Class _ 1L. Book . , Copyright N°___ COPYRIGHT DEPOSIT. PRACTICAL COTTON CALCULATIONS A TREATISE RELATING TO COTTON YARN, CLOTH STRUCTURE, LOOM AND MISCELLANEOUS COTTON MILL CALCULATIONS , BY ERNEST WHITWORTB Formerly Principal ofth Designing and Cloth Analysis Department, New Bedford Textile School PUBLISHED B"i ERNEST WHITWORTB 801 in BRIDGE, M \»>. LIBRARY of CONGRESS Two Cooies Received WAY 24 190f VU Copyright Entry CLASS Ou XXc., No. COPY B. Entered according to Acl of Congress in the year 1907 by ERNEST WHITW< >RTH In the office < >f the Librarian of < longress Washington, I). C. PREFACE TO FIRST EDITION. There are several reasons why the author of this hook has deemed its publication advisable. One reason has been the apparent want of a book dealing only with practical calculations. This h;»s been borne in mind in the compilation of this hook. The principal objecl has been to pu1 into a convenient form for reference a text-book of practical cotton yarn, cloth and general mill calculations. Being the only hook on the market, so far as the author is aware, dealing only with practical cotton calculations, it is submitted to all persons, from student to superintendent, who have occa- sion to deal with cotton, mill calculations. .Most of the rules and methods explained in the following pages are deducted from data gathered from practical experience and have never been printed before. The remainder, with the exception of the yarn numbering and cloth production tables, are common property, and may be found in almost every book on textile calculations. These are principally length and weight calculations, where take-up or contraction is not considered. PREFACE TO SECOND EDITION. The favorable reception accorded the former issue of "Practical Cotton Calculations," and the many commendatory letters as to its value, received from practical cotton mill men, have indicated the advisability of issuing this edi- tion. On account of the growing, use of silk in the finer grades of fabrics composed for the greater part of cotton, data regarding raw silk calcula- tions have been here inserted. More extended references have also been made to fabrics com- posed of various colors; also to fabrics contain- ing more than one counts of yarn in both warp and filling. E. W. May, 1907. GLOSSARY OF TECHNICAL WORDS AND TERMS. In the cotton manufacturing business, va- rious words, forms and terms are used in differ- ed mills to indicate the same thing; for ex- ample, warp yarn is known by one or other of ih«' terms yarn, thread, end. twist, etc. For this reason it has been deemed advisable to define the following list of the principal words and terms which will be used throughout this book: Yarn. The final product of combined fibres after leaving the spinning frame or mule. Ply Yarn. Two or more single yarns folded or twisted together. Cord Yarn. A heavy ply yarn. Cabled Yarn. Two or more ply yarns twisted together. Picks. Pilling yarns. Each filling yarn laid ;it righl angles between the warp yarns is termed a pick. Sley. The number of cuds per inch in the cloth, provided each denl in the vrc(\ in which it w;is made contained an equal number of ends. Pick. The number of picks per inch in the cloth, provided slop or cheek pegs are not used. Average Sley. The average number of ends per Inch in the cloth when some dents contain more ends Hi, -in others. b PRACTICAL COTTON CALCULATIONS Average Pick. The average number of picks per inch in the cloth when check pegs are used. Count of Cloth. The sley and pick of a cloth. If a cloth is said to count 80X100, it means 80 sley and 100 pick. The first number given always indicates the sley and the second num- ber the pick. A cloth is said to be square when the sley and pick are equal. Average Count of Cloth. The average sley and average pick of a cloth. When the average sley is different from the sley, or the average pick is different from the pick, the sley and pick, and average sley and average pick are usually written together, as follows : 80 100 110 124 In some mills this means 80 sley X 100 pick for the ground of the cloth, and 110 sley X 124 pick average, whereas in other mills the top line indicates the average and the lower the count of the base or ground of the cloth. The relative positions, above or below the line, of the ground and average count, are matters of choice. Counts or Numbers of Yarn. The relation- ship of length to weight in determining the size of yarn. Although the term "numbers" is used quite extensively the more universal term "counts" will be given preference in this book. Sley Reed. A reed that will produce a given sley in the cloth, provided two ends are drawn in each dent. PB ICTTCAL COTTON < \ i i i i \ nONS i Warp Pattern. One repeat of the arrange- menl of the differenl counts or differenl colors of llic warp yarns. Filling Pattern. One repeat of the differenl counts or differenl colors of the filling yams. The filling pattern may differ in extent Prom the pattern or effed shown on the face of the cloth. For example, the filling pattern in a Marseilles quill may repeat on a small number of picks, as six or eight, whereas live pattern formed by the weave would occupy an entire quilt. Selvedges or Selvages. Extra ends on the sides of the warp, used to strengthen the edges of the cloth and aid in keeping it at a uniform width. Fabric or Cloth. Warp and filling yarns combined and interlaced together. Multiplier. The oumber to multiply by. Product. The result of a multiplication problem. Sum. The result of an addition problem. Dividend. The number to be divided. Divisor. The number to divide by. Quotient. The resull of a division problem. Deduct. To subtrad or take Prom. -(- Pins or more, addition sign. X Multiplied by sign. -r- Divided by sign. — Minns or less, subtraction sign. R. P. M. Revolutions per minute. 5 PRACTICAL COTTON CALCULATIONS CONSTANTS OR CONSTANT NUMBERS. In dealing with textile calculations there are several numbers that constantly occur, making it feasible in some cases to dispense with one or other by cancelling one into the other. The following list contains the principal con- stants that will lie used in this book: .12; 8.33; .2314; 4.32 in. or 4 5-16 in. ; 764. The above constants, taken in rotation, are obtained as follows: .12 and 8.33. When 7000 (grains) and 840 (yards) occur in the same calculation, the 7000 may be dispensed with and .12 used instead of 840, or the 840 may be dispensed with and 8.33 used instead of 7000, because 840 -f- 7000 = .12, and 7000^ 840 = 8.33. In all calculations where a certain result may be obtained by multiplying by 8.33, the same result may be obtained by dividing by .12, or via vt zrsa, because 1 X 8.33 = 8.33 l-f-.12 =8.33 ( Mic yard of l's cotton yarn weighs 8^ grains. As most of the yarn calculations deal princi- pally with lengths and weights, the rules marked * will also apply to all other systems where higher counts indicate finer yarns by substituting their respective lengths instead of 840. PRACTICAL COTTON CALCULATIONS 9 In calculations where the constant 8.33 ap- pears, the rules will apply to other materials by substituting the following numbers: Worsted, 12.5; Woolen, run system, 4.375; Linen and Woolen, cut system, 23.33. The numbers given indicate the weight in grains of 1 yard of l's yarn in the respective materials. Instead of .12 the following numbers may be used : Worsted, .08 ; Woolen, run system, .228.+ ; Linen and Woolen, cut system, .043 — . If any rule marked * does not contain the number 840 or either of the constants .12 or 8.33, it will apply just as it stands for other materials as well as cotton. .2314 and 4.32. .2314 is used instead of because 7000 (grains) divided by 36 36X840 (inches per yard) and 840 (yards) equals .2314. 4.32 is used instead of — because 36X840 divided by 7000 equals 4.32. 764. This number is used in cloth calcula- tions instead of 840 to allow for contraction in length and width, also for size or dressing on the warp yarns. All cloths contract in length and width to a greater or less degree, making it necessary to allow a certain amount of extra length of yarn for a given length or width of cloth. The 764 allows (adds) 10%. 10% of 764 == 76, and 764 + 76 = 840. The constant 764 cannot be used for all classes of goods because the factors mentioned above 10 PRACTICAL COTTON CALCULATIONS will vary in amount in different cloths. For very coarse goods, or cloths where sizing is added to give weight, a lower constant mnst be used. The rules in which the constant 764 appears have been proved practical for cloths ranging in counts of yarn from 50 's to 70 's, and in counts of cloth from 60 to 80, the warp and filling in any one cloth, and the sley and pick being nearly equal. For some constructions of cloth the constant 764 will have to be substituted by another, higher or lower, according to whether the con- traction is small or great. As perhaps all persons who have occasion to use the rules containing the constant 764 will have access to a weave room, it is advisable that they select a few styles that vary in structure, i. e., that vary in the sley as compared to the pick, or in warp as compared to filling, and note the difference in contraction, if any, and the cause of the same. From data obtained in this manner constants may be formulated that can be used in future when dealing with other cloths of approximately similar constructions. In this connection it will be well to bear in mind the various modifying factors explained under the headings Cloth Contraction and Reed Cal- culations. With the exception of rules 3, 58, 60, 61, 62, 63, 80, 81 and those indicated with a *, the rules in this book may be used to aid in solving prob- lems connected with other textile materials as well as cotton. YARN CALCULATIONS, LENGTH AND WEIGHT STANDARDS. The following standards are used when dealing with cotton calculations: Standard of Lengths for Cotton. If yds. = The circumference of reel, or lwrap. 120 yds. = 1 lea, or 80 wraps of the reel. 840 yds. = 7 leas, or 1 hank. Standard of Weights for all Textile Materials. 437.5 grains = 1 ounce, avoirdupois. 7000 grains = 16 ozs., or 1 pound. The counts of cotton yarns are based on the number of times that the standard of length, 840 yards, is contained in the length of yarn required to balance the standard of weight, 1 pound; thus, if 840 yards of yarn balance lib, the counts are l's. If 4200 yards of yarn balance lit), the counts are 5's, because 4200 -f- 840 = 5 ; and so on, the higher the counts the more yards per pound, therefore the higher the counts the finer the yarn. See page 33 for table of counts and yards per pound of cotton yarns. 