Generator

What Peirce's constant assumes

Yarn diameter against count, computed two ways: from conservation of volume with a stated packing factor, and from Peirce's empirical rule of one over twenty-eight root the cotton count. They agree closely enough that the rule can be inverted.

3 essays call yarn-curve. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the weave its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

Six ways of saying how fine a yarn is. The same four yarns written in six count systems, all placed on one axis of tex. A direct system states mass per unit length and rises as the yarn coarsens; an indirect one states length per unit mass and falls. Both kinds are in daily use and neither says which it is.

Setting and geometry

The yarn count systems, and why there are several

Half the ways of saying how fine a yarn is get bigger as it gets finer and half get smaller. That is not carelessness — and one of the constants buried in the oldest rule of thumb turns out to be a measurement nobody wrote down.

$Where the twenty-eight comes from. The setting a cotton cover factor of 28 prescribes, and the setting at which the threads would cover the surface geometrically, against yarn count. They are one curve: the trade's scale is Peirce's diameter with the units taken out. Below them is the sett at which each weave actually jams, which is a fixed fraction of it.$ Setting and geometry

Where the cover factor comes from

A cotton cover factor is threads per inch over the root of the count, and the scale says twenty-eight means a covered surface. The twenty-eight is not a convention: it is the reciprocal of Peirce's yarn diameter, and the trade's practical ceilings of fourteen and twenty-two fall straight out of it.

The crimp ratios a dense shirting can have. Poplins in 15 tex warp and 20 tex weft at 22 picks, from 32 ends per centimetre to 52. Each bar is the interval of warp-to-weft crimp ratios the construction admits at all: the warp must supply at least the thickness the weft cannot reach, and at most what it can reach itself. The rule at one is this site's standing default. It sits inside the interval up to 44.18 ends per centimetre and outside it beyond — so for a dense shirting an equal division of the crimp is not merely the wrong assumption but a geometric impossibility. The 44-end poplin this site's own cloth table called impossible for a long time sits a fifth of an end below that limit, which is why the solver failed on it: its feasible interval was real and narrow, and a bisection on the whole range walked away from it.

Setting and geometry

The cloth that was called impossible

This site's own table of fabrics carries a note saying a real 44-end poplin has no solution in its geometry at all, and that the poplin row was therefore set at 32 ends. The cloth solves. What had no solution was the search — a bisection that treated a state it could not reach as evidence of having gone too far, and walked away from the answer every time.

The whole library · All essays