198 Proceedings of Royal Society of Edinburgh. [sess. 
2/24s, 3/24s crossbred worsted ; 2/48s Botany worsted ; 2/56 cut 
woollen — and tested them specially for this paper. If I had 
selected seven tests from my previous collection, I might have 
been tempted to select those which agreed best with the theory. 
The percentage contraction for each turn of twist per inch is 
shown in the following tables. 
Table I. — Percentage Contraction for Crossbred Worsted Yarns. 
Turns 
per 
inch. 
2/1 
2s. 
to 
os 
IfJ 
2/24s. 
3/24s. 
Open- 
band 
Cross- 
band. 
Open- 
band. 
Cross- 
band. 
Open- 
band. 
Cross- 
band. 
Open- 
band. 
Cross- 
band. 
1 
■40 
- -16 
•44 
- -20 
•28 
- *12 
•20 
- T1 
2 
1-00 
- -16 
•94 
- *24 
•66 
- *18 
•52 
- T4 
3 
1*74 
-•08 
1-58 
- -20 
1-16 
- *12 
1-01 
-•10 
4 
270 
+ •22 
2-44 
0 
1-72 
- *01 
1-52 
+ -09 
5 
3-84 
•58 
3-32 
+ *28 
2-38 
+ T4 
2T4 
•32 
6 
5*30 
1’12 
4-28 
•60 
3*06 
•26 
2-82 
•68 
7 
6-74 
1*76 
5-50 
1-08 
3-82 
•54 
3-70 
1T1 
8 
8-50 
2-56 
6*84 
1-64 
4-72 
•86 
4-72 
1-52 
9 
10-40 
3-42 
8-18 
2-32 
5-70 
1-22 
5-82 
2-12 
10 
12-50 
4*54 
9-84 
3-04 
6-78 
1'62 
7-01 
2-79 
11 
14-60 
5 ’90 
11-62 
3-84 
7-96 
2-10 
8 '22 
3-41 
12 
7-34 
13*44 
4*92 
9*20 
2-66 
9*53 
4-26 
13 
8-98 
15-28 
6-12 
10-56 
3-26 
10-96 
5-14 
14 
11-02 
7 '50 
12-04 
3-96 
12-38 
6*16 
15 
13-04 
8*92 
13*40 
4-72 
7-24 
Id 
15-16 
10-52 
15*00 
5*62 
8-32 
17 
12-38 
6-58 
9-80 
18 
14-24 
7-56 
11-30 
19 
8-74 
12-68 
20 
10-04 
21 
11-16 
The direction of the twist at the top of each column is that of the 
folded thread. The twist in the singles is open-band. 
The numbers are also plotted on squared paper in fig. 11. 
The ordinates of the graph for each yarn represent percentage 
contraction ; and the abscissae, turns of twist. 
The forms of the graphs in fig. 1 1 suggest that if the origin of 
the diagram be shifted in each case to the point of maximum 
elongation, the equations to the graphs will probably be of the 
family y' = cx m . Let us consider any one of the curves, if its 
