Chapter XII: Textile Calculations (1)

The numbers of cotton yarns are based upon the hank of 840 yards, the number of hanks in 1 lb. being the “counts.”

It follows that if 840--the yards in one hank--be multiplied by the counts, the result will be the yards in 1 lb. of that count.

Thus in 1 lb. of 30’s yarn there will be 840 × 30 = 25,200 yards, and the yards in a pound of any count may be found in the same manner.

The counts of worsted yarns are based upon a hank of 560 yards, and the number of hanks in 1 lb. Avoirdupois is the count of the yarn.

Linen yarns are based on a hank or lea of 300 yards, and the number of these in 1 lb. is the count of the yarn.

Spun silk, which is the silk chiefly used in cotton fabrics for stripes and headings, is numbered on the same system as cotton yarns. The number of hanks of 840 yards in 1 lb. is the count of the yarn.

Net silks or thrown silks are numbered on an altogether different system. The “skein” or hank is 520 yards, and the number of deniers--533⅓ deniers = 1 oz.--which a skein weighs indicates the number of the yarn. In silk manufacture the number of the yarn is called the “size,” the word “count” being used to denote the closeness of the reed.

Another system is used for silk yarns called the Manchester scale. This is based upon the hank of 1,000 yards.

The number of drams which one such hank weighs is the “size” or number of the yarn or thread.

In the former scale the yards per ounce may be found by multiplying the yards in a hank by the deniers in one ounce, and dividing by the number of deniers which a hank weighs.

The yards in an ounce of 40 denier silk will be--

deniers per oz. yards in skein

(533⅓ × 520)
--------------------- = 6933⅓ yards per oz.
40 deniers

In the Manchester silk scale the yards per ounce of a 4 dram silk may be found by multiplying 1,000, the yards in a hank, by 16, the drams in an ounce, and dividing by the number of drams which the hank weighs, viz. 4; thus--

(1000 × 16)
----------- = 4000 yards per oz.
4

=Twofold Yarns= in cotton, worsted, and linen are numbered according to the count of the single yarn, with the number of folds put before it. Thus a 2-40’s yarn means that the yarn is composed of two threads of 40’s single, making a twofold yarn of 20 hanks to the pound.

In spun silk the yarns are nearly always two or more fold, and the number of the yarn always indicates the number of hanks in 1 lb. The number of folds is usually written after the hanks per pound. Thus, 40’s-2 spun silk indicates that the yarn is 40 hanks to the pound, made up of two threads of 80’s single.

It sometimes occurs in fancy yarns that threads of unequal thickness are twisted together. If a 60’s thread and a 40’s thread are twisted together, the count of the doubled thread will not be the same as if two threads of 50 hanks to the pound, but will be something less than this.

It is obvious that when the two threads are twisted together the weight of a hank of the doubled thread will be 1/60 + 1/40 of a pound, and by adding these fractions together the counts of the twofold yarn may be obtained. Thus--

1 1 (3 + 2) 5
-- + -- = ------- = --- = 24’s counts.
40 60 120 120

Another method of obtaining the same result is to multiply the two numbers together, and add them together, and divide one result by the other. Thus--

60 60
40 40
--- ----
100) 2400 (24’s counts.
2400
----

If three or more unequal threads are twisted together the counts of the resulting thread may be found by adding the fractions of a pound which a hank of each count represents.

_Example._--Find the counts of a threefold thread composed of one
thread each of 10’s, 20’s and 60’s cotton.

1 1 1 (6 + 3 +1) 10 1
-- + -- + -- = ---------- = -- = -- or 6’s counts.
10 20 60 60 60 6

Some allowance must be made for the twisting of the threads, but this will vary with the number of turns per inch in the yarn, and so is not taken into account in the example.

If it is required to obtain the weight of each count in 100 lbs. of the threefold yarn, the following is the method.

As one count is to the resulting count, so is the total weight to the weight required of that yarn--

10 : 6 ∷ 100 : 60 lbs. of 10’s
20 : 6 ∷ 100 : 30 lbs. of 20’s
60 : 6 ∷ 100 : 10 lbs. of 60’s
----
100 lbs. Total.

=Reeds and Setts.=--The system of numbering reeds, now almost universal in the cotton trade, is known as the Stockport or Manchester count. The number of dents or splits per inch in the reed with two ends in each dent is the basis of the system. If the reed has 30 dents per inch, it is called a 60 reed, because if there are two ends in a dent in the 30 dents there will be 60 ends per inch. The number of the reed is always the same as the ends per inch in the reed, if the ends are all two in a dent.

