1905-6.] Mr T. Oliver on Take-up in Tivisted Threads. 199 
Table II. — Percentage Contraction for Miscellaneous Yarns. 
Turns 
per 
inch. 
2/1 Os Cotton. 
2/48s Botany Worsted. 
2/56 cut Saxony 
Woollen. 
Open- 
band. 
Cross - 
band. 
Open- 
band. 
Cross- 
band. 
Cross- 
band. 
Open- 
band. 
1 
•68 
- -60 
•16 
- -18 
•34 
- -20 
2 
1*74 
- -84 
•44 
- -28 
•66 
-•36 
3 
2-90 
- *94 
•71 
- -32 
1-16 
- '38 
4 
4-52 
- -60 
1-02 
-•32 
1-76 
- -38 
5 
6-36 
- -14 
1-41 
-•28 
2-32 
-*30 
6 
8-34 
+ *42 
1-81 
- -18 
3-04 
- -20 
7 
10-66 
1-08 
2-22 
- -08 
3-80 
0 
8 
13-16 
1-86 
2-74 
+ •01 
4-64 
+ •22 
9 
15-86 
2-54 
3*24 
•12 
5*44 
•50 
10 
18*46 
3-68 
3-78 
•32 
6-58 
*81 
11 
4-92 
4-41 
•84 
7-64 
1*12 
12 
6-26 
4-98 
1-08 
8-88 
1-56 
13 
7-76 
5-60 
1-32 
10-26 
2*02 
14 
9-36 
6-31 
1-54 
11-78 
2-50 
15 
11-36 
7-06 
1-88 
3-16 
16 
13-40 
7*70 
2-20 
. . , 
3-72 
17 
15-40 
8*56 
2-61 
4-36 
18 
1776 
3-04 
5*10 
19 
3-44 
5-90 
20 
3*92 
6-78 
21 
4-44 
772 
22 
4-94 
8-82 
23 
5*48 
9-94 
24 
6-04 
11-22 
The twist in the cotton and worsted singles is open-hand, and 
cross-hand in the woollen single. 
maximum elongation be represented by a, and let this occur when 
b turns of twist are put on in the inverse direction. 
Then y = y + a 
x = x + b 
or x - b if we consider the inverse direction positive. 
If the general equation is 
y' = cx' m 
then y + a = c(x + b) m in the direction of the twist in the singles 
= c(x-b) m ,, inverse direction. 
To test if this relation is true, we plot on squared paper log 
(y + a) as ordinates, and log (x -f b) or log ( x - b) as abscissae. Fig. 
12 shows the results plotted on a sheet of paper squared logarith- 
