Abstract
Provided that the twisting moment being constant throughout the whole range in a piece of uneven yarn, and that some further assumptions being allowed, the relation between the count of yarn, N, and the density of twist, T, may be given theoretically in a form T=KN2, in which K is a constant. But, in the author's model experiment, the relation T=KNm held good for the most part, and the value of m varied from 1 to 1+α, α being a positive number smaller than unity. In those cases, the coefficient analogous to the modulus of transverse elasticity of yarn was a function of the radius of the yarn. The formula T=KNm may be deduced conveniently, if the coefficient is inversely proportional to the (1+β)-power of the radius of yarn, β being unity or a positive number smaller than unity.
Anyhow, the process of twisting in an ordinary twisting mechanism must be considered as a process, in which a definite number of turns is given on a definite length of yarn. Then the twisting moment cannot always be constant. Kis, therefore, not a constant but a coefficient depending upon the mean density of the twist originating from the twisting mechanism, Tm, numbers of yarn count actually existing in the free range of twisting, N, and their lengths, L, and the relation may adequately be expressed in such a from as T=(Tm∑ L/∑ NmL)Nm, ∑L being the length of a free twisting range, within which the twist may proceed quite freely.
