Visible dichroism reflects the orientation of the amorphous region of a polymer. Thus the dichroism of a polymer must be constant irrespective of the amount of dye on the polymer. It is generally believed, however, that a fiber specimen must not be over-dyed if the dichroism is to be measured quantitatively. The dichroism of cellulose and poly(vinyl alcohol) dyed with Congo Red was measured carefully, and the causes of this phenomenon were investigated. The “over-dyeing” phenomenon is apparent. When the correct absorbance is measured, Lambert-Beer's law holds good over the range of the possible dye content. The orientation of the dye molecules in polymer is independent of the dye content up to saturation.