110 
Proceedings of the Koyal Society of Edinburgh. [Sess. 
“grist” on an inverse system of numbering. This case is considered 
extreme in usual practice, but is quite within the range of practicability 
especially in worsted yarns. 
In this case s would = ^ d 2 
The experimental investigation of this problem requires the apparatus 
shown diagrammatically in fig. 2. Each single thread, carrying a weight 
W at one end, passes over an aluminium pulley, P, and is secured at the 
other end by a clamp. The pulleys are mounted side by side on ball 
bearings. S is a scale on which contractions may be read by different read- 
ings ; N is a needle which determines the length of the two-ply thread. 
Twist is put into the thread A by turning handle H, which communi- 
cates rotary motion to shaft B through toothed wheels T. Worm M 
turns dial D. The number of revolutions is indicated on the dial. 
In each twist, the tensile load W on the single thread was inversely 
proportional to the yarn number or “ grist,” i.e. directly proportional to the 
weight per unit length of yarn. 
Table I. shows the percentage contraction for two-ply twists in cross- 
bred worsted : (a) 6 s and 20’s yarns, carrying loads of 13'3 grams and 
4 grams respectively; (b) 12’s and 24’s yarns, carrying loads of 4 grams and 
2 grams respectively. The results of Table I. are pictured graphically in 
fig. 3. The ordinates of the diagram represent percentage take-up, while the 