A 60 reed Stockport counts, if reeded three ends in a dent, will have 90 ends per inch, because a 60 reed has 30 dents per inch, and if there are three in a dent, there will be 30 × 3 = 90 ends per inch.

Various other systems have been used, but are gradually giving way to the simpler Stockport or Manchester system. Some of these are--

The Bolton count, in which the number of “beers” of 40 ends, or 20 dents, in 24¼ inches is the basis of the system.

The Blackburn count, in which the number of beers in 45 inches was the basis. The beer, as above, being 20 dents, representing 40 ends in a beer.

The Preston count was based on the number of beers in different widths.

The 6-4 count was based on the number of beers of 20 dents--representing 40 ends--in 58 inches.

The 9-8’s count was based on the number of beers in 44 inches.

The 4-4’s count was based on the beers in 39 inches.

The 7-8’s count was based on the beers in 34 inches.

The Scotch system is based on the number of dents in 37 inches. Thus in a 2000 reed there will be 2000 dents in 37 inches, representing 4000 ends in that space.

The Bradford system is based on the number of beers of 40 ends in 36 inches. If there are 50 times 40 ends in 36 inches, it is a “50 sett.”

To find the number of ends per inch in a given sett, it is necessary to multiply the sett by 40 and divide by 36, thus--

(50 sett × 40)
-------------- = 55-20/36 ends per inch.
36

=Quantity of Material in a Piece.=--To find the weight of warp and weft of given counts in a piece, the total length of yarn in the piece may be found, and divided by the yards in 1 lb. of the counts of yarn used. This will give the weight in pounds. The following example will make the principle quite clear:--

_Example._--Find the weight of warp and weft in a piece woven 30
inches wide in a 70 reed (Stockport) cloth 90 yards long, from 95
yards of warp, 80 picks per inch, the counts of twist or warp being
30’s, and counts of weft 40’s.

If the piece is 90 yards long, the length of warp used will be somewhat in excess of this, as the warp in interlacing with the weft is bent out of a straight line. The amount of “milling up,” as it is called, varies according to the number of intersections in the pattern or weave of the cloth, and with the counts of yarn used. It will also vary considerably according to the elasticity of the yarn. Twofold yarns are more elastic than single, and therefore will require a shorter length of yarn for a given length of cloth.

In this example 95 yards of warp are used to weave a 90-yards piece, an allowance of a little over 5 per cent.

In making the calculation for the weft it is necessary to take the width in the reed, as this length of weft is used every pick. The cloth will contract a little owing to the pull of the threads when woven, and when calculating for a given width of cloth care must be taken to calculate for the reed width and not the cloth width only.

In the present example the width in the reed is given, and so the cloth will be somewhat narrower than this when woven.

TO FIND WEIGHT OF WARP.

840 yards in 1 hank 70 ends per inch
30 counts 30 inches in reed
----- ----
25200 yards in 1 lb. 2100 ends in warp
95 yards long
-----
10500
18900
------
199500 yards of twist in piece.

yards
199500
Therefore, weight of warp = ----- = 7 lbs. 14⅔ oz.
25200
yds. in 1 lb.

TO FIND WEIGHT OF WEFT.

840 yards in 1 hank 80 picks per inch
40 30 inches in reed
----- ----
33600 yards in 1 lb. 2400 inches of weft in 1 inch of cloth
36 inches in 1 yard
-----
14400
7200
-----
36)86400 inches of weft in 1 yard of cloth
-----
2400 yards of weft in 1 yard of cloth
90 yards length of piece
----
216000 yards of weft in piece.

216000
Therefore, weight of weft = ------ = 6 lbs. 6-6/7 oz.
33600

Weight of weft = 6 lbs. 6-6/7 oz.

Weight of warp = 7 lbs. 14⅔ oz.

In the weft calculation, the picks per inch multiplied by the width in the reed in inches gives the inches of weft in one inch of cloth. This multiplied by 36 will give the inches of weft in one yard of cloth, and divided by 36, this gives the yards of weft in one yard of cloth. The two 36’s may be left out, as it is obvious that the yards of weft in a yard of cloth are the same as the inches of weft in an inch of cloth. The formula to calculate the weight of warp in a piece is as follows:--

Inches in reed × length of warp in yards × ends per inch in reed
----------------------------------------------------------------
840 × counts

= =weight of warp=.

The formula for the weft is--

Inches in reed × length of piece in yards × picks per inch
----------------------------------------------------------
840 × counts

= =weight of weft=.

