95 
1 906-7. J Normal Take-up in Twisted Threads — Part II. 
From the cloth designer’s point of view, there is doubtless much to be 
said for Ashenhurst’s theory. The problem is, however, far more a 
dynamical than a geometrical one, and it is probable that Buckley’s theory 
is much nearer the truth for crossbred worsted yarns. 
In commerce, ranges of yarns are found with all kinds of relations 
holding between the degrees of twist in their members, according to the 
fancy of the spinner or the demands of his customers. Frequently the 
relation cannot be construed into any simple algebraic form ; as a rule, 
however, the twists in a range of yarns are approximately proportional 
to some power of the yarn number which lies between \ and 1. The 
author’s experiments and analyses on this subject are not yet complete, and 
therefore it is not intended to discuss the matter further than is necessary 
for the working out of the “ take-up ” problem. 
The author has found that between the limits of crossbred numbers 
usually spun, the degree of twist is approximately a linear function of 
the yarn number ; 
i.e. n = aC + b , 
where n = degree of twist in singles. 
C = yarn number. 
a and b are constants. 
In one range of yarns, the degree of twist in turns per inch, 
-3C + 2 . . . . (4) 
between the limits 10’s and 40’s. 
From this range, three threads numbered 12’s, 16’s, and 24’s were 
selected for experiment. Their diameters were measured by means of a 
microscope fitted with an eyepiece micrometer. 
Table I. shows various data necessary to effect a comparison between 
the experimental and analytical results. 
TABLE I. 
Yarn 
number. 
C 
Average 
diameter of 
singles. 
d 
Turns per 
inch in 
singles. 
n 
2 d 2 T2* 
8L ' 
k 
or - 
4 
k 
5 
2 k 
15 
12 
•0145" 
5 5 
•0260 
•0208 
•0139 
16 
•0124" 
7-0 
•0190 
•0152 
•0101 
24 
•0101" 
9-0 
•0126 
•0101 
•0067 
* If x and n in formula (1) be taken as turns per inch, then y = ^-^- . L 2 x(5x + 2 n). 
8L 
taken as 100, so as to give percentage results. 
L is 
