The change of crêped state ₁_??_₂* from the state 1 to 2, which is defined as the ratio between the representation of the state 2 and of the state 1, is denoted theoretically thus: ₁_??_₂*=(1.11_??_0.898)sin a₁/sin a₂ a: the inclination of helical erêped yarn. Taking the results of observations into account the above expression is si_??_plified as written below: ₁_??_₂*=sin a₁/sin a₂

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υFor crêped yarn there establishes
in which ν the number of turns of yarn helix, α the inclination thereof, T the twist of yarn before crêping, _??_ the twist along crêped yarn and γ the radius of yarn helix. As to yarn helix, see Jour. Soc. Chem. Ind., Nippon, 37, No.4.
When _??_ calculated from the above relation (ν, α, γ and T are measurable directly) are compared with _??_ obtained from microscopical observations (after A. Herzog's method), there exist great discrepancies which are inexplicable as experimental errors.
On model experiments it is confirmed that the microscopical measurement of yarn twist is not reliable for hard twisted yarn. From this fact we must resort to the relation (1) to know _??_ so far as there is no direct measurement of it.

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