Working out the previous calculation in this manner, we get--

30 × 95 × 70
------------ = 7 lbs. 14⅔ oz. of warp.
840 × 30

30 × 90 × 80
------------ = 6 lbs. 6-6/7 oz. of weft.
840 × 40

If it is required to find the number of hanks, it is only necessary to leave out the counts in the above formulæ. Thus we get--

Inches wide × length × ends per inch
------------------------------------ = hanks,
840

and using the figures in the previous example--

30 × 95 × 70
------------ = 237½ hanks of warp.
840

Before the actual cost of a piece of cloth can be calculated, it is necessary to know the price to be paid the weaver. In Lancashire the payment is made according to the list agreed upon by both employers and employed. For plain cloths and twills a new uniform list has been agreed upon, and this is now generally accepted. The following is the new list:--

UNIFORM LIST OF PRICES FOR WEAVING.

=1. The Standard.=--The standard upon which this list is based is an ordinary loom, 45 inches reed space, measured from the fork grate on one side to the back board on the other, weaving cloth as follows:--

Width: 39, 40, 41 inches.

Reed: 60 reed, 2 ends in a dent, or 60 ends per inch.

Picks: 15 picks per quarter-inch, ascertained by arithmetical calculation, with 1½ per cent. added for contraction.

Length: 100 yards, 36 inches to the yard, measured on the counter. Any length of lap other than 36 inches to be paid in proportion.

Twist: 28’s, or any finer numbers.

Weft: 31’s to 100’s inclusive.

Price 2_s_. 6_d_., or 2_d_. per pick, per quarter-inch.

=2. Width of Looms.=--A 45-inch reed space loom being taken as the standard, 1½ per cent. shall be added for each inch up to and including 51 inches; 2 per cent. from 51 to 56 inches; 2½ per cent. from 56 to 64 inches; and 3 per cent. from 64 to 72 inches.

1¼ per cent. shall be deducted for each inch from 45 to 37 inches inclusive, and 1 per cent. from 37 to 24 inches, below which no further deduction shall be made. For any fraction of an inch up to the half no addition or deduction shall be made; but if over the half, the same shall be paid as if it were a full inch.

All additions or deductions under this clause to be added to, or taken from, the price of the standard loom 45 inches.

DEDUCTED FROM STANDARD.

+---------+-----------+
| Loom. |Percentage.|
+---------+-----------+
| Inches. | |
| 24 | 23 |
| 25 | 22 |
| 26 | 21 |
| 27 | 20 |
| 28 | 19 |
| 29 | 18 |
| 30 | 17 |
| 31 | 16 |
| 32 | 15 |
| 33 | 14 |
| 34 | 13 |
| 35 | 12 |
| 36 | 11 |
| 37 | 10 |
| 38 | 8¾ |
| 39 | 7½ |
| 40 | 6¼ |
| 41 | 5 |
| 42 | 3¾ |
| 43 | 2½ |
| 44 | 1¼ |
| 45 | standard |
+---------+-----------+

ADDED TO STANDARD.

+---------+-----------+
| Loom. |Percentage.|
+---------+-----------+
| Inches. | |
| 46 | 1½ |
| 47 | 3 |
| 48 | 4½ |
| 49 | 6 |
| 50 | 7½ |
| 51 | 9 |
| 52 | 11 |
| 53 | 13 |
| 54 | 15 |
| 55 | 17 |
| 56 | 19 |
| 57 | 21½ |
| 58 | 24 |
| 59 | 26½ |
| 60 | 29 |
| 61 | 31½ |
| 62 | 34 |
| 63 | 36½ |
| 64 | 39 |
| 65 | 42 |
| 66 | 45 |
| 67 | 48 |
| 68 | 51 |
| 69 | 54 |
| 70 | 57 |
| 71 | 60 |
| 72 | 63 |
+---------+-----------+

=3. Broader Cloth than admitted by Rule.=--All looms shall be allowed to weave to within 4 inches of the reed space; but whenever the difference between the width of cloth and the reed space is less than 4 inches, it shall be paid as if the loom were 1 inch broader: and if less than 3 inches, as if it were 2½ inches broader.

=4. Allowance for Cloth 7 to 15 inches narrower than the Reed Space.=--When the cloth is from 7 to 15 inches narrower than the reed space of the loom in which it is woven, a deduction in accordance with the following table shall be made:--

DEDUCTIONS FOR NARROW CLOTH.

