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1906-7.] The Strength of Twisted Threads. 
( 1) “ That the strength of the whole should equal the sum of the 
strengths of its parts ” appears plausible enough, and it would be substanti- 
ally correct if the fibres were rigid and did not admit of stretching under 
tension, or if all the fibres stretched an equal amount for the same stress, 
and if it could be ensured that all the fibres in the thread were at the 
same tension when the load was applied to the thread. None of these 
conditions can be realised in the actual thread. The first condition, 
“ absolute rigidity,” is far wrong. Every textile fibre is more or less 
plastic, wool and silk especially so. The second condition, “equal degrees 
of plasticity amongst the fibres of a thread,” is not far wrong up to the 
limit of elasticity, because the modulus of elasticity is approximately the 
same for all fibres of the same quality. But threads are often made by 
blending different qualities of the same material, and even different 
materials, e.g. cotton and wool blends. In such there would be a marked 
difference in the degrees of stretching under the same stress. After the 
elastic limit is passed, however, there is no uniformity in the stretching 
of the fibres even of the same quality. The fibres which stretch least 
would take up the greater part of the stress, and would quickly reach their 
ultimate breaking strengths before the average load has reached, say, two- 
thirds the strength of the weakest fibre. After the “ harder ” fibres have 
been ruptured, a correspondingly smaller number of fibres would be left 
to carry the load. So that the strength of the thread may be equal to the 
sum of the strengths of its fibres, each fibre must take up its due share 
of the load, and this can only occur if the fibres are all at equal tension 
to begin with, and if they continue so throughout the pull. This brings 
us to another reason for earlier rupture. 
(2) Let us suppose that a thread contains 90 fibres, the average tenacity 
of which = 10 grams, and that the following table shows the variation of 
strength amongst the fibres : — 
TABLE I. 
5 fibres break separately at 8*5 grains. 
10 
5 ) 
55 
9-0 
5 ? 
20 
55 
55 
9-5 
55 
20 
55 
55 
io-o 
„ 
20 
55 
55 
10-5 
55 
10 
55 
55 
11-0 
55 
5 
55 
55 
11*5 
55 
90 
» 
55 
10 
55 
average. 
Assuming that the fibres are all at the same tension at the beginning, and 
stretch equally throughout the pull, then, when the total load on the thread 
