Chapter XII · TEXTILE CALCULATIONS
Reading edition
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 × 52040 deniers =
6933⅓ yards per oz.
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 × 164 = 4000 yards per oz.
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—
140 + 160 = 3 + 2120 = 5120 = 24’s counts.
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.
110 + 120 + 160 = 6 + 3 +160 = 1060 = 16 or 6’s counts.
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 × 4036 = 552036 ends per inch.
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
Therefore, weight of warp =
19950025200
= 7 lbs. 14⅔ oz.
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.
Therefore, weight of weft = 21600033600 = 6 lbs. 66⁄7 oz.
Weight of weft = 6 lbs. 66⁄7 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 reed840 × counts = weight of warp.
The formula for the weft is—
Inches in reed × length of piece in yards × picks per inch840 × counts = weight of weft.
Working out the previous calculation in this manner, we get—
30 × 95 × 70840 × 30 = 7 lbs. 14⅔ oz. of warp.
30 × 90 × 80840 × 40 = 6 lbs. 66⁄7 oz. of weft.
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 inch840 = hanks,
and using the figures in the previous example—
30 × 95 × 70840 = 237½ hanks of warp.
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 2s. 6d., or 2d. 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.
Loom.
Percentage.
Inches.
Inches.
24
23
35
12
25
22
36
11
26
21
37
10
27
20
38
8¾
28
19
39
7½
29
18
40
6¼
30
17
41
5
31
16
42
3¾
32
15
43
2½
33
14
44
1¼
34
13
45
standard
ADDED TO STANDARD.
Loom.
Percentage.
Loom.
Percentage.
Inches.
Inches.
46
1½
59
26½
47
3
60
29
48
4½
61
31½
49
6
62
34
50
7½
63
36½
51
9
64
39
52
11
65
42
53
13
66
45
54
15
67
48
55
17
68
51
56
19
69
54
57
21½
70
57
58
24
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 Space.
Cloth.
Per cent.
Reed Space.
Cloth.
Per cent.
Reed Space.
Cloth.
Per cent.
72
65
1·38
58
45
9·07
43
33
3·77
72
64
2·76
58
44
9·98
43
32
4·81
72
63
4·14
58
43
10·89
43
31
5·77
72
62
5·52
57
50
1·54
43
30
6·54
72
61
6·9
57
49
2·78
43
29
7·31
72
60
8·28
57
48
4·01
43
28
8·08
72
59
9·66
57
47
5·25
42
35
0·97
72
58
11·04
57
46
6·48
42
34
1·95
72
57
12·19
57
45
7·72
42
33
2·92
71
64
1·41
57
44
8·64
42
32
3·9
71
63
2·81
57
43
9·57
42
31
4·87
71
62
4·22
57
42
10·49
42
30
5·65
71
61
5·62
56
49
1·26
42
29
6·43
71
60
7·03
56
48
2·52
42
28
7·21
71
59
8·44
56
47
3·78
42
27
7·99
71
58
9·84
56
46
5·04
41
34
0·99
71
57
11·02
56
45
6·3
41
33
1·97
71
56
12·19
56
44
7·25
41
32
2·96
70
63
1·43
56
43
8·19
41
31
3·95
70
62
2·87
56
42
9·14
41
30
4·74
70
61
4·3
56
41
10·08
41
29
5·52
70
60
5·73
55
48
1·28
41
28
6·32
70
59
7·17
55
47
2·56
41
27
7·11
70
58
8·6
55
46
3·85
41
26
7·89
70
57
9·79
55
45
5·13
40
33
1·0
70
56
10·99
55
44
6·09
40
32
2·0
70
55
12·18
55
43
7·05
40
31
3·0
69
62
1·46
55
42
8·01
40
30
3·8
69
61
2·92
55
41
8·97
40
29
4·6
69
60
4·38
55
40
9·94
40
28
5·4
69
59
5·84
54
47
1·3
40
27
6·2
69
58
7·31
54
46
2·61
40
26
7·0
69
57
8·52
54
45
3·91
40
25
7·8
69
56
9·74
54
44
4·89
39
32
1·01
69
55
10·96
54
43
5·87
39
31
2·03
69
54
12·18
54
42
6·85
39
30
2·84
68
61
1·49
54
41
7·83
39
29