+------+------+-------+
|Reed |Cloth.| Per |
|space.| | cent. |
+------+------+-------+
| 72 | 65 | 1·38 |
| 72 | 64 | 2·76 |
| 72 | 63 | 4·14 |
| 72 | 62 | 5·52 |
| 72 | 61 | 6·9 |
| 72 | 60 | 8·28 |
| 72 | 59 | 9·66 |
| 72 | 58 | 11·04 |
| 72 | 57 | 12·19 |
| 71 | 64 | 1·41 |
| 71 | 63 | 2·81 |
| 71 | 62 | 4·22 |
| 71 | 61 | 5·62 |
| 71 | 60 | 7·03 |
| 71 | 59 | 8·44 |
| 71 | 58 | 9·84 |
| 71 | 57 | 11·02 |
| 71 | 56 | 12·19 |
| 70 | 63 | 1·43 |
| 70 | 62 | 2·87 |
| 70 | 61 | 4·3 |
| 70 | 60 | 5·73 |
| 70 | 59 | 7·17 |
| 70 | 58 | 8·6 |
| 70 | 57 | 9·79 |
| 70 | 56 | 10·99 |
| 70 | 55 | 12·18 |
| 69 | 62 | 1·46 |
| 69 | 61 | 2·92 |
| 69 | 60 | 4·38 |
| 69 | 59 | 5·84 |
| 69 | 58 | 7·31 |
| 69 | 57 | 8·52 |
| 69 | 56 | 9·74 |
| 69 | 55 | 10·96 |
| 69 | 54 | 12·18 |
| 68 | 61 | 1·49 |
| 68 | 60 | 2·98 |
| 68 | 59 | 4·47 |
| 68 | 58 | 5·96 |
| 68 | 57 | 7·2 |
| 68 | 56 | 8·44 |
| 68 | 55 | 9·69 |
| 68 | 54 | 10·93 |
| 68 | 53 | 12·17 |
| 67 | 60 | 1·52 |
| 67 | 59 | 3·04 |
| 67 | 58 | 4·56 |
| 67 | 57 | 5·83 |
| 67 | 56 | 7·09 |
| 67 | 55 | 8·36 |
| 67 | 54 | 9·63 |
| 67 | 53 | 10·9 |
| 67 | 52 | 12·16 |
| 66 | 59 | 1·55 |
| 66 | 58 | 3·1 |
| 66 | 56 | 5·69 |
| 66 | 55 | 6·98 |
| 66 | 54 | 8·28 |
| 66 | 53 | 9·57 |
| 66 | 52 | 10·86 |
| 66 | 51 | 12·16 |
| 65 | 58 | 1·58 |
| 65 | 57 | 2·91 |
| 65 | 56 | 4·23 |
| 65 | 55 | 5·55 |
| 65 | 54 | 6·87 |
| 65 | 53 | 8·19 |
| 65 | 52 | 9·51 |
| 65 | 51 | 10·83 |
| 65 | 50 | 12·15 |
| 64 | 57 | 1·35 |
| 64 | 56 | 2·7 |
| 64 | 55 | 4·05 |
| 64 | 54 | 5·4 |
| 64 | 53 | 6·74 |
| 64 | 52 | 8·09 |
| 64 | 51 | 9·44 |
| 64 | 50 | 10·79 |
| 64 | 49 | 11·87 |
| 63 | 56 | 1·37 |
| 63 | 55 | 2·75 |
| 63 | 54 | 4·12 |
| 63 | 53 | 5·49 |
| 63 | 52 | 6·87 |
| 63 | 51 | 8·24 |
| 63 | 50 | 9·62 |
| 63 | 49 | 10·71 |
| 63 | 48 | 11·81 |
| 62 | 55 | 1·4 |
| 62 | 54 | 2·8 |
| 62 | 53 | 4·2 |
| 62 | 52 | 5·6 |
| 62 | 51 | 7·0 |
| 62 | 50 | 8·4 |
| 62 | 49 | 9·51 |
| 62 | 47 | 11·75 |
| 61 | 54 | 1·43 |
| 61 | 53 | 2·85 |
| 61 | 52 | 4·28 |
| 61 | 51 | 5·7 |
| 61 | 50 | 7·13 |
| 61 | 49 | 8·27 |
| 61 | 48 | 9·41 |
| 61 | 47 | 10·55 |
| 61 | 46 | 11·69 |
| 60 | 53 | 1·45 |
| 60 | 52 | 2·91 |
| 60 | 51 | 4·36 |
| 60 | 50 | 5·81 |
| 60 | 49 | 6·98 |
| 60 | 48 | 8·14 |
| 60 | 47 | 9·3 |
| 60 | 46 | 10·47 |
| 60 | 45 | 11·63 |
| 59 | 52 | 1·48 |
| 59 | 51 | 2·96 |
| 59 | 50 | 4·45 |
| 59 | 49 | 5·63 |
| 59 | 48 | 6·82 |
| 59 | 47 | 8·0 |
| 59 | 46 | 9·19 |
| 59 | 45 | 10·38 |
| 59 | 44 | 11·26 |
| 58 | 51 | 1·51 |
| 58 | 50 | 3·02 |
| 58 | 49 | 4·23 |
| 58 | 48 | 5·44 |
