684 



SCIENCE 



[N. S. Vol. XL. No. 1036 



sible to pair the elements whose middle points 

 fall to the right with those whose middle 

 points fall to the left in such a way, the long 

 with the short, as to secure the result stated in 



'Fig. 2. Series shown in Fig. 1 bisected, and its 

 left half transposed and turned over. For the 

 sake of simplicity, in Fig. 1 the elements are so 

 assorted that in Fig. 2 they match without rear- 

 rangement. The width of the second series 

 (Fig. 2) equals the mean length of the original 

 elements. 



-^•^ 



Fig. 3. Application of the theorems to the 

 measurement of textile fibers in mass, for in- 

 stance a ' ' pull ' ' of cotton fibers. The pull con- 

 Bisting of about 2,000 fibers is exit in two trans- 

 versely with clean sharp shears. One half of the 

 pull "a," is placed between thin glass plates, 1 

 and 2 (lantern plate covers). The other half is 

 placed between the glass plates 2 and 3. 1 and 2 

 are pressed firmly together with the left hand, as 

 shown, while 3 is held loosely with only its left 

 hand edge in contact with 2 and resting against 

 the left thumb, its right hand edge being lifted 

 so as to enable the operator to move the fibers 

 " 6 " back and forth over the fibers "a" by 

 friction. Or the fibers "6" may be moved back 

 and forth in any one of several different ways. 

 For instance, the left edge of "3" may be used 

 to move " 6 " back and forth on "2." When 

 "a" and "i" are adjusted the three plates of 

 glass are held in the left hand and the measuring 

 scale applied with the right hand. 



the theorem approximately, the degree of ap- 

 proximation depending on the number of the 

 original elements and the uniformity of their 

 increments in length when arranged in the 

 order of their magnitude. 



It has been ascertained by comparison with 

 the resiilts of my accurate method of measur- 

 ing the length of fine crooked fibers, a de- 

 scription of which has already been published, 

 that if a series of textile fibers be arranged in 

 a manner similar to that described in the 

 theorems, the mean length of the fibers can be 

 measured approximately, if proper allowance 

 be made for the "fiy-back," or shortening of 

 the fibers, due to their elasticity. 



Fig. 4. The halves of the "pull" shown in Fig. 

 3 matched ready for measurement. The halves are 

 adjusted against a strong transmitted light and 

 yet with a good top-light; for instance, against 

 sky-light reflected from a mirror laid on a table 

 near a window; "6" is so adjusted over "a" 

 that the fiber masses present the same shade from 

 end to end. This simple optical method is found 

 to approximate the conditions of the theorems. 

 Care should be taken not to disturb the parallelism 

 of the fibers. The width of the series, as arranged 

 in Fig. 4, represents the mean length of the fibers 

 minus the "fly-back." This latter, about one 

 millimeter in twenty-five for well-conditioned cot- 

 ton fibers, has to be added. The results are accu- 

 rate to the fraction of a millimeter. The method 

 is definite, readily learned, and easily applied. 



It is intended to publish details in connec- 

 tion with this approximate method of measur- 

 ing textile fibers in a separate publication. 

 N. A. Cobb 

 BxTEEAu OP Plant Industet, 

 Depabtment op Aqeiodltube, 

 September 25, 1914 



