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synopsisA treatment of the color of textile materials is proposed which is an extension of G. G. Stokes' "pile of plates" problem. Unlike the conventional treatment of this subject, e.g., that by Kubelka and Munk, this approach permits independent determination of all variables: coefficient of absorption of the dye, refractive indexes of the fibers, the effect on color of the geometry of the fabric and yarn, and the distribution of the dye within the fiber. Here, cylindrical, optically homogeneous fibers in a parallel array are assumed. Experimental data show that this treatment predicts far more satisfactorily the color of fabrics at high dye concentrations and low reflectance values than does the Kubelka-Munk approach.

RRcently, the authors have proposed a new approach to the prediction of the color of absorbing-scattering substrates such as fabrics.' One can expand this treatment to take into account the effect of an inhomogeneity of dye distribution, most easily the condition known as ringdyeing. Garrett and Peters2 dealt with this problem by expanding Atherton's3 treatment of the color of fabrics.Since our approach to this problem is based on the optical properties of the fibers and the medium of observation and on the geometry of the system, it is believed to be potentially more significant than the older treatments.In our paper, we showed that the pathlength (Zp) of light in the fiber is (under the restrictions outlined there)

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