁/t{e^β2erfcβ-exp[β²(1-t₁/t)]}·erfc(β√1-t₁/t)+2/√πβ(1-√1-t₁/t)
β=K₁/K₂√k₂t/l
Where, k₁ : thermal diffusivity of a specimen
K₁ : thermal conductivity of a specimen
k₂ : thermal diffusivity of a standard sample
K₂ : thermal conductivity of a standard sample
c, V : constant
t₁ : the time required to reach the temperature V
Using these equations and borosilicate glass as the standard sample, 0.038 kcal/m·hr·°C has been obtained for K₁ of polyester taffeta fabrics of four to six layeres.
(2) Assuming k₁=0.284 × 10^-3m²/h for the same fabrics of 30-40 layers, K₁=0.040 kcal/m·hr · °C has been obtained by the following equations :
v₂(0, t)/V=2/1+σ(a₁t₁/t+a₂)
a₁=∞Σn=0θⁿpn(1/pn+2pn)(erfcpn-erfcpn/√1-t₁/t)-2/√π(e^-pn2-√1-t₁/texp(-pn²/1-t₁/t))
a₂=∞Σn=0θerfcpn/√1-t₁/t
σ=K₂/K₁√k₁/k₂, θ=σ-1/σ+1, pn=(2n+1)p, p=l/2√k₁t
(3) Assuming that an initial temperature beeing zero degree, a surface temperature is maintained at a temperature ct during 0<t<t₁ and then the portions at x=0 and x=2l are maintained at a temperature V₁ and V₂ respectively during t₁≤ t, the central plane temperature v(l, t) of the specimen 0<x<2l is represented by:
v(l, t)/V₁+V₂=a₁/t₁/t+a₂
where, θ=-1.
By using this equation, 0.284 ×10^-3m²/h has been obtained for k₁ of polyester taffeta fabrics.

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