| 58 | 47 | 6·65 |
| 58 | 46 | 7·86 |
| 58 | 45 | 9·07 |
| 58 | 44 | 9·98 |
| 58 | 43 | 10·89 |
| 57 | 50 | 1·54 |
| 57 | 49 | 2·78 |
| 57 | 48 | 4·01 |
| 57 | 47 | 5·25 |
| 57 | 46 | 6·48 |
| 57 | 45 | 7·72 |
| 57 | 44 | 8·64 |
| 57 | 43 | 9·57 |
| 57 | 42 | 10·49 |
| 56 | 49 | 1·26 |
| 56 | 48 | 2·52 |
| 56 | 47 | 3·78 |
| 56 | 46 | 5·04 |
| 56 | 45 | 6·3 |
| 56 | 44 | 7·25 |
| 56 | 43 | 8·19 |
| 56 | 42 | 9·14 |
| 56 | 41 | 10·08 |
| 55 | 48 | 1·28 |
| 55 | 47 | 2·56 |
| 55 | 46 | 3·85 |
| 55 | 45 | 5·13 |
| 55 | 44 | 6·09 |
| 55 | 43 | 7·05 |
| 55 | 42 | 8·01 |
| 55 | 41 | 8·97 |
| 55 | 40 | 9·94 |
| 54 | 47 | 1·3 |
| 54 | 46 | 2·61 |
| 54 | 45 | 3·91 |
| 54 | 44 | 4·89 |
| 54 | 43 | 5·87 |
| 54 | 42 | 6·85 |
| 54 | 41 | 7·83 |
| 54 | 40 | 8·8 |
| 54 | 39 | 9·78 |
| 53 | 46 | 1·33 |
| 53 | 45 | 2·65 |
| 53 | 44 | 3·65 |
| 53 | 43 | 4·65 |
| 53 | 42 | 5·64 |
| 53 | 41 | 6·64 |
| 53 | 40 | 7·63 |
| 53 | 39 | 8·63 |
| 53 | 38 | 9·42 |
| 52 | 45 | 1·35 |
| 52 | 44 | 2·36 |
| 52 | 43 | 3·38 |
| 52 | 42 | 4·39 |
| 52 | 41 | 5·41 |
| 52 | 40 | 6·42 |
| 52 | 39 | 7·43 |
| 52 | 38 | 8·28 |
| 52 | 37 | 9·12 |
| 51 | 44 | 1·03 |
| 51 | 43 | 2·06 |
| 51 | 42 | 3·1 |
| 51 | 41 | 4·13 |
| 51 | 40 | 5·16 |
| 51 | 39 | 6·19 |
| 51 | 38 | 7·05 |
| 51 | 37 | 7·91 |
| 51 | 36 | 8·77 |
| 50 | 43 | 1·05 |
| 50 | 42 | 2·09 |
| 50 | 41 | 3·14 |
| 50 | 40 | 4·19 |
| 50 | 39 | 5·23 |
| 50 | 38 | 6·1 |
| 50 | 37 | 6·98 |
| 50 | 36 | 7·85 |
| 50 | 35 | 8·72 |
| 49 | 42 | 1·06 |
| 49 | 41 | 2·12 |
| 49 | 40 | 3·18 |
| 49 | 39 | 4·25 |
| 49 | 38 | 5·13 |
| 49 | 37 | 6·01 |
| 49 | 36 | 6·9 |
| 49 | 35 | 7·78 |
| 49 | 34 | 8·67 |
| 48 | 41 | 1·08 |
| 48 | 40 | 2·15 |
| 48 | 39 | 3·23 |
| 48 | 38 | 4·13 |
| 48 | 37 | 5·02 |
| 48 | 36 | 5·92 |
| 48 | 35 | 6·82 |
| 48 | 34 | 7·72 |
| 48 | 33 | 8·61 |
| 47 | 40 | 1·09 |
| 47 | 39 | 2·18 |
| 47 | 38 | 3·09 |
| 47 | 37 | 4·0 |
| 47 | 36 | 4·91 |
| 47 | 35 | 5·83 |
| 47 | 34 | 6·74 |
| 47 | 33 | 7·65 |
| 47 | 32 | 8·56 |
| 46 | 39 | 1·11 |
| 46 | 38 | 2·03 |
| 46 | 37 | 2·96 |
| 46 | 36 | 3·88 |
| 46 | 35 | 4·8 |
| 46 | 34 | 5·73 |
| 46 | 33 | 6·65 |
| 46 | 32 | 7·57 |
| 46 | 31 | 8·5 |
| 45 | 38 | 0·94 |
| 45 | 37 | 1·87 |
| 45 | 36 | 2·81 |
| 45 | 35 | 3·75 |
| 45 | 34 | 4·69 |
| 45 | 33 | 5·62 |
| 45 | 32 | 6·56 |
| 45 | 31 | 7·5 |
| 45 | 30 | 8·25 |
| 44 | 37 | 0·95 |
| 44 | 36 | 1·9 |
| 44 | 35 | 2·85 |
| 44 | 34 | 3·80 |
| 44 | 33 | 4·75 |
| 44 | 32 | 5·70 |
| 44 | 31 | 6·65 |
| 44 | 30 | 7·41 |
| 44 | 29 | 8·16 |
| 43 | 36 | 0·96 |
| 43 | 35 | 1·92 |