3·65
68
60
2·98
54
40
8·8
39
28
4·46
68
59
4·47
54
39
9·78
39
27
5·27
68
58
5·96
53
46
1·33
39
26
6·08
68
57
7·2
53
45
2·65
39
25
6·89
68
56
8·44
53
44
3·65
39
24
7·7
68
55
9·69
53
43
4·65
38
31
1·03
68
54
10·93
53
42
5·64
38
30
1·85
68
53
12·17
53
41
6·64
38
29
2·67
67
60
1·52
53
40
7·63
38
28
3·49
67
59
3·04
53
39
8·63
38
27
4·32
67
58
4·56
53
38
9·42
38
26
5·14
67
57
5·83
52
45
1·35
38
25
5·96
67
56
7·09
52
44
2·36
38
24
6·78
67
55
8·36
52
43
3·38
38
23
7·6
67
54
9·63
52
42
4·39
37
30
0·83
67
53
10·9
52
41
5·41
37
29
1·67
67
52
12·16
52
40
6·42
37
28
2·5
66
59
1·55
52
39
7·43
37
27
3·33
66
58
3·1
52
38
8·28
37
26
4·17
66
57
4·4
52
37
9·12
37
25
5·0
66
56
5·69
51
44
1·03
37
24
5·83
66
55
6·98
51
43
2·06
37
23
6·67
66
54
8·28
51
42
3·1
37
22
7·5
66
53
9·57
51
41
4·13
36
29
0·84
66
52
10·86
51
40
5·16
36
28
1·69
66
51
12·16
51
39
6·19
36
27
2·53
65
58
1·58
51
38
7·05
36
26
3·57
65
57
2·91
51
37
7·91
36
25
4·21
65
56
4·23
51
36
8·77
36
24
5·06
65
55
5·55
50
43
1·05
36
23
5·9
65
54
6·87
50
42
2·09
36
22
6·74
65
53
8·19
50
41
3·14
36
21
7·58
65
52
9·51
50
40
4·19
35
28
0·85
65
51
10·83
50
39
5·23
35
27
1·7
65
50
12·15
50
38
6·1
35
26
2·56
64
57
1·35
50
37
6·98
35
25
3·41
64
56
2·7
50
36
7·85
35
24
4·26
64
54
5·4
49
42
1·06
35
22
5·97
64
53
6·74
49
41
2·12
35
21
6·82
64
52
8·09
49
40
3·18
35
20
7·67
64
51
9·44
49
39
4·25
34
27
0·86
64
50
10·79
49
38
5·13
34
26
1·72
64
49
11·87
49
37
6·01
34
25
2·59
63
56
1·37
49
36
6·9
34
24
3·45
63
55
2·75
49
35
7·78
34
23
4·31
63
54
4·12
49
34
8·67
34
22
5·17
63
53
5·49
48
41
1·08
34
21
6·03
63
52
6·87
48
40
2·15
34
20
6·9
63
51
8·24
48
39
3·23
34
19
7·76
63
50
9·62
48
38
4·13
33
26
0·87
63
49
10·71
48
37
5·02
33
25
1·74
63
48
11·81
48
36
5·92
33
24
2·62
62
55
1·4
48
35
6·82
33
23
3·49
62
54
2·8
48
34
7·72
33
22
4·36
62
53
4·2
48
33
8·61
33
21
5·23
62
52
5·6
47
40
1·09
33
20
6·1
62
51
7·0
47
39
2·18
33
19
6·98
62
50
8·4
47
38
3·09
33
18
7·85
62
49
9·51
47
37
4·0
32
25
0·88
62
48
10·63
47
36
4·91
32
24
1·76
62
47
11·75
47
35
5·83
32
23
2·65
61
54
1·43
47
34
6·74
32
22
3·53
61
53
2·85
47
33
7·65
32
21
4·41
61
52
4·28
47
32
8·56
32
20
5·29
61
51
5·7
46
39
1·11
32
19
6·18
61
50
7·13
46
38
2·03
32
18
7·06
61
49
8·27
46
37
2·96
31
24
0·89
61
48
9·41
46
36
3·88
31
23
1·79
61
47
10·55
46
35
4·8
31
22
2·68
61
46
11·69
46
34
5·73
31
21
3·57
60
53
1·45
46
33
6·65
31
20
4·46
60
52
2·91
46
32
7·57
31
19
5·36
60
51
4·36
46
31
8·5
31
18
6·25
60
50
5·81
45
38
0·94
30
23
0·9
60
49
6·98
45
37
1·87
30
22
1·81
60
48
8·14
45
36
2·81
30
21
2·71
60
47
9·3
45
35
3·75
30
20
3·61
60
46
10·47
45
34
4·69
30
19
4·52
60
45
11·63
45
33
5·62
30
18
5·42
59
52
1·48
45
32
6·56
29
22
0·91
59
51
2·96
45
31
7·5
29
21
1·83
59
50
4·45
45
30
8·25
29
20
2·74
59
49
5·63
44
37
0·95
29
19
3·66
59
48
6·82
44
36
1·9
29
18
4·57
59
47
8·0
44
35
2·85
28
21
0·93
59
46
9·19
44
34
3·8
28
20
1·85
59
45
10·38
44
33
4·75
28
19
2·78
59
44
11·26
44
32
5·7
28
18
3·7
58
51
1·51
44
31
6·65
27
20
0·94
58
50
3·02
44
30
7·41
27
19
1·87
58
49
4·23
44
29
8·16
27
18
2·81
58
48
5·44
43
36
0·96
26
19
0·95
58
47
6·65
43
35
1·92
26
18
1·9
58
46
7·86
43
34
2·88
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. Additions to standard.
