No further deduction shall be made when cloth is more than 15 inches narrower than the reed space, or when cloth is narrower than 18 inches. Fractions of an inch not to be recognized under this clause.

5. Reeds.—A 60 reed being taken as the standard, ¾ per cent. shall be deducted for every two ends or counts of reed from 60 to 50, but no deduction shall be made below 50. ¾ per cent. shall be added for every two ends or counts of reed from 60 to 68, 1 per cent. from 68 to 100; 1½ per cent. from 100 to 110; and 2 per cent. from 110 to 132. All additions or deductions under this clause to be added to or deducted from the price of the standard 60 reed.

6. Picks.—Low Picks.—An addition of 1 per cent. shall be made for each pick or fraction of a pick below 11, thus:—

and so on, adding 1 per cent. for each pick or fraction of a pick.

High Picks.—An addition of 1 per cent. shall be made for each pick whenever they exceed the following:—

In making additions for high picks, any fraction of a pick less than the half shall not have any allowance; exactly the half-pick shall have ½ per cent. added; and any fraction over the half-pick shall have 1 per cent. added.

7. Twist.—The standard being 28’s or finer, the following additions shall be made when coarser twist is woven in the following reeds:—

and so on at the same rate.

When twist is woven in coarser reeds no addition shall be made.

8. Weft.—Ordinary Pin Cops.—The standard being 31’s to 100’s, both inclusive, shall be reckoned equal. Above 100’s 1 per cent. shall be added for every 10 hanks or fraction thereof.

In lower numbers than 31’s the following additions shall be made:—

Large Cops.—When weft of the following counts is spun into large cops, so that there are not more than nineteen cops to the lb., the following additions shall be made in place of the allowance provided for pin cops in the preceding table:—

9. Four-stave Twills.—Low Picks.—In four-stave twills an addition of 1 per cent. for each pick or fraction thereof below the picks mentioned in the following table shall be made when using weft as follows:—

High Picks.—When using weft—

In making additions for high picks any fraction of a pick less than the half shall not have any allowance; exactly the half-pick shall have ½ per cent. added, and any fraction over the half shall have the full 1 per cent. added.

10. Splits.—The following additions shall be made for splits:—

Empty dents shall not be considered splits.

11. All the foregoing additions and deductions shall be made separately.

This list is subject to a deduction of 10 per cent.

For fancy cloths the CHORLEY LIST, 1886, is the one most commonly used. This is as follows:—

Double-Lift Jacquards.—To be paid the following over plain cloth prices:—

Brocades, damasks, and crammed stripes with three or more ends in a dent, to be paid for by the number of ends per inch.

Picks 18 to 30 per quarter inch, 1 per cent. per pick; from 30 to 40 picks, ¾ per cent.; all above 40 picks, ½ per cent. instead of 1 per cent.

Lace brocades, 5 per cent. extra.

Single-lift jacquards to be paid 10 per cent. about double-lift machines.

The above applies to Jacquards only.

Dobby and Tappet Looms (except Satins).—To be paid the following above plain cloth prices—

Up to and including—

Stripes and other cloths with three or more ends in a dent to be paid for by the number of ends per inch.

In single-shuttle checks, handkerchiefs, and all special classes of goods in which more than one pick is put in one shed, all lost picks shall be counted.

Plain handkerchiefs, 72 reeds and below, to be paid 5 per cent. extra.

Single-shuttle cord checks with more than two picks in one shed to be paid 2½ per cent. less.

Lace stripes and other special classes of goods shall be paid extra as per special arrangement to be agreed upon by Employers’ and Operatives’ Associations.

The following example will show the method of calculating the price to be paid for weaving under the Uniform List:—

From this must be deducted 10 per cent., as per agreement, which will give 28·5535 pence as the actual price to be paid for weaving this piece of cloth.

The following example includes the allowance for narrow cloth woven in broad looms:—

In making the additions and deductions it is important that they should be made in the above order.

The Cost of a Piece of Cloth.—Besides the cost of material and the weaving wage, the expenses of the manufacturer must be taken into account. When a manufacturer makes only one kind of cloth, his expenses will obviously not be so proportionately great as another manufacturer’s who only takes a single order of a particular make. The expenses also vary with the district and distance from the market, and with other circumstances.

A manufacturer knows from experience exactly what amount of expenses to allow in different classes of fabrics in his own case, and in quoting prices for plain or fancy cloths he usually includes under the term “expenses” all the items of cost from the carriage of the yarn to the delivery of the cloth, including winding, warping, sizing, waste, and other fixed expenses in the mill.

