1905 - 6 .] Mr T. Oliver on Take-up in Twisted Threads. 183 
be placed all twists in which the singles are at equal tension, and 
the contraction may be expected to have some relation to the size 
of the threads and amount of twist. Under the second heading, 
which I have termed “abnormal,” come all yarns in which a 
special “ take-up ” is impressed on the constituent singles according 
as the manufacturer wishes to obtain special effects. One of the 
single threads forms the straight core of the folded thread, while 
the others are made to loop themselves round it by a special 
device on the twisting frame. In the trade these twists are 
termed loops, curls, knops, and gimps. Obviously the “ take-up ” 
can bear no relation whatever to the dimensions or properties of 
the threads. This paper has therefore to deal only with the first 
class of twists. 
It may be assumed that single threads are cylinders of uniform 
density. The term “ uniform density,” as here applied, must not 
be interpreted in the usual way. A thread is composed of 
numerous short fibres of wool, cotton, or other material twisted 
together. Therefore in the completed thread air-spaces separate 
the fibres, and it is evident that the density cannot be uniform 
if infinitesimal areas of the cross section be considered. 
Suppose there are 80 fibres in the cross section of a thread, and 
that when the section is divided into 80 equal parts each part 
contains one fibre. Such is the meaning attached in this case to 
the term “uniform density.” The assumption is sufficiently near 
the truth for all practical purposes. 
If a length l of an untwisted single thread, diameter d , receive n 
turns of twist, then each fibre traces out a spiral under the 
influence of torsion, the dimensions of which depend on the 
distance of the fibre from the central axis of the thread. The 
average length of Botany fibre is about 2 inches. Supposing the 
diameter of a thread to be inch, with 10 turns of twist per 
inch, the average fibre would probably make about 19 turns, if 
an allowance be made for the contraction in twisting. The 
coarser fibres are longer, but the threads into which they are 
formed are thicker and possess less twist per unit length. We 
may thus take the above condition as typical, and in any 
case the continuity of a fibre may be assumed for a number of 
consecutive turns. 