12 PRACTICAL COTTON CALCULATIONS TESTING YARNS FOR COUNTS, BY COMPARI- SON. When analyzing small cloth samples, the average counts of the yarn may readily be found from the cloth by Rule 49. In some cases the warp and filling may vary considerably in counts, making it necessary to find the counts of each separately. The counts of the warp yarn is generally found, the mills usually using but few different warp counts, and varying the weights of the cloths by changing the counts of the filling, if necessary, because it is more practical and convenient. Although short method No. 1, on the following page, may be applied for finding the counts of the yarn by weighing a few inches, the most practical method is by comparing the warp yarn from the cloth with warp yarns of known counts. A B zzazzzzzzzz2zzzzzzzzzzzzr& ; ZZZ uiititittttttittuiiujyj* fffffffffeffffnii mzzzjQcz Fig. 1. B Fig. 2. Fig. 1 illustrates the method of testing known with unknown counts; "A" represents the known and "B" the unknown counts. To get the yarns as here shown place one or more yarns PRACTICAL COTTON CALCULATIONS 13 of the known at right angles to the unknown counts, and twist them, making, as it were, one continuous yarn. If one yarn is coarser than the other, it can readily be seen, after twisting. Fig. 2 shows the yarns in Fig. 1 after being- twisted. It is advisable to wet the yarns, at the point where they are crossed, before twisting. The greater the number of strands of each count used, the less the liability to error. This method of testing is used practically, because a mill usually uses the nearest counts of warp yarn that they have on hand to the counts of the warp in the sample if they intend to duplicate it. Some persons do not care to trust the naked eye when comparing yarns, but prefer to use a magnifying glass of some kind, such as a pick glass, reading glass, or microscope. TESTING YARNS FOR COUNTS, BY WEIGH- ING SHORT LENGTHS. 1. The number of inches that weigh 1 gr. X .2314 = Counts. 2. The number of strands of yarn, each 4 fl- inches or 4.32 inches long that weigh 1 grain = Counts. 3. Number of yards weighed X 8 J -f- weight in grains = Counts. 4. Number of yards weighed -j- .12 X weight in grains = Counts. 5. 1000 divided by weight in grains of 1 lea = Counts. 14 PRACTICAL COTTON CALCULATIONS REELING YARNS. To Find Counts of Yarn from Any Number of Yards Reeled or Measured. *Rule 1. Multiply the number of yards reeled by 84, and divide by the weight in grains. Example. 10 yards of cotton yarn weigh 2 grains. What are the counts? 10 yds. X 8.333 < ., - = 41. bb s counts, Ans. 2 grs. or by "Rule 2. Divide the number of yards r< < led by .12 and the weight in grains. Example. Same as preceding. 10 yds. tH nn . . — — — =- — — = 41.66 s counts, Ans. .12 X 2 grs. Rules 1 and 2 will apply when desiring To Find the Number of Hank of Roving. To Find Counts of Yarn from Bobbins or Cops. Reel one lea each from 1, 2, 3, or 4 bobbins or cops, and use — Rule 3. Add 3 ciphers to the number of leas reeled and divide by the weight of the yam in grains. Example. s One lea is reeled from each of 4 bobbins and found to weigh 50 grains. What are the counts? PRACTICAL COTTON CALCULATIONS 15 4000^-50 grs. = 80's counts, Ans. In the above rule \ of a hank is considered in connection with a corresponding portion of a pound, i. e., } of 7000 grains = 1000 grains. If 1 lea is reeled from each of 4 bobbins, then 4 leas are reeled, or f of a hank. As f of a hank is weighed, the weight must be divided into 4000 grains, or f of a pound. The principal reasons why 1 lea is reeled from each of 4 bobbins in preference to 4 leas from 1 bobbin, or 1 lea from 1 bobbin, are that the yarn may be reeled on an ordinary reel from 4 bobbins at a time, thus saving time, and a better average may be obtained, as there is greater liability for the yarn to vary in size on 4 bobbins than on 1 bobbin. On the four following pages Draper's cotton yarn numbering tables are reproduced by per- mission of the Draper Co., Hopedale, Mass. These tables are based on the weight in grains of 1 lea, or 120 yards. If more than one bobbin or cop is used, and more than one lea weighed, divide the weight in grains by the number of leas. Example. One lea is reeled from each of 4 bobbins, and found to weigh 50 grains. What are the counts ? 50 ^- 4 = 12.5 grains per lea, which shows on the table to be 80 's yarn. 16 PRACTICAL COTTON CALCULATIONS Table for numbering Cotton Yarn by the weight in g'rains of 120 yards or I skein. 120yds Number 120yds Number 120yds. Number 120yds Number 120yds. Number weigh of weigh of weigh of weigh of weigh of grains. Yam. grains. Yarn. grains Yarn. grains Yarn grains. Yarn. 1. 1000. 14. 71.43 21 47.62 28. 35.71 35. 28.57 2. 500. .1 70.92 .1 47.39 .1 35.59 .1 28.49 3. 333.3 2 70.42 2 47.17 .2 35.46 .2 28.41 4. 250.0 3 69.93 3 46.95 .3 35.34 .3 28.33 5. 200.0 4 69.44 .4 46.73 .4 35.21 .4 28.25 5.5 181.8 .5 68.97 5 46.51 .5 35.09 .5 28.17 6. 166.7 .6 68.49 6 46.30 .6 34.97 .6 28.09 6.5 153.8 .7 68.03 .7 46.08 .7 34.84 .7 28.01 7. 142.9 .8 67.57 8 45.87 .8 34.72 .8 27.93 7.5 133.3 .9 67.11 .9 45.66 .9 34.60 .9 27.86 8. 125.0 15. 66.07 23. 45.45 29 34.48 36 27.78 1 123.5 .1 66.23 .1 45.25 .1 34.36 .1 27.70 2 122.0 .2 65.79 .2 45.05 .2 34.25 .2 27.62 3 120.5 3 65.36 .3 44.84 .3 34.13 .3 27.55 4 119.0 .4 64.94 .4 44.64 4 34.01 .4 27.47 5 117.6 .5 64.52 .5 44.44 .5 33.90 .5 27.40 6 116.3 6 64.10 .6 44.25 .6 33.78 .6 27.32 7 114.9 7 63.69 .7 44.05 7 33.67 7 27.25 .8 113.6 .8 63.29 .8 43.86 .8 33.56 .8 27.17 .9 112.4 .9 62.89 .9 43.67 .9 33.44 .9 27.10 9. 111.1 16 62.50 23- 43.48 30 33.33 37 27.03 1 109.9 1 62.11 .1 43.29 33.22 1 26.95 2 108.7 2 61.73 .2 43.10 .2 33.11 .2 26.88 3 107.5 3 61.35 .3 42.92 .3 :'.:>,.< in .3 26.81 4 106.4 4 60.98 .4 42.74 .4 32.89 .4 20.74 5 105.3 .5 60.61 5 42.55 .5 32.79 .5 20.67 6 104.2 6 60.24 .6 42.37 .6 32.68 .6 20..60 .7 103.1 7 59.88 7 42.19 .7 32.57 .7 20.53 .8 102.0 .8 59.52 .8 42.02 .8 32.47 .8 20.46 .9 101.0 .9 59.17 .9 41.84 .9 32.36 .9 26.39 to 100.0 17. 58.82 24. 41.67 31 32.26 38. 20.32 .1 99.01 .1 58.48 1 41.49 .1 32.16 .1 26.25 .2 98.04 2 58.14 2 41.32 .2 32.05 .2 26.18 .3 97.09 3 57.80 3 41.15 .3 31.95 .3 2(5.11 .4 96.15 4 57.47 4 40.98 .4 31.85 .4 20.04 5 95.24 5 57.14 5 40.82 .5 31.75 .5 25.D7 6 94.34 6 56.82 .6 40.65 .6 31.65 .6 25.91 7 93.46 7 56.50 .7 40.49 7 31.55 .7 25.84 8 92.59 .8 56.18 .8 40.32 .8 31.45 .8 25.77 9 91.74 .9 55.87 9 40.16 .9 31.35 .9 25.71 11. 90.91 18. 55.56 25. 40.00 32. 31.25 39. 25.04 1 90.09 1 55. 25 1 39.84 .1 31.15 .1 25.58 2 89.29 2 54.95 .2 39.68 .2 31.06 .2 25.51 3 88.50 3 54.64 3 39.53 .3 30.96 .3 25.45 4 87.72 4 54.35 4 39.37 .4 30.86 4 25.38 5 86.96 .5 54.05 5 39.22 .5 30.77 5 25.32 6 86.21 .6 53.76 .6 39.06 6 30.67 .6 25.25 .7 85.47 .7 53.48 .7 38.91 7 30.58 .7 25.19 .8 84.75 .8 53.19 .8 38.76 .8 30.49 .8 25.13 .9 84.03 9 52.91 9 38.61 .9 30.40 .9 25.06 12. 83.33 19. 52.63 26. 38.46 33. 30.30 *0. 25.00 1 82.64 .1 52.36 38.31 .1 30.21 .1 24.94 .2 81.97 .2 52.08 .2 38.17 .2 30.12 £ 24.88 .3 81.30 .3 51.81 3 38.02 .3 30.03 .ft 24.81 .4 80.65 4 51.55 4 37.88 .4 29.94 .4 24.75 .5 80.00 .5 51.28 5 37.74 .5 29.85 .5 24.69 .6 79.37 .6 51.02 .6 37.59 .6 29.76 .6 24.63 .7 78.74 .7 50.76 .7 37.45 .7 29.67 .7 24.57 8 78.12 .8 50.51 .8 37.31 .8 29.59 .8 24.51 .9 77.52 .9 50.25 .9 37.17 .9 29.50 .9 24.45 13. 76.92 30. 50.00 27- 37.04 34. 29.41 41. 24.39 .1 76.34 .1 49.75 .1 36.90 .1 29.33 .1 24.33 .2 75.76 .2 49.50 .2 36.77 .2 29.24 .2 24.27 .3 75.19 .3 49.26 .3 36.63 .3 29.15 .3 24.21 .4 74.63 .4 49.02 .4 36.50 .4 29.07 .4 24.15 .5 74.07 .5 48.78 .5 36.36 .5 28.99 .5 24.10 .6 73.53 .6 48.54 .6 36.23 .6 28.90 .6 24.04 .7 72.99 .7 48.31 .7 36.10 .7 28.82 .7 23.98 .8 72.46 .8 48.08 .8 35.97 .8 28.74 .8 23.92 .9 71.94 .9 47.85 .9 35.84 .9 28.65 .9 23.87 PRACTICAL COTTON CALCULATIONS 17 Table tor numbering Cotton Yarn by the weight 120 yards or I skein. 120yda Number 120yds 'Number 120yds Number 120yds Number 120yds Number weigh of weigh of weigh of weigh of weigh of grains. YUI-D. graius Yarn. graius Yaru graius Yaru grains. Yarn 42. 23.81 49. 20.41 56 17.86 63 15.87 70. 14.29 .1 23.75 20.37 .1 17.83 .1 15.85 .1 14.27 .2 23.70 '.2 20.33 2 17.79 .2 15.83 .2 14.25 .3 23.G4 .3 20.28 .3 17.70 .3 15.80 .3 14.22 .4 23.58 .4 2H.24 .4 17.73 .4 15.77 .4 14.2< .5 23.53 .5 20.20 .5 17.70 .5 15.75 .5 14.18 .6 23.47 .6 20.10 .0 17.67 .6 15.72 .0 14.1f, .7 23.42 .7 20.12 .7 17.04 .7 15.70 .7 14.14 .8 23.3H .8 20.08 .8 17.G1 .8 15.87 .8 14.12 .9 23.31 .9 20.04 .9 17.57 .9 15.65 .9 14.10 43. 23.20 50. 20.00 57- 17.54 64. 15.62 71. 14.08. .1 23.20 .1 19.90 .1 17.51 .1 15.00 .1 14.06 .2 23.15 .2 19.92 ,2 17.48 .2 15.58 .2 14.04 .3 23.09 .3 19.88 .3 17.45 .3 15.55 .3 14.03 .4 23.04 .4 1 9.84 .4 17.42 .4 15.53 .4 14.01 .5 22.99 .5 19.80 .5 17.39 .5 l5.5ti .5 13.99 .0 22.94 .6 19.76 .6 17.36 .6 15.48 .6 13.97 .7 22.88 .7 19.72 .7 17.33 .7 15.46 .7 13.95 .8 22.83 .8 19.09 .8 17.30 .8 15.43 .8 13.93 .9 22.78 .9 19.05 .0 17.27 .9 15.41 .9 13.91 44. 22.73 51 19.61 58. 17.24 65. 15.38 TA. 13.89 .1 22.08 .1 19.57 .1 17.21 .1 15.30 .1 13.87 .2 22.02 . .2 19.53 .2 17.18 .2 I 15.34 .2 13.85 .3 22.57 .3 19.49 .3 17.15 .3 15.31 .3 13.83 .4 22.52 .4 19.46 .4 17.12 .4 15.29 .4 13.81 .5 22.47 .5 19.42 .5 17.09 .5 15.27 .6 13.79 .6 22.42 .6 19.38 .6 17.06 .6 15.24 .6 13.77 .7 22.37 .7 19.34 .7 17.04 .7 15.22 .7 13.76 .8 22.32 .8 19.31 .8 17.01 .8 15.20 .8 13.74 .9 22.27 .9 19.27 .9 16.98 .9 15.17 .9 13.72 45. 22.22 554. 19.23 59 16.95 6b 15.15 7& 13.70 .1 22.17 .1 19.19 16.92 .1 15.13 .1 13.68 .2 22.12 .2 19.16 .2 16.89 .2 15.11 .2 13.66 .3 22.08 .3 19,12 .3 16.86 .3 15.08 .3 13.64 .4 22.03 .4 19.08 .4 16.84 .4 15.06 .4 13.02 .5 21.98 .5 19.05 .5 16.81 .5 15.04 .6 13.61 .0 21.93 .6 19.01 .6 16.78 .0 15.02 .6 13.59 .7 21.88 .7 18.98 .7 16.75 .7 14.99 .7 13.57 .8 21.83 .8 18.94 .8 16.72 .8 14.97 .8 13.55 .11 21.79 .9 18.9(i .9 10.6!j .9 14.95 9 13.53 4b 21.74 53. 18.87 00. 16.67 67. 14.93 74. 13.51 .1 21.69 .1 18.83 .1 16.64 .1 14.90 .1 13.50 .2 31.85 '.2 18.80 .2 16.61 .2 14.88 .2 13.48 .3 21.60 .3 18.70 .3 16.58 .3 14.80 .3 13.40 .4 21.55 .4 18.73 .4 10.5< A 14.84 .4 13.44 .5 .'1.51 .5 °1 8.011 .5 16.53 .6 14.81 .6 13.42 .0 31,46 .6 18.00 .6 16.51 .0 14.79 .0 13.40 .7 21.41 .7 18.62 .7 16.47 .7 14.77 .7 13.39 .8 31.37 .8 18.59 .8 16.45 .8 14.75 .8 13.37 .9 21.32 .9 18.55 .9 16.42 .9 14.73 .9 13.35 4? 21.28 54. in. 52 61. 10.39 68. 14.71 76. 13.33 .1 21.23 .1 18.48 .1 10.37 .1 1 4.08 .1 13.32 .2 21.1 9 .2 18.45 .2 10.34 .2 1 4.6b .2 13.3o .3 21.14 .3 18.42 .3 10.31 .3 14.04 .3 13.28 .4 21.10 .4 18.38 .4 16.29 .4 14.62 .4 13.20 .6 21.05 .5 18.35 .5 16.26 .5 14.00 .5 13.25 .6 21.01 .6 18.32 .6 16.23 .0 14.58 .0 13.23 .7 20.90 .7 18.28 7 10.21 .7 14.50 .7 13.21 .8 20.92 .8 18.25 .8 16.19 .8 14.53 .8 13.19 .9 20.8.S .9 18.21 9 16.16 .9 14.51 .9 13.18 «b. 20.83 55. 18.18 ua 10.13 6b 14.411 7b 13.10 20.79 .1 18.15 10.10 14.47 .1 13 14 '.2 20.75 .2 18.12 '§ 10.08 '.2 14.45 .2 13.12 .3 20.70 t 18. 