The expenses are usually calculated in proportion to the weaving wage, and a manufacturer quotes “double weaving” or “three times weaving,” according to the class of fabric in question.

The following example will illustrate the principle of estimating the cost of a piece.

Find the cost of a piece, 34 inches full, 75 yards s.s. (short stick), 19 × 18, 32’s/40’s. Twist at 7d. per lb., weft at 7½d. per lb.

Weaving 2s. Expenses equal to weaving.

The 34-inch cloth would stand, say, 36 inches in the reed. The 75-yards cloth, “short stick,” or 36 inches to the yard, will require, say, 78 yards of warp.

A cloth counting 19 × 18, nominal, is usually woven in a 68 or 70 reed, and the picks per inch will be about 66 or 67 actually.

Assuming that the cloth stands 36 inches in a 70 reed, and the picks per inch are 67, we get—

36 inches × 78 yards × 70 reed × 7d.840 × 32’s=51.188d., cost of twist,

and

36 inches × 75 yards × 67 picks × 7½d.840 × 40’s=40.38d., cost of weft.

The amount allowed for expenses in the preceding example is perhaps sufficient for most cloths woven on dobbies, but more is required for jacquard-woven fabrics.

If 11s. 7½d. is quoted for the above cloth, the price is said to be based on “double weaving.”

For jacquard fabrics the price is usually based on 2½ to 3 times weaving, and in special cases, such as new styles, an extra profit is put upon the 3-times weaving.

Sometimes the expenses are said to be 5 or 10 per cent. more than weaving. If the weaving wage were 2s. 6d., and the expenses 10 per cent. more than weaving, the expenses would be 2s. 9d.

Contraction.—The length of warp required to weave a piece of a given length will vary with the pattern or weave of the cloth, and depends also on the elasticity of the yarn and the counts of both warp and weft. Owing to this difference in the elasticity of various classes of yarns, and the variation in the elasticity of the same yarn at different degrees of tension, it is impossible to lay down rules for the calculation of the exact warp length for a given length of piece, or for the exact width in the reed for a required width of piece. The length of warp required can only be obtained with exactness from experience, especially in fancy cloths.

As previously stated, twofold yarns are more elastic than single; indeed, with some kinds of twofold American yarns, such as are used in velvets, the percentage of contraction becomes less with an increase in the number of picks, owing to the increase of tension upon the yarn, which causes it to stretch more.

Roughly, the amount of contraction to allow in the warp can be obtained by taking into account the counts of weft and the number of intersections which the warp makes with the weft. The thicker the counts of weft the more the warp will be bent out of a straight line, also with an increase in the number of picks the amount of take-up or contraction will increase. This does not vary in a regular manner, as the angle which the warp makes in bending over the weft changes with any variation in the picks. Furthermore, the greater the tension on the warp yarn the more it will stretch, and also the more it will compress the weft at the point of intersection.

A rough estimate only can therefore be made if there is no previous experience in the same class of goods to guide the manufacturer.

A method of roughly estimating the percentage of milling-up of the warp is to multiply the intersections of the warp per inch by a number found by experience to give the right result, and to divide this product by the counts of weft used.

For rather heavily picked cloths the multiplier 4 gives a fairly accurate result, and in cloths with a medium number of picks and medium counts the multiplier 3 will be used. In some classes of goods the multiplier requires to be 5; but when a correct multiplier is found for a certain class of goods, it will serve for changes in that class. The system is certainly not accurate in all cases, but it embraces roughly the different causes which alter the percentage of contraction or milling-up in the warp, and is therefore of some use in practice.

In a plain cloth the contraction is much more than in a satin, and the percentage is greater in heavily picked cloths than light ones.

In a plain cloth of, say, 120 picks per inch, 60’s twist, 70’s weft, the percentage of take-up will roughly be as follows:—

In a plain cloth the warp intersects every pick, and so the intersections per inch are the same as the ends per inch. In a “two and two” twill the warp intersects twice in four picks, and the intersections per inch will be one-half the picks.

In more medium cloths the multiplier 3 is used; as, for example:—

Find percentage of contraction in a piece of plain cloth woven with 60 picks per inch, 32’s twist, 40’s weft.

60 × 340’s counts=4½ per cent.

In fancy cloths experience is the only guide as to the warp length required, but in striped cloths and similar fabrics woven from one beam the contraction of the whole will be that of the tightest weave in the pattern.

In a fabric in which there are only a few plain ends in the pattern, the other ends being loosely interwoven, it does not follow that the take-up will be as much as in a plain cloth, as the plain ends will compress the weft more at the point of intersection than could occur if all the ends were weaving plain.