| 43 | 34 | 2·88 |
| 43 | 33 | 3·77 |
| 43 | 32 | 4·81 |
| 43 | 31 | 5·77 |
| 43 | 30 | 6·54 |
| 43 | 29 | 7·31 |
| 43 | 28 | 8·08 |
| 42 | 35 | 0·97 |
| 42 | 34 | 1·95 |
| 42 | 33 | 2·92 |
| 42 | 32 | 3·9 |
| 42 | 31 | 4·87 |
| 42 | 30 | 5·65 |
| 42 | 29 | 6·43 |
| 42 | 28 | 7·21 |
| 42 | 27 | 7·99 |
| 41 | 34 | 0·99 |
| 41 | 33 | 1·97 |
| 41 | 32 | 2·96 |
| 41 | 31 | 3·95 |
| 41 | 30 | 4·74 |
| 41 | 29 | 5·52 |
| 41 | 28 | 6·32 |
| 41 | 27 | 7·11 |
| 41 | 26 | 7·89 |
| 40 | 33 | 1·0 |
| 40 | 32 | 2·0 |
| 40 | 31 | 3·0 |
| 40 | 30 | 3·8 |
| 40 | 29 | 4·6 |
| 40 | 28 | 5·4 |
| 40 | 27 | 6·2 |
| 40 | 26 | 7·0 |
| 40 | 25 | 7·8 |
| 39 | 32 | 1·01 |
| 39 | 31 | 2·03 |
| 39 | 30 | 2·84 |
| 39 | 29 | 3·65 |
| 39 | 28 | 4·46 |
| 39 | 27 | 5·27 |
| 39 | 26 | 6·08 |
| 39 | 25 | 6·89 |
| 39 | 24 | 7·7 |
| 38 | 31 | 1·03 |
| 38 | 30 | 1·85 |
| 38 | 29 | 2·67 |
| 38 | 28 | 3·49 |
| 38 | 27 | 4·32 |
| 38 | 26 | 5·14 |
| 38 | 25 | 5·96 |
| 38 | 24 | 6·78 |
| 38 | 23 | 7·60 |
| 37 | 30 | 0·83 |
| 37 | 29 | 1·67 |
| 37 | 28 | 2·5 |
| 37 | 27 | 3·33 |
| 37 | 26 | 4·17 |
| 37 | 25 | 5·0 |
| 37 | 24 | 5·83 |
| 37 | 23 | 6·67 |
| 37 | 22 | 7·5 |
| 36 | 29 | 0·84 |
| 36 | 28 | 1·69 |
| 36 | 27 | 2·53 |
| 36 | 26 | 3·37 |
| 36 | 25 | 4·21 |
| 36 | 24 | 5·06 |
| 36 | 23 | 5·9 |
| 36 | 22 | 6·74 |
| 36 | 21 | 7·58 |
| 35 | 28 | 0·85 |
| 35 | 27 | 1·7 |
| 35 | 26 | 2·56 |
| 35 | 25 | 3·41 |
| 35 | 24 | 4·26 |
| 35 | 23 | 5·11 |
| 35 | 22 | 5·97 |
| 35 | 21 | 6·82 |
| 35 | 20 | 7·67 |
| 34 | 27 | 0·86 |
| 34 | 26 | 1·72 |
| 34 | 25 | 2·59 |
| 34 | 24 | 3·45 |
| 34 | 23 | 4·31 |
| 34 | 22 | 5·17 |
| 34 | 21 | 6·03 |
| 34 | 20 | 6·9 |
| 34 | 19 | 7·76 |
| 33 | 26 | 0·87 |
| 33 | 25 | 1·74 |
| 33 | 24 | 2·62 |
| 33 | 23 | 3·49 |
| 33 | 22 | 4·36 |
| 33 | 21 | 5·23 |
| 33 | 20 | 6·1 |
| 33 | 19 | 6·98 |
| 33 | 18 | 7·85 |
| 32 | 25 | 0·88 |
| 32 | 24 | 1·76 |
| 32 | 23 | 2·65 |
| 32 | 22 | 3·53 |
| 32 | 21 | 4·41 |
| 32 | 20 | 5·29 |
| 32 | 19 | 6·18 |
| 32 | 18 | 7·06 |
| 31 | 24 | 0·89 |
| 31 | 23 | 1·79 |
| 31 | 22 | 2·68 |
| 31 | 21 | 3·57 |
| 31 | 20 | 4·46 |
| 31 | 19 | 5·36 |
| 31 | 18 | 6·25 |
| 30 | 23 | 0·9 |
| 30 | 22 | 1·81 |
| 30 | 21 | 2·71 |
| 30 | 20 | 3·61 |
| 30 | 19 | 4·52 |
| 30 | 18 | 5·42 |
| 29 | 22 | 0·91 |
| 29 | 21 | 1·83 |
| 29 | 20 | 2·74 |
| 29 | 19 | 3·66 |
| 29 | 18 | 4·57 |
| 28 | 21 | 0·93 |
| 28 | 20 | 1·85 |
| 28 | 19 | 2·78 |
| 28 | 18 | 3·7 |
| 27 | 20 | 0·94 |
| 27 | 19 | 1·87 |
| 27 | 18 | 2·81 |
| 26 | 19 | 0·95 |
| 26 | 18 | 1·9 |
| 25 | 18 | 0·96 |
+------+------+-------+