08 .3 10.05 .3 14.43 .3 13.11 .4 2O.C0 18.05 .4 10.03 .4 14.41 .4 13.09 .5 20.02 .6 IS. 02 .5 16.00 .5 14.39 ,6 13.07 .6 1 20.57 .6 17.99 .6 15.97 .0 14.37 .0 13.05 .7 I 20.53 .7 17.95 7 15.95 7 14.35 .7 13.IM .8 20.49 .8 17 92 .8 15.92 .8 14.33 .8 13.02 .9 20.45 .9 17.89 16.90 .9 14.31 .9 13.00 18 PRACTICAL COTTON CALCULATIONS Table for numbering Cotton Vam by the weight in grains of 120 yards or I skein 120yds. Number liOvds Number 120vds Number 120>ds Number l^OvJs Number weigh of weigh of weigh of weigh ol weigh of grains. Yarn grains Yarn grains Yarn grains Yarn grains. Yarn 77. 12.99 84 11.90 91. 10.99 98. 10.20 105. 9.52 .1 12.97 .1 11.89 .1 10.98 .1 10.19 .1 9.51 .2 12.95 .2 11.88 .2 10.90 .2 10.18 .2 9.51 .3 12.94 .3 11.80 .3 10.95 .3 10.17 .3 9.50 .4 12.92 .4 11.85 .4 10.94 .4 10.10 .4 9.49 .5 12.90 .5 11.83 .5 10.93 .5 10.15 .5 9.48 .li 12.89 .0 11.82 .6 10.92 .0 10.14 .0 9.47 .7 1 2.87 .7 11.81 .7 10.91 .7 10.13 .7 9.40 .8 12.85 .8 11.79 .8 10.89 .8 10.12 .8 9.45 .9 12.84 .:> 11.78 .9 10.88 .9 10.11 .9 9.44 78. 1 2.S2 85. 11.76 92. 10.87 99. 10.10 106. 9.43 12.80 .1 11.75 .1 lO.HO :i 10.0& .1 9.43 '.2 12.79 .2 11.74 .2 10.85 .2 10.08 .2 9.42 .3 12.77 3 11.72 .3 10. «3 .3 10.07 .3 9-41 .4 1 2.7G .4 11.71 .4 10.82 .4 10.00 .4 9.40 .5 12.74 .5 11.70 .5 10.81 .5 10.05 .5 9.39 .6 12.72 12.71 .0 1 1.08 .0 10.80 .0 10.04 .6 9.38 .7 .7 1 1 .07 7 10.79 .7 10-03 .7 9-37 .8 12.09 .8 11.66 .8 10.78 .8 10.02 .8 9.36 .9 12.07 .9 11.64 9 10.70 9 10-01 9 9-35 79. 12.00 86. 11.03 93. 10.75 100. 10.00 107. 9.35 .1 12.04 .1 11.01 .1 10.74 .1 9.99 .1 9.34 .2 12.03 .2 11.00 3. 10.73 2 9.98 .2 933 .3 12.G1 .3 11.59 3 10.72 .3 9.97 .3 9-32 .4 12.59 .4 11.57 .4 10.71 .4 9-96 .4 9-31 .6 12.58 .5 11.50 5 10.70 :I 9.95 .5 9.30 .6 12.50 .6 11.55 6 10.68 9-94 .6 9-29 .7 12.55 .7 11.53 .7 10.67 .7 9.93 .7 9.29 .8 12.53 .8 11.52 .8 10.60 .8 9.92 .8 9.28 9 12.52 .9 11.51 9 10.65 .9 9.91 9 9-27 80. 12.50 87. 11.49 94. 10.64 101. 9.90 108. 9-26 .1 12.48 .1 11.48 .1 10.03 .1 9.89 .1 9-26 .2 12.47 .2 11.47 .2 10.02 .2 9.88 .2 924 .3 12.45 .3 11.45 3 10.00 .3 9.87 .3 9-23 .4 12.44 .4 11.44 4 10.59 .4 9.86 .4 9-23 .6 12.42 .5 11.43 .5 10.58 .5 9.85 .5 9.22 .6 12.41 .6 11.42 .6 10.57 .6 9.84 .6 9.21 .7 12-39 .7 11.40 .7 10.50 .7 9-83 .7 9-20 .8 12.38 .8 11.39 .8 10.55 .8 9.82 .8 9.19 .9 12.30 9 11.38 9 10.54 9 9.81 .9 9.18 81 12.35 88 11.30 95- 10.53 102. 9.80 109. 9.17 .1 12.33 1 11.35 1 10.52 .1 9.79 .2 9.10 .2 12.32 .2 11.34 2 10.50 .2 9.78 .4 9.14 .3 12.30 .3 11.33 .3 10.49 .3 9.78 .6 9.12 .4 12.29 .4 11.31 4 10.48 .4 9.77 .8 9.11 .5 12.27 .5 11.30 .5 10.47 .5 9.70 110. 9.09 .6 12-25 11.29 .0 10.46 6 9.75 .2 9.07 7 12.24 .7 11.27 7 10.45 .7 9.74 .4 9.06 .8 12-22 .8 1 1 .20 .8 10.44 .8 9.73 .6 9.04 .9 12.21 9 11.25 10.43 .£> 9.72 .8 9.03 82- 12-20 89 1 1.24 96 10.42 103 9.71 111. 9.01 .1 12.18 1 11.22 .1 10.41 .1 9.70 .2 8.99 2 12.17 .2 11.21 .2 10.40 .2 9.09 .4 8.98 .3 12.15 .3 11.20 .3 10.38 .3 9.08 .6 8.90 .4 12.14 .4 11.19 .4 10.37 .4 9.07 .8 8.94 .5 12.12 .5 11.17 .5 10.30 .5 9.06 112. 8.93 .6 12-11 .6 11.10 .6 10.35 .6 9.65 .2 8.91 .7 12.09 .7 11.15 .7 10.34 .7 9.64 .4 8.90 .8 12.08 .8 11.14 .8 10.33 .8 9.63 .6 8.88 .9 12.06 9 11.12 .9 10.32 .9 9.G2 .8 8.87 83. 12.05 90. 11.11 97 10.31 104. 9.02 113. 8,85 .1 12.03 .1 11.10 .1 10.30 .1 9.61 .2 8.83 .2 12.02 .2 11.09 .2 10.29 .2 9.60 .4 8.82 .3 12.00 .3 11.07 .3 10.28 .3 9.59 .6 8.80 .4 11.99 .4 11.06 .4 10.27 .4 9.58 .8 8.79 .5 11.98 .6 11.05 .5 10.20 .5 9.57 114. 8.77 .6 11.96 .0 11.04 .6 10.25 .6 9.56 .2 8.70 .7 11.95 .7 11.03 .7 10.24 .7 9.55 4 8.74 .8 1 1 .93 .8 11.01 .8 10.22 .8 9.54 .6 8.73 .9 11.92 .9 11.00 .9 10.21 .9 9.53 .8 8.71 PRACTICAL COTTON CA I.Cl I.ATIONS l'.l Table for numbering Cotton Yarn by the weight in grains of 120 ^yards or I skein 120>>ls Number 120yds Number I20.yds Number 120vds Number 120N.IS Number weigh of weigh of weigh of we.gh of wei^h of graius. Yarn grains. Yarn. grains. Yarn. grains. Yarn grains Yarn. 2.50 115. 8.70 140. 7.14 180. 5.56 250 4.00 400. .2 8.68 .5 7.12 181. 5.52 252. 3.97 405. 2.47 .4 8.67 141. 7.09 182. 5.40 254. 3.94 410. 2.44 .6 8.65 .5 7.07 183. 5.40 256. 3.91 415. 2.41 .8 8.64 142. 7.04 184. 5.43 258. 3.88 420. 2.38 116. 8.62 .5 7.02 185. 5.41 200. 3.85 425. 2.35 .2 8.61 143. 6.99 186. 5.38 202. 3.82 430. 2.3H .4 8.59 .5 6.97 187. 5.35 264. 3.79 435. 2.30 .6 8.58 144. 6.94 1 ss. 5.32 260. 3.76 44H. 2.27 .8 8.56 .5 6.92 189. 5.29 268. 3.73 445. 2.25 117. 8.55 145. 6.90 190. 5.26 270. 3.70 450. 2.22 .2 8.53 .5 6.87 191. 5.24 272. 3.68 455. 2.20 .4 8.52 140. 6.85 192. 5.21 274. 3.65 460. 2.17 .6 8.50 .5 6.83 193. 5.18 276. 3.62 405. 2.15 .8 8.49 147. 6.80 194. 5.15 278. 3.60 470. 2.13 118. 8.47 .5 6.78 195. 5.13 280. 3.57 475. 2.11 .2 8.46 148. 6.76 196. 5.10 282. 3.55 480. 2.08 .4 8.45 .5 6.73 197. 5.08 284. 3.52 485, 2.00 .0 8.43 149. 6.71 198 5.05 280. 3.50 490. 2.04 .8 8.42 .5 6.69 199. 5.03 288. 3.47 495. 2.02 119. 8.40 150. 6.67 300 5.00 290. 3.45 500. 2.00 .2 8.39 .5 6.64 201. 4.98 292. 3.42 505. 1.98 .4 8.38 151. 6.62 202. 4.95 294. 3.40 510. 1.96 .6 8.36 .5 6.60 203. 4.93 290. 3.38 515. 1.94 .8 8.35 152. 6.58 204 4.90 298 3.36 520. 1.92 120. 8.33 .5 6.56 205. 4.88 300. 3.33 525. 1.90 .2 8.32 153. 6.54 206. 4.85 3(12. 3.31 530. 1.89 .4 8.31 5 6.51 207. 4.83 304. 3.29 535. 1.87 .6 8.29 154. 6.49 208. 4.81 306. 3.27 540. 1.85 .8 8.28 5 6.47 209. 4.78 308. 3.25 545. 1.83 121. 8.26 155. 6.45 210. 4.70 310 3.23 550. 1.82 .4 8.24 .5 6.43 211. 4.74 312 3.21 555. 1.80 .6 8.22 156. 6.41 212. 4.72 314. 3.18 500. 1.79 .8 8.21 .5 6.39 213. 4.09 316. 3.17 505. 1.77 122. 8.20 157. 6.37 214. 4.07 318. 3.14 570. 1.75 .5 8.16 .5 6.35 2 1 5. 4.65 320. 3.12 575. 1.74 123. 8.13 158. 6.33 216. 4.63 322. 3.11 580. 1.72 5 8.10 5 6.31 217. 4.61 324. 3.09 585. 1.71 124. 8.06 159. 6.29 218. 4.59 320. 3.07 500. 1.00 .5 8.03 5 6.27 219. 4.57 328. 3.05 595. 1.68 125. 8.00 160. 6.25 220 4.55- 330 3.03 600. 1.67 .5 7.97 5 6.23 221 4.52 3:*, 2. 3.01 010. 1.04 126. 7.94 161. 6.21 222. 4. 5H 334. 2.99 020. 1.61 .5 7.91 5 6.19 223 4.48 336. 2.98 030. 1.59 127. 7.87 162. 6.17 224 4.46 338. 2.96 040. 1.50 ■5 7.84 .5 6.15 225 4.44 340. 2.94 050. 1.54 128. 7.81 163. 6.13 226. 4.42 342. 2.92 660. 1.52 .5 7.78 5 6.12 227 4.41 344. 2.91 070. 1.49 129. 7.75 164. 6.10 228. 4.39 346 2.89 080. 1.47 5 7.72 .5 6.08 229 4.37 348 2.87 690. 1.45 130. 7.09 165. 6.06 3.30. 4.35 350 2.86 700. 1.43 5 7.66 .5 6.04 231. 4.33 352 2.84 710. 1.41 131. 7.63 166. 6.02 232 4.31 354. 2.82 720. 1.39 .5 7.60 .5 6.01 233. 4.29 350 2.81 730. 1.37 132. 7.53 167. 5.99 234 4.27 358 2.79 740. 1.35 .5 7.55 .5 5.97 235. 4.26 360. 2.78 750. 1.33 133. 7.52 168. 5.95 236. 4.24 302. 2.76 760. 1.32 .5 7.49 .5 5.93 237. 4.22 304. 2.75 770. 1.30 134. 7.46 169. 5.92 238. 4.20 306. 2.73 780. 1.28 .5 7.43 5 5.90 239. 4.18 368. 2.72 790. 1.27 136, 7.41 170. 5.88 240. 4.17 370 2.70 800. 1.25 .?» 7.38 171. 5.85 241. 4.15 372. 2.69 820. 1.22 13G. 7.35 172 5.81 242. 4.13 374. 2.07 840. 1.19 .5 7.33 173. 5.78 243. 4.12 376. 2.66 800. 1.16 137. 7.30 174. 5.75 244. 4.10 378. 2.65 880. 1.14 .5 7.27 175. 5.71 245. 4.08 380. 2.03 900. 1.11 138. 7.25 176. 5.68 246. 4.07 382. 2.02 925. 1.08 .5 7.22 177. 5.65 247. 4.05 385. 2.60 950. 1 .05 139. 7.19 178. 5.62 248. 4.03 390. 2.56 075. 1.03 .6 7.17 179. 5. 5J) 249 4.0? 395. 2.53 1000. 1.00 20 PRACTICAL COTTON CALCULATIONS SYSTEMS OF NUMBERING YARNS OF VA- RIOUS MATERIALS. The following systems, where higher counts indicate finer yarns, are used in the United States : Raw silk = number of yards per ounce. Spun silk — 840 yards per hank. Cotton = 840 yards per hank. Worsted = 560 yards per hank. Woolen = 1600 yards per rain. Woolen = 300 yards per cut. Linen = 3( M ) ya r( Is per cut. The cut system of woolen counts is principally used in the vicinity of Philadelphia. The yarn calculations applying' to cotton will also apply to any of the above systems, using their respective standard lengths instead of 840. EQUIVALENT COUNTS. To Find Equivalent Counts of Yarn from One System to Another. Rule 4. Multiply the given counts of yarn by its standard length and divide by tin standard length in the system desired. Example. What counts of worsted is equal to a 30 's cotton yarn? 30 's counts X 840 cotton standard .-, 560 worsted standard a ' Short Methods to Find Equivalent Counts of Yarn in Woolen, Worsted, Linen, Raw Silk, or Metric System of Counting Cotton to a Given United States Cotton Yarn. .525 X counts of cotton yarn = woolen counts, run system. PRACTICAL COTTON CALCULATIONS 21 1.5 X counts of cotton yarn =worsted counts, hank system. 2.8 X counts of cotton yarn = linen counts, cut system. 2.8 X counts of cotton yarn = woolen counts, cut system. 52.5 X counts of cotton yarn — raw silk counts, yds. per oz. system. 1.69 X counts of cotton yarn = metric system of numbering cotton. Short Methods to Find Cotton Counts Equivalent to Any Given Counts of Woolen, Worsted, Linen, Raw Silk, or the Metric System of Counting Cotton Yarn. 1.905 X counts of woolen yarn, run system. .857 X counts of woolen yarn, cut system. .357 X counts of linen yarn, cut system. .666 X counts of worsted yarn, hank system. .019 X counts raw silk yarn, yds. per. oz. system. .59 X counts of cotton in metric system= cot- ton counts in United States system. The preceding constants are obtained as follows : 840 -r- 1600 = .525 for woolen, run system. 840 -f- 560 = 1.5 for worsted, hank system. 840^ 300 = 2.8 for linen and woolen, cut system. 840-^ 16 (ozs. per lb) =52.5 for raw silk. yds. per oz. system. 1600 -f- 840 = 1.905 for woolen, run system. 300 ~ 840= ..357 for linen and woolen, cut- system. 560 r- 840= .666 for worsted, hank system. 16 -r- 840 = .019 for raw silk, yds. per oz. system. 22 PRACTICAL COTTON CALCULATIONS RAW SILK CALCULATIONS. Owing to the growing use of silk yarns in the finer grades of fabrics composed for the greater part of cotton, the relative silk and cotton stan- dards are here indicated. When a problem presents itself in which silk yarns have to be considered, first obtain the equivalent cotton counts and proceed according to the rules regarding cotton yarns and fabrics. In addition to the system of numbering raw silk by the number of yards per ounce, where higher numbers indicate finer yarns, there are two other systems used in America and Great Britain. These are known as the dram system and the denier system. They differ from the cotton and spun silk systems in having higher numbers indicate coarser yarns. The dram system is based on the weight in drams of 1000 yards of yarn. For example, a 4-dram silk means that a length of 1000 yards of yarn weighs 4 drams. There are several so-called denier systems, but the one recognized by the New York and London conditioning houses, and one extensive- ly used in France, is based on the weight in deniers of a skein of 476 metres, or 520.56 yards. For example, a 19/21 denier raw silk means that a skein 520.56 yards long weighs from 19 to 21 deniers. For calculation purposes a 19/21 yarn would be considered a 20 's yarn. The num- ber 520 is usually used instead .of 520.56. A denier is a small weight equal to .8196 of a. grain, or .02997 of a dram. The relative values of the dram, denier and grain standards of weights are as follows: PRACTICAL COTTON CALCULATIONS 23 1 dram = 33^ deniers = 27.34 grains. 