Testing Yarn.—It often occurs that only a short length of yarn is available for being weighted when it is required to test it for the counts. If it is required to test the weft in a piece of grey cloth it is usual to take out of the cloth 120 yards, or one “lea.” This is one-seventh of a hank, and therefore if the weight of 120 yards is divided into 1,000 grains—the one-seventh part of a pound—the quotient will be the counts of the yarn. The reason of this will be obvious when it is remembered that if the weight of one hank is divided into 7000 grains, or 1 lb., the result is the number of hanks in 1 lb., or the counts.

The counts are based upon the number of hanks in 1 lb. avoirdupois, and as this weight is not suitable for weighing small quantities, it is necessary to weigh them in Troy weight. As nearly as possible 7000 grains Troy = 1 lb. avoirdupois.

If it is required to know the number of grains which 120 yards of any count should weigh, the method of procedure is the reverse of the foregoing.

When testing the counts of cops, it is usual to wrap two, three, or four cops, in order to arrive at a more satisfactory test.

If two leas, or two-sevenths of a hank, are weighed, the counts can be obtained by dividing the weight into 2000 grains, or two-sevenths of 1 lb. If three leas, or 360 yards, are weighed, divide the weight into 3000 grains, and the result is the counts. If 480 yards are weighed, the dividend is 4000; if 600 yards, or five leas, are weighed, the dividend will be 5000; if six leas, or 720 yards, are weighed, the dividend is 6000; and when seven leas, or one hank, is weighed, the dividend will be 7000 grains, or 1 lb.

As it takes a considerable time to take 120 yards of weft out of a piece, a shorter length is often weighed and the counts found therefrom. A balance is extensively used which registers the counts when twenty yards of yarn are put upon the pointer. This is a very useful, though not always accurate, method.

When any odd length of yarn is weighed, the counts may be obtained by proportion, thus—

If 34 yards of yarn have been found to weigh 8 grains, what count is it?

The yards in 1 lb. can first be found as follows:—

29750840=35·41 counts.

From this we get the formula:—

7000 × yards weighed840 × counts=counts.

This is a very useful formula, as when only a small piece of cloth is available to be tested it is necessary to get as near as possible to the counts from weighing sometimes only 10 or 15 yards, or any odd length.

A calculation may occur in the following form:—

How many grains should 16 yards of 20’s cotton weigh?

There are 840 × 20 = 16,800 yards of 20’s in 1 lb., or 7000 grains.

Then if 16,800 yards weigh 7000 grains, how many grains will 16 yards weigh?

This may be stated in a formula as follows:—

7000 × yards weighed840 × counts=weight in grains.

Staub’s Yarn Balance is a small balance which is made to test the counts of very small quantities of yarn. A template is given with the balance, and the yarn is cut into lengths the size of the template, about two inches. One end of the balance is slightly heavier than the other, and the number of threads the size of the template which are required to draw the balance indicate the counts of the yarn. If twenty threads or about 40 inches balance the small weight, the count of the yarn is 20’s, and so on.

The principle is the same as if a 1 lb. weight were put on one end of a balance, in which case the number of hanks required to draw the weight would indicate the counts, because if 20 hanks = 1 lb. the counts are 20’s, and if 21 hanks = 1 lb. the counts are 21’s. The balance may be made to weigh any length, according to the weight on one end of the balance.

The form in which it is usually made makes it specially suitable for testing the counts in small patterns of a few inches.

The test is, of course, only approximate, as could only be expected from weighing so short a length.

If the foregoing examples are thoroughly understood, the following will not be found difficult.

If a warp has 2000 ends, and is 500 yards long, and weighs 60 lbs., what counts is it?

The ends multiplied by the length will give the total length of yarn in the warp, and this divided by 840 will give the hanks. If the hanks are divided by the weight, the result will be the counts. The result may be obtained at once as follows:—

2000 × 500840 × 60=19·84 counts.

If a beam has 2200 ends, the counts being 40’s, and the weight 50 lbs., find the length.

By multiplying 40 by 840 the yards in 1 lb. are obtained, and multiplying this by 50, the yards of yarn on the beam are arrived at. If this is divided by the ends in the warp, the result will be the length of warp thus:—

40 × 840 × 502200=763·6 yards.

A simple method of mentally calculating the number of hanks in a piece is as follows:—

A warp 84 yards long will contain just one-tenth as many hanks as ends. Thus a warp of 2000 ends, 84 yards long, contains 200 hanks. This can be proved as follows:—

2000 × 84840=200 hanks.

