1906-7.] Normal Take-up in Twisted Threads — Part II. 
93 
XIII. — The Relation between Normal Take-up or Contraction and 
Yarn Number for the same degree of Twist in Twusted 
Threads. By Thomas Oliver, B. Sc. (London and Edinburgh), 
Carnegie Research Fellow. Communicated by Dr C. G. Knott. 
(MS. received December 17, 1906. Read same date.) 
In a former paper * communicated to this Society in February, the 
author worked out experimentally and analytically a relation between 
normal take-up and degree of twist in the same thread. 
This relation for the take-up in the second twisting of a two-ply 
yarn is 
- r2/7 2 
y = -^x(6x + 2n) . . . . . (1) 
where d = diameter of single thread. 
L = length of single thread under experiment. 
x = turns of twist impressed in the second twisting. 
n = turns of twist in each single. 
The present investigation deals with the problem in which a; is a 
constant in different sizes of threads. Therefore n and d are the only 
variables on the right-hand side of the equation. 
Single threads are approximately cylinders. But as the sections in any 
one thread are not uniform, and are difficult to measure, it is found totally 
impracticable to number yarns in the same way as wires are gauged, i.e. 
proportional, directly or indirectly, to their diameters. 
The only practical basis of numbering is the relation of length to 
weight. All systems of numbering yarns in use in the textile industries 
may be classified under one or other of two categories, viz., “ inverse ” or 
“ direct.” In the “ inverse ” systems, the yarn number is inversely pro- 
portional to the weight of unit length. In the “ direct ” systems, on the 
other hand, the yarn number is directly proportional to the weight of unit 
length. It is probable that more than 90% of the yarns throughout the 
world are numbered inversely. The only notable exceptions are jute, 
reeled and thrown silk ; these are numbered on direct systems. Cotton, 
spun silk, linen, worsted, and practically all woollen yarns, are numbered 
inversely. 
* Proc. Roy. Soc. Edin ., 1906, vol. xxvi., pt. iii. p. 189. 