16 drams = 533J deniers = 437.5 grains = 1 oz. 256 drams = 8533 deniers = 7000 grains = 16 ozs. = 1 lb. Short Methods to Find Equivalent Counts in the Dram Silk, Denier Silk and Cotton Systems. 304.76 -=- dram silk counts = cotton counts. 5282 -=- denier silk counts = cotton counts. 304.76 -~ cotton counts = dram silk counts. 5282 —- cotton counts = denier silk counts, denier silk counts -=- 17.366 (17^) = dram silk counts, dram silk counts X 17.366 (17J) = denier silk counts. The preceding constants are obtained as fol- lows : 256 grains X 1000 yards — nTF{ — — t — — =oU4.7o 840 yards 8533 deniers X 520 yards __ _ 840 yards 1000 yards : 1 dram : : 520.56 yards : 17.366 deniers. If 1000 yards in the dram system weighs 1 dram for No. l's yarn, 520.56 yards in the denier system will weigh 17.366 deniers for the same counts. 17-J- is usually used instead of 17.366. The words "organzine" and "tram," used in connection with silk, refer to warp and filling yarn respectively. Organzine silk usually con- tains more fibres than tram silk, and is harder twisted. 24 PRACTICAL COTTON CALCULATIONS COUNTS OF TWISTED OR PLY AND CABLE YARNS. When single yarns are twisted together to form a ply yarn, the result is usually a heavier yarn than the counts divided by the number of ends twisted together, owing to the contraction in twisting. This can be proved by twisting two yarns together to a certain length, weighing them, and comparing the weight with the weight of single yarns of a similar length of the original counts. For calculation purposes, however, a cotton ply yarn composed of two or more yarns of equal counts is regarded as being the size of the single yarns divided by the number of strands; thus a yarn composed of two strands of 60 's twisted together is considered equal to one of 30's single; a yarn composed of three strands of 60 's is con- sidered equal to one of 20's single, but the more twist there is put into a yarn the more it will contract in length and the coarser will be the actual counts. Ply yarns which are composed of single strands of equal size of yarn are indicated by the number of strands which are twisted together and the counts of the single yarns written after- wards; thus 2/40 's means two yarns of 40 's twisted together, 3/100 's means three yarns of 100 's twisted together. These yarns would be equal to single yarns composed of 20 's and 33.33 's respectively. Cable yarns are composed of two or more ply yarns twisted together to form a fancy yarn. A 4/2/50 's cable yarn would be composed of four PRACTICAL COTTON CALCULATIONS 25 ends of 2/50 's twisted together, making in all eight ends of 50 's yarn, and would be equal to a single yarn of 6| counts. Unless used for fancy yarns for special pur- poses, two single yarns of unequal counts are sel- dom or never used, as equal single yarns com- bined make the best ply yarns. To Find the Counts of a Single Yarn Equal to a Ply Yarn Composed of 2 Single Yarns of Un- equal Counts. Rule 5. Divide the product of the two counts by their sum. Example. What counts of a single yarn is equal to a yarn composed of 30 's and 20's twisted together? 3 X 20 600 10 , ■30T2T = -55- = = 12floonntB,Aiw. To Find Counts of a Single Yarn Equal to a Ply Yarn Composed of 2 or more Yarns of Un- equal Counts. Rule 6. Divide the highest eon nix by itself and by each of the lower counts in succession; add results and divide into tin highest counts. Example. What would be equal in a single yarn to a ply yarn composed of 50 's, 80 's and 100 'sf 100 100 100 100 = 1.00 80 = 1.25 50 = 2.00 4.25 100 -r- 4.25 = 23.53 's counts, Ans. 26 PRACTICAL COTTON CALCULATIONS To Find Counts of a Yarn to Twist with a Given Yarn to Produce a Required Ply Yarn. Rule 7. Multiply the required counts by the given counts and divide by their difference. Example. What counts of yarn is required to twist with a 30 's to make a ply yarn equal to a 12 's? 30 X 12 360 OA , . , — — = — — = 20 7 s counts, Ans. o\) — 1Z lo To Find Weight of Each Counts of Yarn Re- quired to Make a Given Weight of Ply Yarn when Yarns of Unequal Counts are Twisted Together. First, when only 2 counts are twisted together. Rule 8. Divide the highest counts by itself and by the other counts in succession. Add the quotients and divide into the total weight. The result will be the weight of the highest counts. Deduct the latter from the total weight to find the weight of the other counts. Example. It is desired to make 75 lbs. of ply yarn composed of 80 's and 60 's. What weight of each is required ? 80 -5- 80 = 1 80 -s- 60 = lVs ¥k 75 lbs. -*■ 2% = 32.14 lbs. of 80's, Ans. 75 — 32.14 = 42.86 lbs. of 60's, Ans. If it is required to find the weight when more than two yarns are used the above rule will have to be modified. PRACTICAL COTTON CALCULATIONS Zt Example. It is required to make 100 lbs. of ply yarn composed of 100 's, 80 's and 50 's. What weight of each is required? 100 100 100 100 = 1 80 = 1.25 50 = 2 4.25 100 lbs. -r- 4.25 = 23.529 lbs. of 100 's, Ans. 23.529 X 1.25 = 29.411 lbs. of 80's, Ans. 23.529 X 2 =47.058 lbs. of 50 's, Ans. 99.998 lbs. total weight. Rules 5 to 8 are only approximately correct because when yarns of unequal counts are twisted together, the coarser yarn has a tendency to retain a straight line and deflect the fine. yarn. For a given length of ply yarn it would there- fore be necessary to use a longer length of the fine than the coarse. Rules 5 to 8 will apply in all the systems, except spun silk, mentioned on page 20. To Find Weight of Each Kind of Warp Yarn Re- quired in a Group of Warps of Equal Length when Number of Ends of Each Kind, Counts, and Total Weight Are Known. Rule 9. Divide the number of ends of each counts by its own counts. Add quotients. The result is to the total weight as each quotient is to the weight required of the respective counts. Example. A set of warps are arranged as follows: 1st, 144 ends of 3/24 's; 2d, 88 ends of 4/32's; 3d, 2400 ends of 50 's. What weight of 28 PRACTICAL (OTTOX < \W.< TLATIONS each Avarp is required to make a total weight of 100 lbs., provided the warps are all the same length? 144 ends of 3/24 's = 432 ends of 24 's 88 ends of 4/32 's = 352 ends of 32 's 432 ends -r- 24 's counts = 18 352 ends -=- 32 's counts == 11 2400 ends -~ 50 's counts = 48 77 77 : 100 lbs. :18 : 23.38 lbs. of 24 's, Ans. 77 : 100 lbs. :11 : 14.28 lbs. of 32 's, Ans. 77 : 100 lbs. :48 : 62.34 lbs. of 50 's, Ans. 100.00 lbs. total weight. COUNTS OF SPUN SILK PLY YARNS. Spun silk is counted like cotton when in the single yarn, but when writing the counts of ply silk the first number indicates the actual counts ; thus 30/2, or 30 's 2 fold, means two strands of 60 's. An equivalent to this in cotton would be written 2/60 's. 30/3, or 30 's 3 fold in spun silk means three strands of 90 's, whilst 3/30 's in cotton means three strands of 30 's. In some mills cotton ply yarn counts are written with the number of strands last, thus 30 •), which means that it is equal to a 10 \s, but as this method conflicts with the silk method it is not as generally used as the method previously explained, i. e., writing the number of ply first. PRACTICAL COTTON CALCULATIONS 29 TO FIND COUNTS, LENGTH OR WEIGHT OF COTTON YARN. To Find Counts of Cotton Yarn when Length and Weight Are Known. *Rule 10. Divide the length by the weight and by 840. Example. If 126000 yards of yarn weigh 6 lbs. what are the counts .' 126000 yards 6 lbs. X 840 -25 s counts,^. To Find Length of Cotton Yarn when Counts and Weight Are Known. *Rule 11. Multiply fin counts by the ir s counts Rule 17 may be applied when desiring To Find Weight of Warp Yarn in a Piece of Cloth but it must be understood that the slashing length, not the cloth length, must be taken. The table on the following page indicates the number of yards of cotton yarn per pound, in counts ranging from 1 to 250. This will be PRACTICAL COTTON CALCULATIONS 33 found useful when dealing with problems in which the product of 840 and the counts, as in the preceding example, has to be considered. Cotton Yards per Cotton Yards per Cotton Yards per Counts. Pound. Counts. Pound. Counts. Pound. l 840 35 29,400 78 65,520 1% 1,260 36 30,240 79 66,360 2 1,680 37 31,080 80 67,200 2% 2,100 38 31,920 82 68,880 3 2,520 39 32,760 84 70,560 m 2,940 40 33,600 86 72,240 4 3,360 11 34,440 88 73,920 J'l- 3,780 42 35,280 90 75,600 5 4,200 13 36,120 92 77,280 5% 4,(320 41 : 16, 960 94 78,960 6 5,040 45 37,800 96 80,640 li'o 5,460 46 38,640 98 82,320 7 5.880 47 39,480 100 84,000 7'-> 6,300 48 10,320 105 88,200 8 ~ 6,720 19 41,160 110 92,400 8% 7,140 50 42,000 115 96,600 9 7. 560 51 12,840 120 100,800 '.•'•. 7,980 52 43,680 125 105,000 10 S,ll)l) 53 14,520 130 109,200 11 9,240 51 45,360 135 113,400 12 10,080 55 16.200 140 117,600 13 10,920 56 17,040 145 121,800 14 11.76(1 57 47,880 150 126,000 15 12,600 58 18,720 155 130,200 16 13,440 59 19,560 160 134,400 17 14.280 60 50,400 165 138,600 18 15,120 61 51,240 170 1 12,800 19 15,960 62 52 080 175 147,000 20 16,800 63 52,920 180 151,200 21 17,640 64 5;;. 76i) 185 155,400 22 18,480 65 54,600 190 159,600 23 19,320 66 55,440 195 163,800 24 2(1,160 67 56,280 200 168,000 25 21,000 68 57,120 21 15 172,200 26 21,840 69 57,960 210 176,400 27 22,680 70 58,800 215 180,600 28 23,520 71 59,640 220 184,800 29 24,360 72 60, ISO 225 189,000 30 25,200 7:'. 61,320 230 193,200 31 26,040 74 62,160 235 197,400 32 26.8S0 75 63,000 'J 10 201,600 33 27,720 76 63,840 245 205,800 34 28,560 77 64,680 250 210, 34 PRACTICAL COTTON CALCULATIONS FINDING WEIGHT OF YARN ON BEAMS IN THE LOOMS. When taking stock of the amount of yarn in the looms, it is customary for the overseer to figure the weight of a cut of yarn on each style made, by Rule 17. By ascertaining the number of cuts of yarn in the looms and multiplying by the weight per cut, the weight of yarn on the respective styles is obtained. Example. A style of goods is made with 2400 ends of 60 's cotton yarn, 55 yards per cut (slashing length). It is required to find the weight of yarn per cut, and also for 20 cuts. By Rule 17— 24 ol end L^ 55y ! -- 2.619 lbs. per cut, Ans. 840 X 60 's counts L 2.619 lbs. of yarn per cut X 20 cuts = 52.38 lbs., weight of 20 cuts, Ans. Some mills do not trouble to ascertain how many cuts of each style there are when taking stock, but assume each beam to be half full, and figure accordingly. This method, although per- haps serving the purpose, is not accurate unless the person who does the calculating accidentally guesses the total number of cuts of each style, which is not probable. To Find length of Yarn on a Beam when Counts, Weight and Number of Ends Are Known. *Rule 18. Multiply the counts by the weight and by 840, and divide by the number of ends. PRACTICAL COTTON CALCULATIONS 35 Example. What is the length of a cotton warp of 1000 ends of 35 's yarn if the weight is 40 pounds ? 35 's counts X 40 lbs. X 840 .