The number of hanks in a warp 84 yards long can thus be seen at once, and it is a very simple matter to mentally calculate the difference for any other length.

The hanks of weft can also be calculated mentally in a similar manner.

If the piece is 84 yards, the counts multiplied by the width and divided by 10 will give the number of hanks required for 84 yards. Thus, find the hanks of weft in a piece 34 inches wide, 84 yards long, 60 picks per inch.

60 × 3410=204 hanks.

The calculation is really simpler than it looks in the above form, as the dividing by 10 can be done by simply pointing off the last figure in the product of the picks and width. The formula may be proved correct by working out fully as follows:—

34 × 84 × 60840=204 hanks.

This system of mentally calculating the hanks is very useful, as it serves as a check upon a full calculation.

The Firmness of Cloth.—The number of ends and picks per inch which can advantageously be put into a fabric depends upon the number of intersections per inch in the pattern or weave, and on the counts or diameters of the yarns used. In a plain cloth woven with 32’s twist and 32’s weft, the number of threads per inch which could be put into the cloth without undue compression would be a little more than one-half the number which could be laid side by side touching each other. The reason for this is that the warp and weft threads interlace with each other every pick, and therefore, supposing that 156 threads of 32’s occupy one inch when laid side by side, one-half of these threads would have to be left out to allow of the intersection of the weft between every end.

In a “two and two” twill the weft intersects once for every two ends, or twice in the pattern; therefore there are four threads and two intersections in the pattern. It is obvious, therefore, that to keep the same firmness in the twill as in the plain cloth with the same yarns, a larger number of threads per inch both in warp and weft will be required.

To keep the same “firmness” the threads must be kept as close together in one cloth as in the other, and as in a plain cloth one-half the threads which occupy one inch are dropped out, so in a twill with two intersections for four ends there must be one-third of the ends occupying one inch left out. Thus with 32’s yarn, of which the diameter is 1/156 of an inch, there will require to be about 102 threads per inch in a “two and two” twill.

A perfectly balanced plain cloth may be defined as a cloth in which the warp and weft yarns are equal in diameter, and the spaces between the threads are equal to the diameter of the yarn.

If the diameters of yarns of various counts are known, it is an easy matter to find the number of threads per inch which will produce the desired firmness in any simple weave.

The diameters of yarns of cotton, woollen, worsted, and other threads are given by the late Mr. T. R. Ashenhurst in an excellent little work on “Textile Calculations and the Structure of Fabrics,” which has done much to promote this branch of the art of weaving.

Mr. Ashenhurst estimates the diameter of a 32’s cotton yarn at the 1148th part of an inch; but this is probably somewhat under the mark, and in the following table I have taken 1156th inch as the diameter of 32’s.

The variation in the thickness of any yarn, and the fact that they are not strictly cylindrical, renders measurements of little avail, but taken in conjunction with an examination of a range of woven cloths, the approximate or practical diameter can be estimated.

TABLE OF DIAMETERS OF COTTON YARNS.

The preceding is a table of the diameters of cotton yarns from 1’s counts to 200’s. The number given as the diameter is the number of threads which occupy the space of one inch when laid as close together as possible without compression.

A perfectly balanced plain cloth will require one-half this number of threads per inch, plus, perhaps, 5 per cent. for the threads being forced somewhat out of the same plane in weaving.

Relative Diameters of Yarns.—The “counts” of yarns indicate the number of hanks in 1 lb., and therefore a given length of 30’s is twice as heavy as the same length of 60’s; but the diameter of the 30’s will not be twice that of the 60’s, as the yarns are cylindrical, and the diameters will vary as the square roots of the areas, which in this case are as 1: 2.

If one thread is four times as heavy as another, and if it is of the same density—which in these calculations is assumed, although it is not strictly correct—the diameters of the two threads will be as 2: 1. For example, looking at the tables, the diameter of a 60’s is seen to be the 1/213 of an inch, whilst the diameter of a thread four times the weight, viz. 15’s, is seen to be 1/106½ of an inch, or exactly twice the diameter of the 60’s thread.

The diameter of one yarn being known, the diameter of any other may be obtained by the following rule:—

Rule.—As the square root of one count is to the square root of another count, so is the diameter of one to the diameter of the other.

In this form the calculation necessitates the extraction of two square roots, and with most numbers would require the use of two fractions in the calculation. By squaring all the three terms the calculation is much simpler, as in the following example:—

The number of ends and picks per inch required to make plain cloths of equal firmness from different counts may be at once seen from the table of diameters, as one-half the number given as the diameter is required.

