Geometric torsion and curvature accurately describe three-dimensional forms of crimp. The usual parameters of crimp frequency and indices of amplitude or extensibility for idealized planar or helical crimp forms are expressible by specific relationships of geometric torsion and curvature. The more common, nonideal crimp forms are characterized by distribution statistics of these two fundamental parameters along the fiber. Mathematical techniques and analytical expressions were developed for describing crimp this way with data from an automatic crimp-measuring instrument and use of a digital computer. Examples are given from measurements made on several commercial man-made and natural fibers.

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The Copolymerization EquationThe copolymerization equation (ref. 1-3), which relates instantaneous copolymer composition to instantaneous reactor composition and reactivity ratios for a free-radical copolymerization, may be given in the form: where r1 and r2 are the two reactivity ratios, and 2 , s and 212 are polymer and reactor compositions expressed as mole ratios of monomer 1 to monomer 2. It is the purpose of this paper to point out a particularly useful and simple method of plotting this relation. Further, it will be shown how this plot may be used to follow reactor and copolymer composition changes with conversion in a batch reaction.The two variables y and z are defined as y = In Z12 (2.4)