„_„ . . =1176 yds., Ans. 1000 ends To Find Number of Ends on a Beam when Counts, Weight and Length Are Known. "Rule 19. Multiply the counts by the weight and by 840, and divide by the length. Example. What is the number of ends on a warp 1176 yards long, of 35 's yarn, if the weight is 40 lbs. ? 35 's counts X 40 lbs. X 840 , .._ _ t r i„n y— - — 10()() en( H Ans - 1176 yards The above rule is of a theoretical nature and will give only approximate results. The four preceding rules, 16 to 19, may be summarized in — Formula C. To Find Cotton Counts, Weight, Length or Number of Ends on a Beam. 840 er of ends are X - equal - Weight in pounds i in yards to X j , Counts of yarn Rule. Divide the product of the remaining factors of the group containing the required item into the product of the other group. 36 PRACTICAL COTTON CALCULATIONS To Find Average Counts of Yarn in a Set of Warps Containing* Different Counts of Yarns. Rule 20. Divide the number of ends of single yarn of each counts by its own counts; add the >■< suits and divide into the total number of ends. Example. A warp pattern is arranged 5 ends of 20 's and 2 ends of 10 's. What are the average counts ? 5 ends-=-20's = .25 2 ends-h-10's=.2 7 .45 7 ends -=- .45 = 15.5 's average counts, Ans. It is advisable to find the total number of ends of each counts of yarn before proceeding as above. Example. A set of 3 warps contains 288 ends of 3/20 % 136 ends of 4/28 's, and 2552 ends of 40 's. What are the average counts of the single yarns? 288 X 3 = 864 single ends of 20 's 136 X 4 = 544 single ends of 28 's 864 ends -r- 20 's counts = 43.20 544 ends -r- 28 's counts = 19.43 2552 ends -=- 40's counts = 63.80 3960 ends 126.43 3960 total ends -^ 126.43 =31.32 's average counts, Ans. To Find Number of Ends in an Equally Reeded Warp when Sley and Width of Cloth Are Known. Rule 21. Multiply the sley by the cloth width PRACTICAL COTTON CALCULATIONS .",7 and add the necessary number of ends for sel- vedges. Example. How many ends would there be in an 88 sley cloth, 32 inches wide, allowing 24 ends extra for selvedges? 88 sley X 32 inches = 2816 ends. 2816 + 24 extra for selvedges = 2840 ends, Ans. The selvedges mentioned in the preceding example would consist of 48 ends. One half of these, 24 ends, are considered when multiplying the sley by the width. To Find Number of Hanks of Warp Yarn in a Piece of Cloth when Sley and Cloth Width Are Known. *Rule 22. Multiply sley by width; add sel- vedge ends; multiply answer by slashing length and divide by 840. Example. A cloth is made 32 inches wide, 110 sley and 100 yards long, the take-up of the warp being 7%. How many hanks of warp are there in the cloth ? 110 sley X 32 inches = 3520 + 32 for selvedges = 3552 ends in warp. 100 yds. cloth + 7% = 107 yds. slashing length. 3552 ends X 107 yards ACn AC , . e ' — = 452.45 hanks of warp, 840 Ans. To Find Number of Hanks in a Warp when Num- ber of Ends and Length Are Known. *Rule 23, Multiply the number of ends by the length, and divide by 840. 38 PRACTICAL COTTON CALCULATIONS Example. How many hanks are there in a cotton warp 800 yards long, containing 1920 ends? 1920 ends X 800 yards ._ 9Qri nAri - — ■ = 1828.6 hanks, Ans. 840 ' To Find Length of a Cotton Warp when Number of Hanks and Number of Ends Are Known. *Rule 24. Multiply the number of hanks by 840, and divide by the number of ends. Example. What is the length of a warp of 2000 ends that can be made with 350 hanks of cotton yarn ? 350 hanks X 840 2000 ends = 147 yards, Ans. To Find Number of Ends in a Warp with Any Unequally Reeded Pattern when Sley Reed, Width and Warp Layout Are Known. First find the number of full patterns by Rule 26 and apply — Rule 25. Multiply the number of ends per pattern by the number of full patterns; add extra ends for any fraction of a pattern, accord- ing to warp layout; also add selvedge ends. Example. A fancy cloth is required to be 32 inches wide and woven in a 90 sley reed. Allowing 64 ends in 16 dents for selvedges, how many ends will be required in the warp if the following warp layout is used? PRACTICAL COTTON CALCULATION JS Top Beam. Bottom Beam. Dei i/40's yarn 50 's vara 80 " 40 1 6 1 1 6 1 Skip 1 1 6 1 1 6 1 39 X 6 ends 116 ends 48 dents By Kule 26 there are 29 full patterns and 32 dents extra. 116 ends 50 's X 29 patterns = 3364 ends 50 's 6 ends 3/40 's X 29 patterns = 174 " 3/40 's 32 extra dents X 2 ends per dent == 64 " 50 's 64 ends for selvedges = 64 50 's 3666 total ends Arts. If it is required to know the total number of ends of single yarn the 174 ends of 3/40 's would be figured as 522 single ends, making a total of 4014 ends required in the warp. To Find Number of Patterns in an Unequally Reeded Cloth when Sley Reed, Width and Number of Dents per Pattern Are Known. Rule 26. Multiply one-half the sley reed by the width; deduct the number of dents for sel- vedges and divide by the number of dents per pattern. Example. A cloth is required to be 32 inches wide and woven in a 90 sley reed ; there are 48 40 PRACTICAL COTTON CALCULATIONS dents per pattern. Allowing 16 dents for sel- vedges, how many patterns will there be? 90 sley reed -=- 2 = 45 dents per inch. 45 X 32 = 1440 total dents in warp. 1440 — 16 dents for selvelges == 1424 dents. 1424 dents on , , . 00 1 , = 29 patterns + 32 dents, 48 dents per pattern Arts. To Find Percentage of Size on Warp Yarns. Rule 27. Deduct the weight of the yarn before sizing from the weight of the yarn after sizing; add two ciphers to the answer, or multiply by 100, and divide by the weight of the unsized yarn. Example. A warp weighs 140 pounds after sizing and 130 pounds before sizing. What per- centage of size has been added ? 140 — 130 = 10; 10X100 = 1000; 1000 -$- 130 == 7.69 percentage of size, Ans. To Find Weight of Warp, in Ounces, per Yard of Cloth. *Rule 28. Divide the number of ends in the warp by 52.5 and the counts. (840 yards -f- 16 ozs. = 52.5) Example. A warp contains 3200 ends of 60 's yarn. What is the weight per yard, in ounces? 3200 ends 52.5 X 60 's counts = 1.016 ozs., Ans- PRACTICAL COTTON CALCULATIONS 41 WARP AND FILLING CALCULATIONS. After finding the number of yards per lb from a small piece of cloth it is sometimes necessary — To Find the Counts from the Weight of a Few Inches of Yarn. For this purpose use — *Rule 29. Multiply the number of incites of yarn that weigh 1 grain by .2314. (See con- stants. ) Example. 170 inches of yarn weigh 1 grain. What are the counts? 170 inches X .2314 = 39.338 's counts, Ans. To Find Weight of Warp or Weight of Filling per Cut when Weight of Cut, % Warp or % of Filling Are Known. Rule 30. Multiply the weight of the cut by % warp to find the weight of the warp. Deduct the weight of the warp from the weight of the cut to find the weight of the filling. Example. A cut of cloth weighs 6 lbs. and contains 55% warp. What are the separate weights of warp and filling ? 6 lbs. X -55 = 3.30 lbs. warp, Ans. 6 lbs. — 3.30 = 2.70 lbs. filling, Ans. 42 PRACTICAL COTTON CALCULATIONS Example No. 2. A cut of cloth weighs 8 lbs. and contains 47% filling. What are the separate weights of filling and warp ? 8 lbs. X .47 = 3.76 lbs. filling, Ans. 8 lbs. — 3.76 = 4.24 lbs. warp, Ans. To Find Weight of Warp or Filling Required per Day When Number of Yards per Pound, Pro- duction and % of Warp Are Known. Rule 31. Divide the number of yards per day by the number of yards per lb. to find number of lbs. of cloth per day. Multiply the number of lbs. per day by the % of warp to find the weight of warp. Deduct the weight of the warp from the total weight to find the weight of the filling. This does not allow for waste, which must be added. Example. A cloth 6J yards per pound is produced from a loom at the rate of 39 yards per day. 55% of it is warp. What weight of warp and filling is required per day ? 39 — 6^ = 6 lbs. of cloth per day. 6 lbs. X .55 = 3.30 lbs. warp per day, Ans. 6 lbs. — 3.30 = 2.70 lbs. filling per day, Ans. PRACTICAL COTTON CALCULATIONS 43 FILLING CALCULATIONS. To Find Number of Hanks of Filling in a Piece of Cloth when Pick, Width in Reed and Cloth Length Are Known. *Rule 32. Multiply the pick by the width of the warp in the reed and the cloth length, and divide by 840. See tables on pages 81 and 82. Example. A cloth is made 100 X 120, 32 inches wide and 50 yards long. How many hanks of filling does it contain ? By Rule 63 a 100 sley cloth 32 inches wide would be woven 34 inches wide in the reed. 120 pick X 34 inches X 50 yards _._ D . . — ^j^r — - = 242.8 hanks y4U of filling, Am, To Find Length of Cloth that can be Woven with a Given Counts and Weight of Filling when Width in Reed and Pick Are Known. *Rule 33. Multiply the counts by 840 and the weight, and divide by the pick and the width of the warp in the reed. Example. 7.5 lbs. of 70 's filling is on hand to insert into a cloth to be woven 40 inches wide in the reed with 220 picks per inch. What length of cloth can be woven with it ? 70 's counts X 840 X 7.5 lbs. rA11 , t^k — —, ^-. — P — = — — r- = 50.11 yards, 220 picks X 40 inches in reed ^ 44 PRACTICAL COTTON CALCULATIONS To Find Weight of Filling Required per Cut When Width in Reed, Pick, Cloth Length and Filling Counts Are Known. . ' :: Rule 34. Multiply width in reed in inches by pick and length of cloth in yards, and divide by 840 and the counts. If the weight in ounces is desired, multiply the result by 16. Example. A cloth is desired 56 yards long, with 220 picks of 70 's filling. The width in the reed is 40 inches. How many pounds of filling are required. 40 inches X 220 picks X 56 yards Q qft , 840 X 70 's filling counts - An*. When estimating the weight of filling required for stop peg checks, the average pick, not the ground pick, must be considered. To Find Weight of Each Separate Color of Fill- ing in Ginghams, Tartans and Similar Check Patterns. *Rule 35. Multiply the total weight of filling (see Rule 34) by the number of picks per pat- tern of the required color, and divide by the total number of picks per pattern. Example. Supposing the pattern of the filling in the preceding example contains 4 picks of twist, 16 picks of black and 24 picks of white, how many pounds of each color are required for each cut of cloth ? PRACTICAL COTTON CALCULATIONS 45 4 + 16 + 24 = 44 picks per pattern. 8.38 X 4 44 8.38 X 16 44 8.38 X 24 44 = .7618 pounds twist, Ans. — 3.0472 pounds black, Ans. = 4.5709 pounds white, Ans. Total, 8.3799 pounds. If the number of picks of each color, as in this example, bear a direct proportion to 1, and to each other, the problem may be simplified in the following manner : 4, 16 and 24 are in the same proportion as 1, 4 and 6. 1 + 4+6=11 8.38X1 - C1Q = ./618 pounds twist, Ans. 11 7618 X 4 = 3.0472 pounds black, Ans. 7618 X 6 = 4.5708 pounds white, Ans. Total, 8.3798 pounds. To Find Weight of Each Separate Count or Kind of Filling" in Embossed Fabrics Such as Welts, Piques, Quilts, etc. *Rule 36. Multiply width in reed by pick, length of cloth in yards and number of picks of required counts per filling pattern, and divide by 840, counts of filling, and number of picks in the filling pattern. 