Thus if a plain cloth with 78 threads per inch of 32’s is taken as the standard, and it is required to make a cloth of equal firmness, with 60’s yarns, the number of threads per inch required would be 106½. In 20’s yarns about 62 threads would be required. In 16’s yarns 55 threads per inch, and so on.

In twills, or other regular weaves, the following rule will give the number of threads per inch required of any count:—

Rule.—As the sum of the ends and intersections in the pattern is to the ends, so is the diameter to the number of threads required.

One of the most useful purposes to which a knowledge of this principle can be put is in changing the weave of a fabric, to find the threads per inch of a given count of yarn required to keep the same firmness as in a sample cloth.

It must be remembered that the word “firmness” is here used as implying that the space between the threads bears the same relation to the diameters of the threads in both cases, or, if the given cloth is perfect, the proposed one will also be perfect.

Suppose it is desired to make a “two and two” twill of the same “firmness” as a plain cloth made with 103 threads per inch.

The yarns being the same, the number of threads per inch required will be as the ends plus intersections in a given number of ends in both patterns.

In the above question the given cloth is plain, with 103 threads per inch, and the proposed cloth is a “two and two” twill. Taking the same number of threads in each case, we get—

It must not be forgotten that it is necessary to take an equal number of ends of each pattern in this class of calculation. In more complex patterns it is often advisable to take the number of ends which is the L.C.M. of the ends in the two patterns in order to get a complete number of intersections in each case.

This may be proved correct by referring to the table of diameters on page 335, where it will be seen that a plain cloth with 82½ threads per inch of 36’s is “perfect,” and a “two and two” twill with 82½ threads of 20¼’s counts is equally perfect.

To change the Counts, the pattern and threads per inch remaining the same.

If a sample cloth has 78 threads per inch of 32’s yarn, and it is proposed to make a cloth of the same weave with 55 threads per inch, what counts of yarn are required to keep the same “firmness”?

This is simple enough. The diameters of yarns vary as the square root of their counts, and therefore as the threads in one cloth are to the threads in another, so will the square root of the counts in one be to the square root of the counts in the other.

On referring to the table of diameters (p. 335), it will be found that a plain cloth with 78 threads of 32’s is “perfect,” and that a plain cloth with 55 threads of 16’s is also perfect. Therefore the above calculation is correct.

To change the Threads per Inch, the counts and pattern remaining the same.

If a sample has 78 threads per inch of 32’s, and it is proposed to weave a cloth of the same pattern, but with 60’s yarns, find the number of threads per inch required to keep the same firmness.

This is simply a continuation of the previous statement.

If the two counts are known, the number of threads will vary as the square roots of the counts; thus—

One advantage gained by a knowledge of the principle of cloth “balance” is that the number of picks per inch which a given pattern or weave will take can easily be obtained by calculation. This is of great advantage to designers for Jacquard weaving, as it often occurs that a design is made and the cards cut for a pattern which will not admit of the required number of picks of the given counts being put in the cloth, which a slight alteration in the ground weave would have rendered possible.

To alter the Weight.—If the weight of a cloth is required to be altered, and the same firmness kept, the threads per inch and counts can be found on the same principle.

If a cloth is made heavier it must be done by using coarser yarns and fewer threads; it cannot be done by using more threads, and preserve the same “firmness” or “perfection.”

Suppose a sample piece of cloth weighing 10 lbs. is made with 93 threads of 45’s, and it is proposed to make a piece of the same length and width, but weighing 15 lbs. To find the threads per inch and counts of yarn to keep the same firmness.

The weights of two cloths will vary as the square roots of the counts if they are of the same perfection.

Therefore—

To find the threads per inch required of the above counts—

To see if both cloths are of the same firmness, the table of diameters may be referred to. It will there be seen that a plain cloth with 93 threads per inch of 45’s yarn is “perfect,” and also that the altered cloth with 62 threads of 20’s is equally perfect.

It thus proves the principle of the calculation to be correct.

A lighter cloth may be made, and the same firmness kept. The formula is the same in both cases. If a cloth is made lighter it must be done by using finer counts and more threads. It cannot be done by using fewer threads, as the firmness could not be kept and the required weight obtained.

In altering the weights of cloths some allowance would have to be made for the difference in milling-up with different counts of yarns and numbers of threads. If a cloth is made heavier, thicker yarns would be used, and the warp length to give a certain length of piece would be different in the sample to the altered cloth. But this is a comparatively small matter, which can be adjusted with a slight alteration in the basis of the structure.