New interpretation of the fibrogram

The original theory of the fibrogram as developed by Hertel more than fifty years ago has served as the basis of all subsequent cotton length measurements, Hertel's mathematical derivation is based on the assumptions that the sampling probability of each fiber in forming a fiber beard is proportional to its length and the holding point along the fiber is random. Since the longer fibers have a greater probability of being sampled, the length distribution in the fiber beard is biased toward the longer fibers. Thus the mean length of the fiber beard must be greater than that of the original fiber sample. This appears to be correct for fiber beards prepared using sliver clamps. For fiber beards prepared using a fibrosampler, however, the length measurements of the original fiber samples and samples removed from the comb show that the measured length differences are too small to satisfy the original assumptions. If we modify Hertel's assumptions so that all fibers have an equal probability to be caught by the needles on the comb, then the fiber length distributions will be the same for both the original fiber sample and the fiber beard. This implies that fibers are sampled by the fibrosampler in clumps rather than individually. The mathematical techniques used by Hertel in deriving the relationships between various curves and fiber properties may be modified for this assumption, providing a different interpretation of the fibrogram.