46 PRACTICAL COTTON CALCULATIONS Example. If it is desired to weave a cut of Marseilles quilts, what weight of each kind of nlling will be required if the cloth is made to the following particulars: width in reed, 96 inches; pick, 162; cut length, 30 yards; filling pattern, 2 picks of 10 's and 4 picks of 50 's alternately, 6 picks completing the round? 96 X 162 X30 X 2 840 X 10 X 6 96 X 162 X30 X 4 = 18.5 lbs. of 10 's, Ans. = 7.4 lbs. of 50 's, Ans.. 840 X 50 X 6 To find counts of nlling required the following factors must be dealt with : number of yards per pound, cloth or cut length, slashing length of each warp used, warp counts., number of ends of each counts, % of size or dressing on warp yarns, picks per inch and width in reed, there- fore — To Find Counts of Filling Required in Any Cloth Use— *Rule 37. Divide the number of yards per cut by the number of yards per pound. This gives the weight of the cut in pounds. Multiply the number of ends of each counts by the slushing length per cut of the respective Warps and divide by 840 and the counts; add a certain % for size, if necessary. This gives the weight of the warp yarns. Deduct the weight of the warp from the weight of the cut. This gives the weight of the nlling. PRACTICAL COTTON CALCULATIONS 47 Multiply the picks per inch by the width in the reed and the cloth length, and divide by 840 and the weight of the filling. Example. A cloth is required 76 X 80, 28 inches wide, 12 yards per pound, with 60 's warp. Allow 3% for take-up and 4% for size on the warp. What counts of filling is required? Assume a certain length of cut, say 100 yards. 100 yard cut -f- 12 yards per tb = 8.5 lbs., weight of cut. 76 sley X 28 inches = 2128 ends + 32 for sel- vedges =2160 ends. 100 yard cut + 3% = 103 yards, slashing length. 2160 ends X 103 yards , AH ,. 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To Find Number of Ounces per Yard or Yards per Pound. Rule 65. itf-r- number of ounces per yard — - number of yards per pound. 16 -=- number of yards per pound = number of ounces per yard. To Find Number of Yards of Cloth per Pound from a Small Portion of Cloth when Analyz- ing" Fabrics. Rule 66. Multiply the number of square inches weighed by 7000 grains and divide by the weight in grains, width of cloth in inches, and by 36. Example. A cloth is 18.5 inches wide; 6 square inches weigh 8 grains. How many yards are there per pound? 7000 grains X 6 inches 5 : vy io g - — T. — w oa = '- ,ss > yards per 8 grains X 18.5 inches X 36 ^ Ans ^ In Rule 66, 7000 and 36 are constant factors. 7000 — 36 = 194.44, therefore instead of the above rule use the following: For 1 square inch -r- 194.44 by weight in grains and cloth width. For 4 square inches -=- 777.77 by weight in grains and cloth width. For 9 square inches -f- 1750 by weight in grains and cloth width. For 12 square inches -r- 2333.33 by weight in grains and cloth width. For cloth cut to any other size use Rule 67. PRACTICAL COTTON CALCULATIONS 75 To Find Number of Yards per Pound of a Cloth Containing" Different Counts of Yarns, or Pat- terns that are Unequally Reeded; it is necessary to cut a piece of cloth containing only full patterns before weighing* and proceed- ing by- Rule 67. Multiply 194.41 by the number of square indies weighed, and divide by the weight in grains and the widtli of the cloth in indies. Example. A stripe pattern is reeded 2 ends in a dent for 40 ends and 4 ends in a dent for 20 ends; the complete pattern in the cloth measur- ing f of an inch. A piece 3 inches warpway, i. e., lengthway, and 5 patterns fillingway weighs 6 grains. The width of the cloth desired is 28 - inches. How many yards per pound will the cloth weigh? 5 patterns X f inches per pattern = 3^ inches 3 J X 3 = 9} square inches weighed 194.44 X 9.375 inches — : . — = 10.8o yards per lb , 6 grains X 28 inches , It is advisable to cut a certain number of pat- terns on a certain number of inches, if possible, to avoid fractions. To Find Number of Yards of Cloth per Pound when 2 or More Warps are Used, when Counts and Number of Ends on Each Warp, Contraction of and Size on Each Warp, Width in Reed, Pick and Counts of Filling Are Known. Assume a certain length of cloth, say 100 yards, and use — 76 PRACTICAL COTTON CALCULATIONS *Rule 68. Multiply the ends of each counts by the slashing length, and divide by 840 and the respective counts; add to this for size, if neces- sary. This gives weight of warp. Note. — When size is put on a warp, the con- traction and size are usually considered together when finding weight. Multiply the picks per inch by the width in reed and length of cut, and divide by 840 and the counts of the filling. This gives weight of filling. Add weight of warp and weight of filling together and divide into length of cut == Ans. Example. A cloth is required 28 inches wide, made with 100 ends of 3/24 ? s, 200 ends of 4/32 's, 2500 ends of 50 's and 84 picks per inch of 60 's filling. Allow 5% for contrac- tion on the 3/24 's warp, 45 % for contraction on the 4/32 's warp, and 10% for contraction and size on the 50 's warp. How many yards of cloth will there be per lb ? Assume a 100 yard cut. 100 ends of 3/24 's= 300 ends of 24 's 200 ends of 4/28 's = 800 ends of 28 's 300 ends X 105 yds. slashing length „ r/> „ „ Q , A vy ;;,, - = 1.066 lbs. 840 X 24 s counts f 3/24 's warp 800 ends X 145 yds. slashing length r ,. 840 X 32 's counts of ^33 > s ^ 2500 ends X HO yds. slashing length r ^ ,, 840 X 50 's counts \)F50's warp PRACTICAL COTTON CALCULATIONS 77 For 28 inch cloth, say 30 inches in reed, 84 picks per in. X 30 in. X 100 yds, cnt ^ „ 840 X 60 's filling counts oFfiUing 1.566 lbs. of 3/24 's warp 4.315 lbs. of 4/32 's warp 6.548 lbs. of 50 's warp 5.000 lbs. of 60 's filling 17.429 100 yd. cut ^-17.429 lbs. = 5.738 yds. per lb, Ans. To Find Number of Yards of Cloth per Pound when Sley, Pick, Width and Average Counts Are Known. -Rule 69. Multiply the average counts by 761 (see constants) and divide by the width and the sun) of sley and pick. Example. A cloth is made 96^X 150 and is 334 inches wide ; the average counts is 58. How many yards of cloth are there in a pound? 58 average counts X 764 _ 96 -f- 150 X 33i inches " 5 ^ 77 3 ards per ^ To Find Number of Yards of Cloth per Pound when Sley; Pick, Width, Warp and Filling Counts Are Known. * Rule 70. Divide sley by warp counts = A. Divide pick by filling counts = B. Add A to B = G. Divide 764 (see constants) by C and the width =±= Ans. See Rule 71. 78 PRACTICAL COTTON CALCULATIONS Example. A cloth is desired 64 X 124, 33^ inches wide, with 36 's warp and 48 's filling. How many yards will there be in a ponnd of cloth ? 64 -=- 36 = 1.77 = A 124 -4-48 = 2.58 ==B 1.77 + 2.58 = 4.35 = 4.35^33.515. = 5 " 24 yardS Per ft ' Am ' Another rule dealing with the factors men- tioned in the preceding example is as follows : *Rule 71. Divide the number of hank* for the sley and width given on the following table by the counts of the warp and the filling yarns; add both results together and allow for contraction a ad size, and divide into 100 {yards). Example. A cloth is made 28 inches, 72 X 68, with 80 's warp and 100 's filling; allow 10% for contraction and size. How many yards of cloth are there per pound? By examining the table 72 sley cloth, 28 inches wide contains 240 hanks of warp. A 68 pick cloth contains 226.66 hanks of filling for the same width. 240 hanks warp -4- 80 's counts = 3 226.66 hanks filling -4- 100 's counts = 2.266 5.266 add 10% .526 Weight of 100 yards of cloth, 5.792 lbs. 100 -f- 5.792 = 17.265 yards per lb, Ans. PRACTICAL COTTON CALCULATIONS 79 *The tables on pages 80 and 81 will be found useful when finding the weight of warp or filling yarns in 100 yards of cloth. Allowance has not been made in this table for contraction or size, as these will vary in different classes of goods. The width in the reed instead of the width of the cloth should be considered in dealing with filling calculations. To Find Number of Ounces per Yard from a Small Piece of Cloth. Rule 72. Multiply the width of the cloth in inches by the weight of a small piece in grains and by 36, and divide by 437.5 (grs. per oz.) and the number of square inches weighed. Example. A piece of cloth 4 inches square weighs 16 grains. What is the weight in ozs. per yard of cloth 28 inches wide? 28 inches X 16 grains X 36 jT^rfr = rr-Tc : — x. — = 2 -3 ozs. per yd., 437.5 grams X 16 sq. inches Ans In the above rule 36 and 437.5 are constant numbers, therefore the 36 above the line could be dispensed with and 12.152 used instead of 437.5 below the line. (437.5 grs. per oz. -^ 36 inches per yard — 12.152.) Using the preceding example the working would be as follows : 28 inches X 16 grains 101 r OV1c = — r — =2.3 ozs. per yd., Ans. 12.152 X 16 sq. inches 80 PRACTICAL COTTON CALCULATIONS NUMBER OF HANKS OF YARN, WARP OR FILLING, IN 100 YARDS OF CLOTH. See note (*) on preceding page. r = ?J - z- * - — . 'X CO -T tl X CO i~ :~ -I T- -~ >Z 71 •— CT. I- CO tt - — — X tl CO tt I- — I" — . TICCT/.H I* ~. tt '-. — . ~t f " ''. ~: M ' tg 35 — ' M CO 30 ~ I- 1 6 x' © t i i.c" I -' C C I — 1 - 35 rJ -r co' 3 i — M CO 30 © *" /. - ^ :i :: - c i> / r. - :i :: - c i- / r. c :i :: - '" l- x — c ti t: ^ r - r . r _ r . r . r , r -'M'M:i:i:i:i:i-i:: :: ;: -- -- -- ~~ :r -r -r -r fc ?i ^ to r. x i •- co It -r tt ~i £i i—_ r. x f- co >'-: -V ft ti r-n ~ ~. x i - co id i~ ai © cn -t -o' x © ti -r co x © -— ' tt it' i- oc — ' tt it i- oc! x r. — — tt — i - ~ i - — . ~ — t i tt ' " - i - x ~ - t - HriHHHrHHrHTlTi:i:i:i?i:iTl?i:Cr — r- co /: ~. ~ • tt tt -.-. tt tt -r - -r X i -' X SBSSSg c i x so x ec • ti tt -r >~. co i~ x — c c — ti tt -r it co i- x r- © r-i ti to — . t co i - x r.Cr-::-it--i-y. ~ ~ — 1 1 tt i.t co i- x ' >-i h h h h r- ri ti ti :i ti ri :i :i :i ::::■::":::: " :: : — x • x tt — x co -r 1 1 — . co — 1 1 r- co 1 1 1 1 x . t :t x — tt — x tt x ti i- tj i- r- co i-; co © it © it — r. — ; r. tt x tt x ? : :' tt — - — ' ' '. ' t vo -o' i ~ 1 ~ x x' r! re c ©" ©' >- • -— t-i t i rt tt -r -r iC ii; tc -.r OQOOOOOOOOOOOOOOOQQOOOOOOQQO< i- /. r. c r- :i :: - c c i- /. r. ; ^- :i :: - it - i - /. r. c - :i :: - i HH-iiHt-r-rHriHiH:i:Kiriti:i:i:iti:i:c""""' - i TJ o ■'" 5 3 ' oS x x r. c c ^-' ti :-. — It •- i - x r. r -- t'l :t r-Tl-Mtltl-Mtl-Mtlt-ltltl-tCtTtrt 't co ■-: t-t-oo x ~.'~. ; " /. i^ -it -r:t ti— , _ _- x i~ "^ it - ~ tt ti — — . -- x i_* — ~. — — ~ ti tt -r it ■- i- x r. — c r- ti tt -p it co i- x x r. c — '^. -: >> • ! ~ x I- it — .•-I- x r. - -T 1 1 X -O tt ■' — t I X -T 1 1 l~ t — _ i - 1 1 X — ' t — . i - 1 1 X_ -r it r 1 - 1 1 ■ 1 1 ti :t -t i -r t— x ■- -r -.