245 
1906-7.] The Strength of Twisted Threads. 
points M and N. When tension is applied to the thread, A and B will 
not slip, while the fibres forming C and D will. 
In X millimetres, all the lines of fibres, i.e. n, will on the average have 
become discontinuous. 
Therefore, in x millimetres, n— fibres will he discontinuous. 
X 
.*. n(\ — fibres will be continuous throughout the range of x mm. 
Each of these latter fibres offers k grams resistance to rupture. 
.*. n(y 1 — — ^ of these latter fibres offer nk(l — — ^ grams resistance to 
rupture. 
The discontinuous fibres do not offer any resistance in this respect, 
because they are already broken within the limits M and N. 
A 
c 
B 
D 
Fig. 1. 
Each fibre offers /xX grams resistance to slipping on its entire length, 
and therefore /ux grams resistance to slipping on x millimetres of its length. 
n — fibres offer 
X 
n/A. 
x 2 grams resistance to slipping. 
The total resistance of the thread to rupture 
TlfXX/ 
+ nk( 1 
as shown by Professor Hartig. 
Now, it will be instructive to examine the matter a little more closely, 
and to see if this simple formula can represent the actual conditions, and 
if not, wherein it fails. 
In the first place, yarn-testing is only useful in so far as it enables us 
to ascertain the weaving qualities of a yarn. Therefore the conditions of 
test should approximate as closely as possible to those conditions which 
shall hold during weaving. The warp threads are subjected to considerable 
tensile stress in the loom by “ weighting” the warp beam. This stress, 
however, is not nearly up to the limit of elasticity of the threads. It 
is in the forming of the “shed” that breakages occur. Fig. 2 shows 
diagrammatically the conditions of shedding the warp in the loom. 
E represents the breast beam of the loom, over which the cloth passes 
after being woven. F, the back beam, over which the warp passes. 
