1906-7.] Normal Take-up in Twisted Threads — Part III. 
® 3 f Graph I. represents the actual results for the 6’s yarn. 
115 
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g 1 
l 1 
II. 
„ 20’s „ 
r oS 
.2 
f ” 
A x 
5? 
„ 6’s „ 
*-4-3 
o3 
g w 
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a 2 
„ 20’s „ 
-4-3 
55 
5) 
» 6’s „ 
55 
b 2 
5? 
„ 20’s „ 
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5^ 
5) 
C 
V 
i') 
5J for either yarn, 
that the tak 
The 
elbow 
at the 
origin 
on each curve c 
}' 
if corresponding points on the axes 
of the singles revolved in the same 
circle. 
if corresponding points on the axes 
of the singles revolved about the 
centroid of the cross-section. 
more pronounced than the corresponding change at the origin in the curves 
of fig. 3. If we consider the great difference in structure of woollen and 
worsted threads, we may expect the latter to give more uniform results 
than the former. The worsted thread contains only the long fibres of the 
wool staple arranged parallel to the axes of the thread before twist is put 
on in the process of spinning ; the short and curly fibres of the staple are 
all combed out and rejected as “ noil.” The woollen thread, on the other 
hand, contains every fibre of the wool staple, long and short, straight and 
curly ; further, the fibres are mixed in every conceivable direction in the 
carding operation. 
To summarise the main conclusions which may be drawn from a study 
of the analytical and experimental data shown in the tables and diagrams, 
let us consider first the direct twist or positive side of fig. 5. The graphs I. 
and II. plotted from the experimental data are lower than and A 2 
plotted on the assumptions (1) that corresponding points on the axes of the 
singles revolve in the same circle, (2) that the individual fibres in the singles 
have perfect freedom of rotation. Further, the relative positions of the 
curves are inverted ; Graph II., with the results for the smaller thread, is 
higher than Graph I. with the results for the thicker thread. The above 
hypothesis gives the graph A x for the thicker thread higher than the 
graph A 2 for the smaller thread. The numbers in Tables I. and II. and the 
graphs in figs. 3 and 4 all show that the contraction is invariably greater in 
the smaller thread. The graphs B x and B 2 obtained on the hypothesis (1) 
that corresponding axial points revolve about the centroid of the cross- 
section, (2) that individual fibres in the singles rotate freely, show vastly 
greater contraction on the smaller thread. Graphs I. and B x for the thick 
thread practically coincide throughout the “ direct ” twisting. 
On passing over to consider the negative side of fig. 5, we at once notice 
(1) that the elongation in the initial stages of the “ inverse ” twisting is 
much more pronounced in the hypothetical conditions than in the actual ; 
(2) that as twisting proceeds, the hypothetical contractions increase much 
faster than the contractions actually observed in the threads. The graphs 