-. r. it ti x ■ eo o 06 to tt - it CO co i- x 88§: i ri cc" .co -r i— r. i — h ti ~ i^ it 1 1 ~ x it :t ~ x \o tt r- ~ -o ~~->'^ .'t or-'i-iH oo ir: it co I- i~ — x tt co — co — x tt i- ti -r r- 1 1 — ' t I - X r-tlTltl^OC ci — - — x it ti ~ i — "-'/.itrici;-- /'t :i; oc rH ti ti tt — i-t i- co i- i- x tct-ti: ; - it 5 ft CO DO CO tt C: co' tt — it co -O l » ( O — tt o co tt c -o: tt C co tt C co tt C co tt C co to . c o r- ti ti tt -r — it co co i- x x r. c r r- t t tt ^Hi-r-HHr-i-r-Hr^HHHr-tltltltltlt) ao Aais ssg?i?;s^ft?J^f?ft c ti -r cc x ctitcecccei^coco LOiOiOtftiO PEACTICAL COTTON CALCULATIONS SI NUMBER OF HANKS OF YARN, WARP OR FILLING, IN 100 YARDS OF CLOTH. See note (*) on page 79. GO W b g i— i b r- c PH o B H Q ICl 445.72 458.1 470.48 482.86 495.25 507.62 520 5:!2.:;s 544.76 557.14 5(1! 1.52 581 .91 594.29 606.66 619.06 631.45 643.84 65(1.21 668.58 (ISO. '.15 693.33 705.72 718.1 730.47 742.SH 755.25 767.62 780 792.38 o ." — ■' ci 01 H 33 X 1^ CO I'O d CC 01 r-" C CC X U CO '0 — CO ci 01 rH - ?' ^ Li ~~. l ~ * ? ? -J : i T "2 ^r * '^ PS rr 71 rr il :? ! r .5 - ■- fj - ^ - 00 411.4 1 422.86 434.28 4 15.71 457.15 468.57 -ISO 491 .42 502.84 514.28 525.72 537.15 548.57 560 571.11 5S2.S6 594.28 (105.72 617.16 62S.5S 640 651 .43 662.86 674.28 6S5.71 697.15 708.57 720 731.43 CO X>T( .0 '-. cOOlcO CO rH CO 01 1- 01 1- CI 1- cc r- -r —. -P '0 CO oi oi oi p-j r-j q r. r. x x i~ i- q q i.q >q -t -t cc cc oi :iHrq q uC -r cc :c cc — ^r d — — — — — — ~. Ic i'o .'- .0 i*o ic >c >~ iO cc cc cc cc 3 cc co OOOOOOOOOOOOQOOOOOOOQOOOOOOOC ■:i-/ r. - t— o i cc -t 1 1 -o i - x r. r i— ? i c: -r i c -o i - / r. o -— o i cc -r :c :::::: -r -r t t -r t -r -r t •* .0 '0 iO '0 «o 'O >o >o i0 .0. cc co cc co cc O 3.42. 84 352.37 361.90 371.43 380.95 : 190. is loo 109,52 119.04 428.56 438.08 147.61 157.14 466.66 176.18 185.73 495.28 504.77 514.26 52:!. 79 533.33 542.86 552.38 561.9 571.43 5S0.96 590.47 600 (109.52 X 0? ;;25.72 334.77 343.82 352.86 361.91 370.96 380 3S9.04 398.08 407.13 416.18 425.24 134.29 443.33 45-.'.: is 461.43 170. is 479.53 188.58 497.62 506.6(1 515.72 521.76 533.8 542.S6 551.91 560. 95 540 579.nl cc co -r oi ~ co cc cc o i x cc cc cc o i x -o -p o i i — p rH — cc :o i - .qt-Hi-oix-T iCr-i-:]-/. h icncrr/.r ,ff . r 1 l .*! y -. _ '"-. X 1 - ' O -p" CJ rH q x" 1 - ' — ' 0J rH = 30 1_; lO — ' Cj r-' - y' \J i Q — C i — i O / CO 291.44 29! 1.5:; 307.62 315.71 323. SI 331.9 340 348.08 356.16 364.26 380'.47 388.57 396.66 404.76 412.84 420.92 429.04 437.16 445.24 453.33 161.43 46! 1.52 477.62 185.71 193.81 501.9 510 518.09 CO 274.28 281.9 289.52 297.14 304.75 312.38 320 327.62 335.24 342.86 350.48 358.10 388.55 396.16 103 79 111.42 419.04 426.66 134.29 441.9 149.52 157.11 464.76 172.38 ISO 187.61 o CO C 1 1 - C 1 1 - — CC — X 1 CO r- CO — CC — CO X — -/. TII-h.C -r r- 1 c i — ; i q i - x r- c i — . q i - x r- ■ o i — i o q x r-:i-T,:i-. x r-j i- — 1-5 »" id riot'f'HoQioNC i- — : — x" .c ci c i- -p" -—" x' d oi r i~ .0 cc 1- 1- x re r — ci ci cc — ic 1.0 1- 1- / ~ — ~ r- 01 01 cc — • : .0 01 ci ci ci 01 ci cc cc :c :c cc cc cc :: :c :c :c :c :c :: - — X OI ^S^SKSS^S^SSSl^^i^^SS^^iiSsiS a a 1 ao 'IS s^sisg§gssg8B88a5$^g||8|gggss|gg§g * 82 PRACTICAL COTTON CALCULATIONS PERCENTAGE OF WARP OR FILLING. To Find % of Warp or Filling in Any Cloth. *Rule 73. Multiply the number of ends in each warp by the slashing length, and divide by 840 and the counts. Add the results to obtain the weight of warps. Multiply the width in reed by the number of picks of each count of filling per inch and the cloth length, and divide by 840 and the counts. Add results for weight of filling. Add weight of warp and weight of filling to find weight of cut. Divide weight of each counts by the total iveight to find %. Example. An embossed quilt fabric is con- structed as follows: 7200 ends of 40 's yarn for face warp; 3600 ends of 20 's warp for stitching; 60 's filling for face and back; 12 's filling for wadding; 160 picks per inch, arranged in the proportion of 3 fine to 1 wadding; 98 inches in the reed; slashing length of 40 's warp, 110 yards; slashing length of 20 's warp, 105 yards; length of cut, 100 yards. What is the % of each count of yarn in the cloth? 7200 ends X HO yards nn rr7 „ M AiX% Q , n ^ A( C ~ = 23.57 lbs. of 40 's warp. 840 X 40 s counts ^ 3600 ends X 105 yards rn Q/1A v/ OA , - = 22.50 lbs. of 20 's warp. 840 X 20 's counts F Total weight of warp, 46.07 lbs. 98 inches X 120 picks X 100 yard s _ 840 X 60 's counts of "^ ' m - n * PRACTICAL COTTON CALCULATIONS 83 98 inches X 40 picks X 100 yards _ ss 840 X 12 's counts of wad 7 ing ' fining. Total weight of filling, = 62.21 lbs. 23.57 22.50 23.33 38.88 108.28 lbs., weight of 100-yard cut of cloth. 23.57 -5- 108.28 = .217, or 21.7%, 40's warp, Ayig 22.50 -r- 108.28 = .207, or 20.7%, 20 's warp, 23.33 -r- 108.28 = .215, or 21.5%, 60's filling, 38.88 -v- 108.28 = .359, or 35.9%, 12 's filling, Ans. The % may be found without finding the weight, as in the preceding example, by dispens- ing with the 840 and dividing by the counts only. Using the preceding problem as an illus- tration : 7200 X HO 40 3600 X 105 = 19800 20 92 X 120 X 100 = 18900 60 98 X 40 X 100 = 19600 12 = 32666 90966 84 PRACTICAL COTTON CALCULATIONS 19800 18900 19600 32666 90966 = .211, or 21.7%. 90966 = .207, or 20.7%. 90966 = .215, or 21.5%. 90966 = .359, or 35.9%. Total, .998, or 99.8%. Rules to indicate the methods usually used for finding % of warp or filling in equally bal- anced cloths of one warp and one filling. Nor- mal contractions in length and width of cloth, one balancing the other, are assumed when these are applied. To Find % of Warp or Filling in a Piece of Cloth when Ends in Warp, Pick, Warp, Filling and Width of Cloth Are Known. Rule 74. Divide the number of ends in the warp by the warp counts = A. Multiply the pick by the width of the cloth, and divide by the filling counts = B. Divide A by sum of A and B for % warp = Ans. Divide B by sum of A and B for % filling = An s. Or deduct % warp from 100% for % filling = Ans. Example. A cloth 30 inches wide contains 2160 ends of 60 's warp and 68 picks per inch of 85 \s filling. What are the relative percentages of warp and filling? PRACTICAL COTTON CALCULATIONS 85 2160 ends -±- 60 's counts = 36 = A 68 picks X 30 inches 85 filling counts 36 + 24 = 60 36 -^ 60 = .60 or 60% warp, Ans. 100%,— 60%, = 40% filling, Ans. To Find % Warp or Filling when Weight of Warp and Weight of Cut Are Known. Rule 75. Divide weight of warp by weight of cut for % warp = Ans. Deduct '/< warp from 100% for % filling = Ans. Example. A cut of cloth weighing 8 lbs. contains 4.8 lbs. of warp. What are the rela- 1 ive percentages of warp and filling? 4.8 lbs. warp -f- by 8 lbs. cut = .60 or 60% warp, Ans- 100%, — 60% == 40% filling, Ans. To Find % of Warp or Filling in a Piece of Cloth When Sley, Pick, Warp and Filling Counts Are Known. Rule 76. Divide the sley by the warp counts = A. Divide the pick by the filling counts ==B. Divide A by sum of A and B for % warp — Ans. Divide B by sum of A and B for % filling = Ans. Or deduct % warp from 100% for % filling = Ans. 86 PRACTICAL COTTON CALCULATIONS Example. A cloth 72 X 68 is woven with 60 's warp and 85 's filling. What are the rela- tive percentages of warp and filling? 72 sley -f- 60 's counts warp = 1.2 = A 68 pick ~i- 85 's counts filling = .8 = B 1.2 + .8 = 2 .8-^2= .40 or 40% filling, Ans. or 100 — 60 = .40 or 40% filling, Ans. To Find % Warp or Filling in a Piece of Cloth when Sley, Pick, Average Counts and Warp Counts Are Known. Rule 77. Add sley and pick together and divide by the average counts — A. Divide sley by warp counts = B. Divide B by A = % warp = Ans. Deduct % warp from 100% for % filling = Ans. Example. A cloth is made 104 X 112. The average number is 90 and the warp 80 's. What is the % warp? 104 sley + 112 pick = 216 -f- 90 's average counts = 2.4 = A. 104 sley -=- 80 's warp counts = 1.3 = B. 1.3 -r- 2.4 = 54% warp, Ans. The preceding rule may be applied to find % filling by substituting the filling counts for the warp counts and dividing the pick by the filling counts to find B. Note. — If % warp or % filling is found it is only necessary to deduct same from 100% to find the % of the other. PRACTICAL COTTON CALCULATIONS 87 To Find Number of Square Yards in a Piece of Cloth. Rule 78. Multiply inches in width by length in yards and by 36 (inches in a yard) and divide by 1,296 (square inches in a yard). Example. How many square yards are there in a piece of cloth 42 inches wide and 56 yards long ? 42 inches X 56 yards X 36 inches _. 1296 sq. ins. in a sq. yd. = ^ l Ans In the above rule, 36 inches to a yard, and 1296 square inches to a square yard, are con- stant factors; by dividing 1296 by 36 the result is 36, which can be used as a constant, and the 36 and 1296 dispensed with, giving — Rule 79. Multiply width in inches by length in yards and divide by 36. Using the preceding example the working would be as follows: 42 inches X 56 yards nrA — wn~ —=65^ sq. yards, Ans. TWISTS PER INCH IN YARNS. The number of turns or twists per inch to put into yarns varies somewhat according to the quality of the material used and the use to which the yarn is to be subjected. The following list is copied from two of the leading textile journals of England, "The Textile Manufacturer" and "The Textile Recorder," and may be said to be the generally accepted standard of twists per inch in Eng- land : Hosiery, sq. root of counts of yarn X 2.5 to 2.75. Filling (medium), sq. root of counts of yarn X 3.25. Filling (fine), sq. root of counts of yarn X 3.183. Warp (medium), sq. root of counts of yarn X 3.75. Warp (fine), sq. root of counts of yarn X 3.606. Warp (extra hard ring), sq. root of counts of yarn X 4. Warp (Sea Island stock), sq. root of counts of yarn X 4.75. The square roots of the counts, from 1 to 140, will be found in the tables on pages 90 and 91. PRACTICAL COTTON CALCULATIONS 89 The following list shows the number of turns per inch that are generally accepted as standards in the United States : Hosiery, sq. root of counts of yarn X 2.75. Mule Filling, sq. root of counts of yarn X 3.25. Mule Warp, sq. root of counts of yarn X 3.75. Mule Warp (extra), sq. root of counts of yarn X 4.00. Ordinary Warps, sq. root of counts of yarn X 4.75. The preceding twist constants are practically used only for guidance. When a progressive mill management starts out to get a yarn suitable for a given purpose, it experiments and varies the amount of twist until a satisfactory result is obtained. Although warp yarn is usually twisted more than filling, there are some mills that do not use a constant greater than 3.25 for warp yarn. TWIST TABLE. On pages 90 and 91 will be found twist tables, used by permission of Draper Co., Hopedale, Mass. These show the square roots of all counts from 1 to 140, also the number of turns per inch for the last four kinds of yarns in the U. S. list. 90 PRACTICAL COTTON CALCULATIONS TWIST TABLE, Showing the square root of the numbers or counts from 1 to 140 hacks in the pound, with the twist per inch for diffeient kinds of yarn. Counts or Square Root Ordinary Warp Warp Extra Mule Warp Mule Warp Twist Mule Filling Numbers. Twist. Twist Twist. Twist. 