DETERMINING THE AVERAGE FIBER LENGTH 



IN WOOL YARNS* 



In studies relating to the standardization of fabricated 

 wools, one of the problems is that of determining the 

 average fiber length in yarns forming the material. In- 

 asmuch as the methods in use are far from satisfactory, a 

 new method based on a simple principle, namely, the 

 number of fiber ends in a given section of a sample, is 

 presented. 



Since the number of ends is twice the number of fibers, 

 one obtains the aggregate length of all fibers, assuming 

 them continuous, and divides the result by one half the 

 number of ends. The latter determination is based on an 

 average from a series of counts in random cross-sections 

 under a microscope. Thus knowing the length (s) of 

 any sample, the number (n) of fibers in a cross-section 

 and the average number of ends (e), the formula for av- 

 erage length ( 1 1 ) is expressed by a simple equation ( 1 ) 



1 1=2 (sn/e) ( 1 ) 



applicable to any textile thread of yarn composed of 

 ordinary fibers. 



There are several peculiarities in yarns, however, which 

 need consideration, one the irregular arrangement of 

 fibers, particularly in woolens, the other the twisting of 

 the yarn in spinning. While fibers composing a worsted 

 are relatively long and straight, those in a woolen yarn 

 are short and irregular in position. This irregularity us- 

 ually presents some recurved fibers, particularly at the 

 surface, and the number thus added to a cross-section 

 gives results approximating those obtained for worsteds. 

 In connection with the process of spinning, one may con- 

 sider the fibers as helices with an angle (^) measuring the 

 pitch. This presents two possibilities. 



If the axial fibers are not under a longitudinal tension 



* Reprinted from Science, vol. 83 (1936), p. 353. 



