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What cloth is
A fabric is a structure before it is a material. Interlacement, the draft as a matrix, and the question of whether a cloth holds together at all.
A fabric is a population of contacts
Only a fifth of a knitted fabric's yarn is inside a diameter of its neighbour. So a fabric's friction lives in a fifth of its length, and every calculation this collection makes about withdrawal, slippage and fraying has assumed it lives everywhere.
A repeat has to fit the width
A repeat tiles the plane and a warp has two edges, so somewhere between them a repeat is cut through. The set of repeat widths that divide a warp exactly is the set of divisors of its body, and a body of a few thousand ends has a few dozen — two to eight per cent of the candidates. So a designer choosing a repeat for any reason except the width chooses one that does not fit, and the leftover averages half a repeat, split between the two selvedges.
A repeat has to fit the panel, and the panel is cut
The warp's width is fixed at warping and a piece's length is not, so the fitting problem in the two directions is not the same problem. Along the length a repeat has to fit a *panel*, because every panel of a patterned cloth must start at the same phase or the pattern breaks at the seams — and the allowance is a whole repeat per panel. A ten-centimetre repeat costs a seventy-centimetre panel twelve and a half per cent and a sixty-four-centimetre repeat costs it forty-eight.
A profile draft is a notation whose alphabet is weaves
The rung below measured four notations for a single weave and left open the notations for something larger. A profile draft is the first of them: a grid of blocks, each carrying a figure weave or a ground weave. Its image is enumerable and it is tiny — every pair of two-by-two weaves against every assignment of two-by-two blocks reaches 306 of the 22,874 interlacing four-by-four drafts, which is 1.34 per cent. And the 306 are the ones anybody weaves.
A lifting plan says nothing without a threading
The second of the notations for something larger than a weave is a pair, not a notation: a threading and a lifting plan, and neither alone expresses anything. The pair's image is exactly the drafts with no more distinct columns than there are shafts — 98 at two shafts, 5,282 at three, all 22,874 at four — and it is not nested with the profile draft's in either direction. The profile reaches 192 drafts that need all four shafts, and misses 64 of the 98 a two-shaft loom weaves.
Two lots of one cloth drift apart down a drop
A pattern repeat is a count of picks, and its length in the finished cloth is whatever that count's loom length became after the cloth gave back its crimp. Two lots woven with the warp held a tenth harder give back 1.13 points more of their length — so matched at the top, two lengths from the two lots are thirty millimetres apart at a 250 cm hem, and visibly apart a quarter of a metre down. The size of the repeat does not enter, and no cutting allowance can take it out.
A skew steps at every seam and a bow at none
A finished cloth's weft rows are seldom square to its selvedges, and on a patterned cloth the weft rows are the pattern rows. A skew — rows straight but slanting — puts its whole rise across every seam where two widths meet: two per cent on a 140 cm width is a 28 mm step, and matching the steps out tips the whole hanging instead, 112 mm across four widths. A bow — rows curving between level selvedges — matches perfectly at every seam and scallops each width in between. A three-millimetre match needs a skew under a quarter of a per cent, and down the seam a lot difference overtakes it.
The census counted two systems and a surface has one
Two drafts of twenty-two thousand touch at points, and the two are the plain weave. That is a count of the crown line both systems carry, and a bearing curve sees one: a plate meets whichever crown stands higher and meets nothing else until it has sunk past the step. Counted the way a surface is read, 494 drafts touch at points rather than two — and which 494 depends on a crimp division already called a convention rather than a measurement.
Four drafts in five have no path along their own crowns
A 2/2 twill and a 2/2 hopsack carry exactly the same length of bearing crown line, which the surface census noted and could not explain. One of them is a ridge running diagonally across the cloth without a break; the other is a field of square islands with no path between them. Counted over the whole catalogue, 4,016 of 22,874 drafts have a crown path that reaches the far side, 1,616 have one in both directions, and 130 have crowns with no neighbour at all.
A cotton's own water is a twentieth of what a cloth holds
A wet cloth keeps water in three places and only one of them is the fibre. A sheeting saturated holds 113 per cent of its own dry weight: 7.5 per cent of that inside the cotton as regain, 39 per cent in the channels between the fibres of its yarns, and 54 per cent in the holes four threads bound. The same construction in polyester, whose regain is a fortieth of cotton's, holds 105 per cent — an eight-point difference from a fortyfold one, because absorbency is a geometry with a fibre in it rather than a fibre with a geometry round it.
A wet fibre is stiffer and a wet yarn is not locked
The intuitive reason a damp cloth stiffens is that water pulls the fibres together — a meniscus is curved, the pressure inside it is below atmospheric, and the suction presses the assembly exactly as twist does. Computed, that suction is worth the first 186 turns a metre of twist and nothing after them: six per cent of what an ordinary yarn's twist already supplies, and nowhere near enough to stop the fibres sliding. What wetting actually does is fatten the fibres, and a fibre's bending rigidity goes as the fourth power of its diameter — so a wet cotton fibre is 2.07 times as stiff with no contact in the argument at all.
A specification can name a cloth that is not there
The three notations measured so far write drafts, and every draft is a cloth somebody could weave. A mill works from none of them: it works from a count, two setts and a weave quoted together, and that is the first notation whose image has holes in it. Of 2,560 specifications across the trade's own working range, 2,097 name no cloth at all — and in the 240 where the weave field decides anything, both numbers the trade quotes to decide it rank the catalogue wrongly.
