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The main parameter used to describe the geometry of the crimp of a fiber is the crimp diameter. This corresponds to an average amplitude of the fiber in space while the fiber is kept in a static position of stress. In order to measure the crimp diameter, it is necessary to measure the coordinates of a sufficient numher of points on the fibers. From these measurements, a "fiber axis" can be defined as the straight line for which the sum of squares. S. of the distances of the fiber points from this line is minimal. The crimp diameter is then defined as D=2√S N, where N is the number of points measured along the fiber. The calculation of S according to this definition involves the solution of third-order equations. Therefore a simplified equation is suggested. It was found that this equation can. for all practical purposes, serve as a satisfactory approximation for the results obtained when S is calculated according to the definition . i.e., from the fiber axis. In order to measure the crimp diameter, a special apparatus had to be built. A series of limitations of the rotatory crimp apparatus led to the modification of the measuring method and to the, development of the method of two perpendicular planes. This method was applied to various types of fiber, such as cotton and fine wools.

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Statistical formulae based on generally accepted models for cellulose microfibril structure were developed to calculate the mean length of microfibril segments which do not contain molecular chain‐ends, i.e., “continuous segments.” The calculated length of such “continuous segments” for microfibrils of 2–3 mμ cross section, containing molecules of a degree of polymerization from 2 × 103 to 6 × 103, is in the range of 300–1500 A. The relationship between “continuous segments” and crystalline and amorphous regions of cellulose microfibrils is discussed.