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.

+--------------------+
| Deductions |
| from standard. |
+--------+-----------+
|Count of|Percentage.|
| reed. | |
+--------+-----------+
| 50 | 3¾ |
| 52 | 3 |
| 54 | 2¼ |
| 56 | 1½ |
| 58 | ¾ |
| 60 | standard |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
+--------+-----------+

+------------------------------------------+
| Additions to standard. |
| |
+--------+-----------+
|Count of|Percentage.|
| reed. | |
+--------+-----------+
| 62 | ¾ |
| 64 | 1½ |
| 66 | 2¼ |
| 68 | 3 |
| 70 | 4 |
| 72 | 5 |
| 74 | 6 |
| 76 | 7 |
| 78 | 8 |
| 80 | 9 |
| 82 | 10 |
| 84 | 11 |
| 86 | 12 |
| 88 | 13 |
| 90 | 14 |
| 92 | 15 |
| 94 | 16 |
| 96 | 17 |
| 98 | 18 |
| 100 | 19 |
| 102 | 20½ |
| 104 | 22 |
| 106 | 23½ |
| 108 | 25 |
| 110 | 26½ |
| 112 | 28½ |
| 114 | 30½ |
| 116 | 32½ |
| 118 | 34½ |
| 120 | 36½ |
| 122 | 38½ |
| 124 | 40½ |
| 126 | 42½ |
| 128 | 44½ |
| 130 | 46½ |
| 132 | 48½ |
+--------+-----------+

=6. Picks.=--_Low Picks._--An addition of 1 per cent. shall be made for each pick or fraction of a pick below 11, thus:--

Below 11 to and including 10, 1 per cent.
„ 10 „ „ 9, 2 „
„ 9 „ „ 8, 3 „
„ 8 „ „ 7, 4 „

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:--

Weft below 26’s. when picks exceed 16
„ 26’s to 39’s inclusive „ „ „ 18
„ 40’s and above „ „ „ 20

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:--

Below 28’s to 20’s in 64 to 67 reed inclusive, 1 per cent.
„ „ 68 „ 71 „ „ 2 „
„ „ 72 „ 75 „ „ 3 „
Below 20’s to 14’s in 56 „ 59 „ „ 1 „
„ „ 60 „ 63 „ „ 2 „
„ „ 64 „ 67 „ „ 3 „

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:--

For 30’s add 1 per cent.
„ 29’s, 28’s, add 2 per cent.
„ 27’s, 26’s, „ 3 „
„ 25’s, 24’s, „ 4½ „
„ 23’s, 22’s, „ 6½ „
„ 21’s, 20’s, „ 8 „
„ 19’s, 18’s, „ 10½ „
„ 17’s, 16’s, „ 13 „
„ 15’s, 14’s, „ 16 „

_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:--

For 29’s, 28’s, add 1 per cent.
„ 27’s, 26’s, „ 2 „
„ 25’s, 24’s, 23’s, „ 3 „
„ 22’s, 21’s, 20’s, „ 4½ „
„ 19’s, 18’s, „ 6 „
„ 17’s, 16’s, „ 8 „
„ 15’s, 14’s, „ 10 „