The shortest notation has the longest mistakes
Four essays of this account have asked what each notation can express. None has asked what happens when one is written down wrong, and the answer is an identity rather than a tendency: a notation's symbols partition the cloth, so the count of symbols times the reach of one is the piece, in every notation, with nothing to trade. One threading digit decides 810,000 intersections of a square metre and one of a jacquard's holes decides one — and only the threading can be wrong while the cloth is right.
A second wrong digit is silent only by cancelling the first
One wrong threading digit leaves the cloth exactly as it was 576 times in 252,968, all on three-shaft drafts. The obvious guess about two was that silence would become the rule, since two changed digits can swap two shafts and swapping shafts is the harness's own freedom. Counted over all 1,074,972 pairs, two wrong digits are silent 1.29 per cent of the time — five and a half times as often, on fifteen times as many cloths — and never by adding one silent slip to another. Every silent pair is two audible errors cancelling, and at two errors point paper and lifting plans, which can never be wrong silently by one symbol, are silent almost as often.
A ridge in the matrix is not a ridge in the cloth
A 2/2 twill's crowns join into a ridge across its matrix and a 2/2 hopsack's are islands, so a thin film on the twill should be continuous from the first gram and on the hopsack a scatter of patches. Laid on the cloth's own surface rather than its matrix, both films are patches — the twill's ridge crosses from one end to the next, and between two ends lies the gap the sett leaves. On a sheeting both join at the same depth, 116 grams into the 186 that flatten the face, and the weave's whole influence is a window of up to 27 grams at the setts where it opens at all.
Silence lives in the lifting plan
Two wrong threading digits leave a four-end cloth exactly as it was 1.3 times in a hundred, and the question left was whether a longer repeat makes that rarer or commoner. At eight ends the answer depends on something the question did not name. With a lifting plan of unrelated rows, silence all but vanishes; with a twill's plan — one row slid a pick at a time — nine four-shaft threadings in ten can be silently mis-threaded, and even single errors are silent one time in five hundred. The repeat hardly matters. The plan's symmetry does.
A proof plan has no slide in it
A threading error that a 2/2 twill hides is invisible in the cloth and still wrong on the loom, and it shows only when the loom is re-pegged. Re-weaving every silent error under eight other plans says which do the showing. The twill run the other way and plain weave never expose one. A 1/3 twill exposes 44 per cent, a broken twill 70, and a plan of eight unrelated rows all but 864 — and those 864 are not errors at all, because each is the right threading started at another end. So the plans nest: whatever a broken or a point twill hides, the 2/2 hides too, and a threading proved under a 2/2 twill has passed the weakest test there is.
A spin leaves the water a fibre swelled by
A washing machine's spin is a centrifuge, and it drains a cloth in the order its pores give up water: the holes between the yarns at a few g, the channels inside the yarns only far enough from the drum's wall, and the water inside the fibre never. That last reservoir is not the regain. A soaked cotton fibre holds the volume it swelled by — 30 per cent of its dry weight, three and a half times the regain — and it is the floor under every spin speed there is.
An eight-shaft error hides in the row's mirror
At four shafts the lifting plans nest, with the 2/2 twill hiding every threading error the others hide. An eight-shaft loom has satins as well as twills, and their slides are different slides, so the order was expected to break. It does not. Over every threading that puts one end on each of eight shafts, the 4/4 twill hides every double error any of eleven other plans hides, and a satin hides exactly what a 1/7 twill hides, error for error. What decides it is not the slide. Every silent error is an exchange that turns the threading into a copy of itself, the slide accounts for one in six of them, and the rest hide in the row's mirror.
A spun cloth dries by its weight
Every plain cotton of 150 grams a square metre contains the same fibre, and the count only arranges it: the coarsest is three times as thick as the finest. Laid out wet without a spin, the thick one holds four and a half times as much water, all of it in its holes. Spun, every one of them keeps 40.9 per cent of its weight and dries in the same time — because a spin empties the holes, and what it leaves in the yarns is not their volume but the fibres' surface, which the weight has already fixed.
A half-drop wastes less, cut in the right order
A straight match has one place in the repeat where every drop may start, so a cutting room loses half a repeat between drops on average and a whole one at worst, in any order. A half-drop has two, because alternate widths start half a repeat lower — and that gives the cutter a choice the straight match never offers. Cut in the order the widths hang, a half-drop loses exactly what a straight match loses. Cut with like drops together when the remainder favours it and alternated when it does not, four drops of a pair of curtains lose a third less, and a long run half as much: (r/4)·n/(n − 1) a gap, against r/2. The rule needs one subtraction before the first cut.
A bay window wastes less than a wall
When a job's drops are all one length, a half-drop's best cutting order has one forced move, because the cutter has to change class once whatever the drops would prefer. Mix the lengths, as a bay window or a window over a radiator does, and each length sets its own price for what follows it. Six drops then lose a quarter of a repeat a gap instead of three tenths. Whether every drop can have its way is the bridges of Königsberg on two islands, and for a straight match mixing the lengths does almost nothing: its order can only choose which drop is cut last.
After the loom
The cloth that comes off the loom is not the cloth anybody buys. Shrinkage as the crimp coming back, the yarn flattened and swollen, the floats raised into a nap, and the fibres entangled until the weave is no longer the only thing holding the fabric together.
What comes off the loom is not the cloth
Every number on this site so far describes a fabric in one particular condition — held under tension, stretched to the reed width, never wetted — and none of them says so. That condition lasts until the cloth is taken off the machine, which is the first thing that happens to it.
Relaxation is the crimp coming back
A cloth that shrinks in the wash has not lost any thread. The thread is exactly as long as it was; more of its length is now spent going up and down rather than along, and the difference is the shrinkage, computable to the last figure from the woven geometry alone.