Count of reed. Percentage. Count of reed. Percentage. Count of reed. Percentage.
50 3¾ 62 ¾ 98 18
52 3 64 1½ 100 19
54 2¼ 66 2¼ 102 20½
56 1½ 68 3 104 22
58 ¾ 70 4 106 23½
60 standard 72 5 108 25
74 6 110 26½
76 7 112 28½
78 8 114 30½
80 9 116 32½
82 10 118 34½
84 11 120 36½
86 12 122 38½
88 13 124 40½
90 14 126 42½
92 15 128 44½
94 16 130 46½
96 17 132 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,
„
2
„
„
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.
2d.
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.
2d.
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.
50750 = 10·14 picks per quarter inch.
2·0116 × 10·14 picks × 75 yards100 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 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.
d.
51.188
cost of twist
40.38
cost of weft
24.00
weaving wage
24.00
expenses
139.568
cost of piece
= 11s. 7½d.
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.
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 × 470’s counts
= 4 per cent. contraction.
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
(66⁄7 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 × 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.
Example.—If 120 yards of cotton weft weighs 20 grains, what counts is it?
100020 grains = 50’s counts.
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 grains40’s counts = 25 grains.
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:—
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?
yards
yards
grains
16800
:
16
7000
:
6·6 grains.
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.
Counts.
Diameter.
Counts.
Diameter.
Counts.
Diameter.
1
27½
28
145½
80
246
2
39
30
151
82
249
3
47½
32
156
84
252
4
55½
34
160½
86
256½
5
62
36
165
88
258½
6
67½
38
169
90
261
7
73
40
174½
92
264
8
78
42
178½
94
267
9
83½
44
183
96
270
10
87½
46
187
98
272½
11
91
48
191
100
275½
12
95
50
195
105
282
13
99
52
198½
110
289
14
103
54
202½
115
295½
15
106½
56
206½
120
302
16
110
58
210
125
308
17
113
60
213
130
314
18
117
62
216½
135
320
19
120
64
220½
140
326
20
123½
66
224
145
331½
21
126
68
227
150
337
22
129½
70
230½
160
349
23
132
72
233½
170
359
24
135
74
237
180
369
25
138
76
240½
190
380
26
140½
78
243
200
390
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.
Example.—If the diameter of a 16’s yarn is the 1/110th part of an inch, find the diameter of a 36’s.
√16
:
√36
110
4
:
6
110
:
165 Ans.
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:—
Example.—If the diameter of a 32’s is the 1/156 of an inch, what is the diameter of a 50’s?
32’s
:
50’s
1562
:
x2
or 32
:
50
24336
:
x2
50
32)
1216800
(38025
96
256
256
80
64
160
160
and √38025 = 195 Ans.
As the diameters of yarns vary as the square root of their counts, it follows that the diameters will always bear a certain relation to the yards in 1 lb. If this relation is once obtained, it becomes easy to calculate the diameter of any yarn on this principle.
Taking the diameter of a 32’s yarn from the table, viz. 156, it will be found that this is equal to the square root of the yards in 1 lb., less 5 per cent.
Example.
840
32
1680
2520
26880
yds. in 1 lb. of 32’s.
√26880 =
164
8
= 5 per cent.
156
= diameter of 32’s.
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.
Example 1.—How many threads per inch are required to make a perfectly balanced “2 and 1” twill cloth, with 24 yarns, warp and weft?