=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:--

Below 26’s, the addition shall begin at 13
26’s to 39’s, inclusive, „ „ „ 14
40’s and above, „ „ „ 15

_High Picks._--When using weft--

Below 26’s, the addition for high picks shall begin at 21
26’s to 39’s, inclusive, „ „ „ „ „ „ 22
40’s and above, „ „ „ „ „ „ 23

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:--

One split uncut, add 5 per cent.
Two splits „ „ 7½ „

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:--

For cloths with plain grounds, 30 per cent.
For cloths with satin grounds, 25 „

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--

4 staves 12 per cent.
5 „ 13 „
6 „ 14 „
7 „ 15 „
8 „ 16 „
9 „ 17 „
10 „ 18 „
11 „ 19 „
12 „ 20 „
13 „ 21 „
14 „ 22 „
15 „ 23 „
16 „ 24 „
17 „ 25 „
18 „ 26 „
19 „ 27 „
20 „ 28 „

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:--

_Example._--Find the weaving of a 44-inch cloth, 40 yards long,
woven in a loom 48-inch reed space, 92 reed, 30 picks per
quarter-inch, 40’s twist, 60’s weft.

2_d._ per pick standard
·09 = 4½ per cent. added for reed space
-----
2·09
·3135 = 15 per cent. added for reed
------
2·4035 = price per pick, 100 yards, with standard picks
30 picks
-------
72·1050 = price for 30 picks 100 yards
40 yards
----------
100)2884·2000
----------
28·84200 = price for 40 yards
2·884200 = 10 per cent. added for high picks
---------
31·726200 Total.

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:--

_Example._--Find the weaving price for 38-inch cloth woven in a
48-inch reed space loom, 50 reed, 507 dividend, 50 change wheel, 75
yards long, 32’s twist, 36’s weft.

2_d._ per pick standard
·09 = 4½ per cent. added for reed space
---
2·09
·078375 = 3·75 per cent. deducted for reed
--------
2·011625 = price per pick, 100 yards, 50 reed, 48-inch loom.
507
--- = 10·14 picks per quarter inch.
50

2·0116 × 10·14 picks × 75 yards
-------------------------------
100 yards

= 15·283218 price for 75 yards
·152832 = 1 per cent. added for pick
---------
15·436050
·637508 = 4·13 per cent. deducted for narrow cloth
---------
14·798542 = price per list
1·4798542 = 10 per cent. deduction
----------
13·3186878 = net price.

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 7_d._ per lb., weft at 7½_d._ per lb.

Weaving 2_s._ 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 × 7_d._
------------------------------------- = 51.188_d._, cost of twist,
840 × 32’s

and

36 inches × 75 yards × 67 picks × 7½_d._
----------------------------------------- = 40.38_d._, cost of weft.
840 × 40’s
_d._
51.188 cost of twist
40.38 cost of weft
24.00 weaving wage
24.00 expenses
-------
139.568 cost of piece = 11_s._ 7½_d._

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 11_s._ 7½_d._ 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 2_s._ 6_d._, and the expenses 10 per cent. more than weaving, the expenses would be 2_s._ 9_d._

=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.

_Example._--Find the length of warp required to weave a piece of
5-stave satin 94 yards long (36 inches to the yard), 94 reed, 180
picks per inch, 60’s twist, 70’s weft.

The number of intersections per inch will be two-fifths of the
number of picks, as the warp intersects twice every five picks or
pattern.

∴180 × ⅖ = 72 intersections per inch;
and 72 × 4
----------- = 4 per cent. contraction.
70’s counts

The length of warp required to weave the 94 yards piece would
therefore, roughly, be 98 yards.

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:--

Intersections per inch = 120

4
---
70)480(6-6/7 per cent. contraction.
420
---
60

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 × 3
----------- = 4½ per cent.
40’s counts

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.

_Example._--If 120 yards of cotton weft weighs 20 grains, what
counts is it?

1000
--------- = 50’s counts.
20 grains

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.

_Example._--How many grains should 120 yards of 40’s yarn weigh?

1000 grains
----------- = 25 grains.
40’s counts

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:--

grains grains yards
8 : 7000 ∷ 34

34
-------
8)238000
-------
29750 yards in 1 lb.;

and this divided by 840 will give the counts, thus:--

29750
----- = 35·41 counts.
840

From this we get the formula:--

7000 × yards weighed
-------------------- = counts.
840 × 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?

yards yards grains
16800 : 16 ∷ 7000 : 6·6 grains.