Abstract
For avoiding the troubles due to the structural irregularities of fibres with which the yarns are composed, I assumed that the' folded yarns are made of single yarns that have a cylindrical form, and a compact structure built with fine straight and perfect elastic fibres. Treating` the subjects mathematically as in applied mechanics, the following conclusions are obtained:
1. The relation between the number of twist of two folded yarn gained naturally by its elasticity, and those applied initially to its elements may be expressed genera-lly by the following equation,
N=n2+{r14(n1-n2)-(16/L2)(n13r16+n23r26)}/(r14+r24)
where N is the number of twist of the two folded yarn, r1 and r2 the radii of the two elements, and n1 and n2 the numbers of their twist respectively.
2. The relation between the number of twist of three folded yarn of equal elements, and those of its elements may be expressed by the equation
N=n-64n3r02/3L2
where N is the number of twist of the three folded yarn, r0 the radius of its elements, and n the number of their twist.