There are 3 ends and 2 intersections in the pattern; therefore
3 ends + 2 intersections = 5;
and as 5 : 3 ends
135
diameter : x
3
5)
405
81
threads per inch required.
Example 2.—How many threads per inch are required to make a perfectly balanced “3 up, 2 down, 2 up, 2 down twill” with 44’s yarns?
In this pattern there are 9 ends and 4 intersections; therefore
as 9 + 4 : 9
183
diameter of 44’s : x
or, as 13 : 9
183
9
13)
1647
(126 threads per inch required
13
34
26
87
78
9
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—
Ends + Intersections in proposed twill cloth. Ends + Intersections in given plain cloth.
4+2 : 4+4 103 : x
or 6 : 8 103
8
6)824
Ends required in twill cloth = 137⅓
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.
Another Example.—If a “two and two” twill cloth is made with 137 threads per inch, and it is proposed to make a cloth with the same counts of yarns in a “5 up, 2 down, 1 up, 2 down” twill, how many threads per inch are required to keep the same firmness?
In 40 ends of the proposed cloth there are 16 intersections, and in 40 ends of the sample cloth there are 20 intersections.
Then as
40 + 16
:
40 + 20
137
or
56
:
60
137
60
56)
8220
(146·8 threads. Ans.
56
262
224
380
336
440
If it is required to make a cloth with the same number of threads as a sample cloth, and to change the pattern and keep the same firmness, it is necessary to change the counts on the following principle:—
Rule.—As the sum of the ends and intersections in the sample cloth is to the sum of the ends and intersections in the proposed cloth, so is the square root of the counts in the sample to the square root of the counts in the proposed cloth.
Example.—If a plain cloth has been made with 36’s yarns, and it is proposed to make a “two and two” twill with the same number of threads per inch, find the counts required to keep the same “firmness.”
Ends + Inters. in sample cloth.
Ends + Inters. in proposed cloth.
or
4 + 4
:
4 + 2
√36
:
√x
8
:
6
6
:
6
8)36
4½
And 4½2 = 20·25 counts required.
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.
Threads in sample. Threads in proposed cloth. Counts in sample.
78 : 55 √32 : √x
or as 782 : 552 32
6084 : 3025 32
32
6050
9075
6084) 96800 (15·91, or 16’s nearly = counts required
6084
35960
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—
Counts in sample.
Counts in proposed cloth.
Threads in sample.
√32
:
√60
78
:
x
or as 32
:
60
782
:
x2
6084
60
32)365040
11407½
√11407 = 106.8 threads required.
The above may be proved correct by referring to the table of diameters. A plain cloth with 78 threads per inch of 32’s is “perfect,” and so is a plain cloth with 106½ threads per inch of 60’s.
The same principle must be employed if the warp and weft are of different counts, or if the threads per inch are not equal in warp and weft.
Example.—A sample cloth is made with 78 ends per inch of 32’s and 91 picks per inch of 44’s. How many picks will be required to keep the same firmness, if the weft only is changed to 60’s?
Counts in sample.
Counts in proposed cloth.
√44
:
√60
91
:
x
or as 44
:
60
912
:
x2
8281
60
44)496860
11292
=
x2
and √11292 = 106½ ∴ picks per inch required = 106½
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—
Weight of proposed cloth.
Weight of sample.
As 15 lbs.
:
10 lbs.
√45
: √x counts
or 152
:
102
45
to x
225
:
100
45
100
225)
4500
(20’s
counts required
450
0
To find the threads per inch required of the above counts—
Weight of proposed cloth.
Weight of sample.
15
:
10
93
10
15)
930
(62 threads required.
90
30
30
Then to make a piece of the same perfection or firmness as the sample piece, and to alter the weight from 10 lbs. to 15 lbs., the counts must be changed from 45’s to 20’s, and the threads per inch from 93 to 62.
To prove this is correct take a piece 20 inches wide, 102 yards long, 93 threads per inch both in warp and weft of 45’s yarns.
The weight of this sample piece will be—
20 × 102 × 93840 × 45 = 5 lbs. of twist;
and as there is the same weight of weft, the total weight of the piece will be 10 lbs.
Now calculate the weight of a piece of the same length and width with 62 threads per inch of 20’s yarns:—
20 × 102 × 62840 × 20 = 7½ lbs. of twist;
and with the same quantity of weft, the total weight of the piece will be 15 lbs.
This proves the calculation to be correct so far as altering the weight goes.
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.