1 1 .0000 4.75 4.SO 4.00 3.75 3.85 2 1.4142 6.72 6.36 6.66 5.30 4.60 3 1.7321 8.23 7.79 6.93 6.50 5.63 4 2.0000 9.50 9.00 8.00 7.50 6.50 6 2.2361 10.62 10.06 8.94 8.39 7.27 6 2.4495 11.64 11.02 9.80 9.19 7.96 .7 2.6458 12.57 11.91 10.58 9.92 8.60 8 2.8284 13.44 12.73 11.31 10.61 9.19 9 3.0000 14.25 13.50 12.00 11.25 9.75 g? 3.1G23 15.02 14.23 12.65 11.80 10.28 3.3100 15.75 14.92 13.27 12.44 10.78 12 3.4041 16.45 15.59 13.80 12.99 11.26 13 3.0056 17.13 16.22 14.42 13.52 11.72 14 3.7417 17.77 16.84 14.97 14.03 12.16 15 3.8730 18.40 17.43 15.49 14.52 12.69 16 4.0000 19.00 18.00 16.00 15.00 13.00 17 4.1231 19.58 18.55 10.49 15.40 1 3.40 18 4.2426 20.15 19.09 10.97 15.91 13.79 19 4.3589 20.70 19.62 17.44 16.35 14,17 20 4.4721 21.24 20.12 17.89 16.77 14:53 21 4.5826 21.77 20.62 18.33 17.18 14.89 22 4.6904 22.28 21.11 18.76 17.59 15.24 23 4.7958 22.78 21.58 19.18 17.98 15.59 24 4.8990 23.27 22.05 19.60 18.37 15.92 26 5.0000 23.75 22.50 20.00 18.75 16.25 26 5.0990 24.22 22.95 20.40 19.12 16.57 27 5.1962 24.68 23.38 20.78 19.49 16.89 28 5.2915 25.13 23.81 21.17 19.84 17.20 29 5.3852 25.58 24.23 21.54 20.19 17.50 30 5.4772 20.02 24.65 21.91 20.54 17.80 31 5.5678 20.45 25.05 22.27 20.88 18.10 32 6.6569 20.87 25.46 22.63 21.21 18.38 33 5.7446 27.29 25.85 22.98 21.54 18.67 34 5.8310 27.70 26.24 23.32 21.87 18.95 36 5.9161 28.10 26.62 23.66 22.19 19.23 36 6.0000 28.50 27.00 24.00 22.50 19.50 37 6.0828 28.89 27.37 24.33 22.81 19.77 38 6.1644 29.28 27.74 24.66 23.12 20.03 39 6.2450 29.06 28.10 24.98 23.42 20.30 40 6.3240 30.04 28.46 25.30 23.72 20.55 41 6.4031 30.41 28.81 25.61 24.01 20.81 42 6.4807 30.78 29.16 25.92 24.30 21.00 4? 6.5574 31.15 29.51 26.23 24.59 21.31 44 6.6332 31.51 29.85 26.53 24.87 21.56 45 6.7082 31.80 30.19 26.83 25.16 21.80 46 6.7823 32.22 30.52 27.13 25.43 22.04 47 0.8557 32.60 30.85 27.42 25.71 22.28 48 6.9282 32.91 31.18 27.71 25.98 22.52 49 7.0000 33.25 31.50 28.00 26.25 22.75 no 7.0711 33.59 31.82 28.28 26.52 22.98 5J 7.1414 33.92 32.14 28.57 20.78 23.21 .-.2 7.2111 34.25 32.45 28.85 27.04 23.44 53 7.2801 34.58 32.76 29.12 27.30 23.66 54 7.3485 34.91 33.07 29.39 27.56 23.88 66 7.4162 35.23 33.37 29.00 27.81 24.10 56 7.4833 35.55 33.67 29.93 28.06 24.32 67 7.6498 35.86 33.97 30.20 28.31 24.54 58 7.6158 36.17 34.27 30.46 28.56 24.75 59 7.6811 36.49 34.57 30.72 28.80 24.96 60 7.7460 36.79 34.86 30.98 29.06 25.17 61 7.8102 37.10 35.15 31.24 29.29 25.38 62 7.8740 37.40 35.43 31.60 29.63 25.59 63 7.9373 37.70 35.72 31.75 29.76 25.80 64 8.0000 38.00 36.00 32.00 30.00 26.00 66 8.0623 38.30 36.28 32.25 30.23 26.20 66 8.1240 38.59 36.56 32.50 30.47 26.40 67 8.1854 38.88 36.83 32.74 30.70 26.60 68 8.2462 39.17 37.11 32.98 30.92 26.80 69 8.3066 39.46 37.38 33.23 31.15 27.00 70 8.3666 39.74 37.66 33.47 31.37 27.19 PRACTICAL COTTON CALCULATIONS 91 TWIST TABLE. Continued. Counts OT Square Root. Ordinary Warp Warp Extra Mule Warp Mule Warp Twist Mule Filling Numbers. Twist. Twist Twist. Twijt. 1 1.0000 4.7P 4.50 4.0O 3.75 3.25 71 8.4261 40.02 37.92 33.70 31.60 27.38 72 8.4853 40.31 38.18 33.94 31.82 27.58 73 8.5440 40.58 38.45 34.18 32.04 27.77 74 8.6023 40.86 38.71 34.41 32.26 27.96 75 8.6603 41.14 38.97 34.64 32.48 28.15 76 8.7178 41.41 39.23 34.87 32.69 28.33 77 8.7750 41.68 39.49 35.10 32.91 28.52 78 8.8318 41.95 39.74 35.33 33.12 28.70 79 8.8882 42.22 40.00 35.55 33.33 28.89 80 8.9443 42.49 40.25 36.78 33.54 29.07 81 9.0000 42.75 40.50 36.00 33.75 29.25 82 9.0554 43.01 40.75 36.22 33.96 29.43 83 9.1104 43.27 41.00 36.44 34.16 29.61 84 9.1652 43.53 41.24 36.66 34.37 29.79 85 9.2-195 43.79 41.49 36.88 34.57 29.96 86 9.2736 44.05 41.73 37.09 34.78 30.14 87 9.3274 44.31 41.97 37.31 34.98 30.31 88 9.3808 • 44.56 42.21 37.52 35.18 30.49 89 9.4340 44.81 42.45 37.74 35.38 30.66 90 9.4868 45.06 42.69 37.95 35.58 30.83 91 9.5394 45.31 42.93 38.16 35.77 31.00 92 9.5917 45.56 43.16 38.37 35.97 31.17 93 9.6437 45.81 43.40 38.57 36.16 31.34 94 9.6954 46.05 43.63 38.78 36.36 31.51 95 9.7468 46.30 43.86 38.99 36.55 31.(58 96 9.7980 46.64 44.09 39.19 36.74 31.84 97 9.8489 46.78 44.32 39.40 36.93 32.01 98 9.8995 47.02 44.55 39.60 37.12 32.17 99 9.9499 47.26 44.77 39.80 37.31 32.34 lOO 10.0000 47.50 45.00 40.00 37.50 32.50 101 10.0499 47.74 45.22 40.20 37.69 32.66 102 10.0995 47.97 45.45 40.40 37.87 32.82 103 10.1489 48.21 45.67 40.60 38.06 32.98 104 10.1980 48.44 45.89 40.79 38.24 33.14 105 10.2470 48.67 46.11 40.99 38.43 33.30 106 10.2956 48.90 46.33 41.18 38.61 33.46 107 10.3441 49.13 46.55 41.38 38.79 33.62 108 10.3973 49.36 46.77 46.98 41.57 38.97 33.77 109 10.4403 49.59 41.76 39.16 33.93 110 10.4881 49.82 47.20 41.95 39.33 34.09 111 10.5357 50.04 47.41 42.14 39.51 34.24 112 10.5830 50.27 47.62 42.33 39.69 34.39 113 10.6301 50.49 47.84 42.52 39.86 34.55 114 10.6771 50.72 48.05 42.71 40.04 34.70 115 10.7238 50.94 48.26 42.90 40.21 34.85 116 10.7703 51.16 48.47 43.08 40.39 35.00 117 10.8167 51.38 48.67 43.27 40.56 35.15 118 10.8628 51.60 48.88 43.45 40.74 35.30 119 10.9087 51.82 49.09 43.63 40.91 35.45 130 10.9545 52.03 49.30 43.82 41.08 35.60 121 11.0000 52.25 49.50 44.00 41.25 35.75 122 11.0454 52.47 49.70 44.18 41.42 35.90 123 11.0905 52.68 52.89 49.91 44.36 41.59 36.04 124 11.1355 60.11 44.54 41.73 36.19 125 11.1803 53.11 50.31 44.72 41.93 36.34 126 11.2250 53.32 50.51 44.90 42.09 36.48 127 11.2694 53.53 60.71 46.08 42.26 36.63 128 11.3137 53.74 60.91 45.25 42.43 36.77 129 11.3578 53.95 61.12 45.43 42.59 36.91 130 11.4018 54.16 61.31 45.61 42.76 37.06 131 11.4456 64.37 51.50 45.78 42.92 37.20 132 11.4891 54.57 61.70 45.96 43.08 37.34 133 11.5326 54.78 51.90 46.13 43.25 37.48 134 11.5758 54.99 62.09 46.30 43.41 37.62 135 11.6190 55.19 62.29 46.48 43.57 37.76 136 11.6619 55.39 62.48 46.65 43.73 37.90 137 J 1.7047 11.7473 55.60 52.67 46.82 43.89 38.04 138 55.80 62.86 47.99 44.06 38.18 139 11.7898 66.00 63.05 47.16 44.21 38.32 140 11.8322 66.20 63.24 47.33 44.37 38.46 92 PRACTICAL COTTON CALCULATIONS DIAMETERS OF YARNS. The question of the diameter of yarns has very little bearing on practical calculations. About the only practical value that can be quoted is that of guiding a person to prevent him from attempting to make an impossible construc- tion of cloth. There is a limit to the sley and pick of a cloth that can be woven with a given weave and a given amount of material, the number varying according to the number of interlacings in the weave and the counts of yarn. It is well known that yarns of similar counts but of different grades of cotton vary in diame- ter, the natural tendency of some being to bed into each other more than others, thereby form- ing a yarn with a smaller diameter. A yarn made in a room containing a moisten- ing apparatus will also be of smaller diameter than one made in a hot, dry room in which there is considerable electricity, because the fibres have a tendency to cling together better in a damp room. The diameters of cotton yarns vary inversely as the square roots of the counts, and the follow- ing is given: To Find the Diameter of a Cotton Yarn, or the Number of Strands of Cotton Yarn of Any Counts that can be Placed Side by Side in One Inch. Rule 80. Multiply 840 by the counts of yam; extract the square root of the answer and deduct 10% for compression. (See Rule 81.) PRACTICAL COTTON CALCULATIONS 93 Example. What is the diameter of l's yarn? 840 X 1 = 840; sq. root 840 = 28.98; 10% of 28.98 = 2.89. 28.98 — 2.89=26.09 or 26.1, W.t indies, diameter of yarn, Ans. That is, 26.1 strands of l's yarn can be placed side by side in the space of 1 inch. As the diameter of No. l's yarn is 1/26.1 inches, Rule 81 may be substituted for Rule 80. Rule 8i. Multiply the square root of the counts of yarn by 26.1. Example. How many strands of 36 's yarn can be placed in 1 inch, flat? Sq. root 36 = 6 ; 6 X 26.1 = 156.6, Ans. That is, a 36 's yarn is rsi.e inches in diameter. The tables on pages 90 and 91 show the squaie i«)o1 of all counts from 1 to 140, therefore to find the diameter of any cotton yarn it is only neces- sary to multiply the square root of the counts desired, as found in the table, by 26.1 to give the number of strands of yarn of that count that can be laid in the space of one inch. TESTING YARNS FOR STRENGTH. The method generally adopted when testing yarns in hank form for strength is to reel one lea from each of 1 to 4 bobbins, and place each lea separately on a machine made for the pur- pose which automatically indicates the breaking strength of the yarn. It is advisable to have 94 PRACTICAL COTTON CALCULATIONS the testing machine run by power because when making comparative tests the pull on each hank should be uniform. Yarns of similar counts but different grades of cotton vary in breaking strength, and it is impos- sible to state just how strong a yarn should be. The number of turns or twists per inch will also vary the breaking strength. By referring to the table on page 96 it will be noticed that the yarns do not vary in breaking strength in similar proportion to the counts. BREAKING WEIGHTS OF AMERI- CAN YARNS SPUN FROM AMERICAN COTTON. • The table on page 96, used by permission of Draper Company, Hopedale, Mass., indicates the average breaking weights of sample skeins from several hundred American mills. The old breaking weight referred to in the table is an old standard obtained by tests from 225 mills in 1886, and is here shown for the pur- pose of comparison with the new standards. The first new table represents average tests of carded yarns made from stock averaging about strict middling in grade. The combed warp table represents tests of yarns made from stock slightly under good middling. The table of soft twisted yarn is based on yarns averaging 3.25 times the square root of the counts in twist, the stock averaging about strict middling. All the yarns were tested on a power tester. OLD NEW NEW NEW OLD NEW PJ fee 2 o Breaking Weight of Warp Yarn. Breaking Weight of Warp Yarn. Breaking Weight Combed Warp. Breaking Weight Soft Twist Yarn. '- <-' Breaking Weight of Warp Yarn. cj i, e k 1000 1 19.6 51 3".6 47— 5U0 2 19.2 52 3.1 46 333.3 3 530 634+ 863— 620+ 18.9 53 35.5 45H 250 4 410 476— 646 462 18.5 54 34.9 44- 200 5 330 381 516 367 18.2 55 34.4 43- 166.7 6 275 318— 429+ 367+ 304— 17.9 50 33.8 42^ 142.9 •7 237.6 272+ 258+ 17.5 57 33.4 42— 125 8 209 238+ 321 224+ 17.2 58 32.8 41— 111.1 9 186.5 212+ 285- 198+ 17 59 32.3 4C+ 100 10 168.7 191 256 177 16.7 60 31.7 39+ 90.9 11 154.1 174— 232+ 160— 16.4 61 31.3 39— 83.3 12 142 159+ 147+ 213- 145+ 133+ 16.1 62 30.8 38— 76.9 13 131.5 196 15.9 63 30.4 37+ 71.4 14 122.8 137- 182- 123— 15.6 64 30 - 37- 66.7 15 115.1 128— 169+ 158+ 114— 15.4 65 29.6 36 62.5 16 108.4 120— 106- 15.2 66 29.2 35+ 58.8 17 102.5 113— 149- 99— 14.9 67 28.8 35- 55.6 18 97.3 107— 140+ 93- 14.7 68 28.5 34+ 52.6 19 92.6 101 133— 87 14.5 69 28.2 34— 50 30 88.3 96 126 82 14.3 70 27.8 33+ 47.6 21 83.8 914- 87+ 120— 77+ 14.1 71 27.4 33- 45.5 22 79.7 114+ 73+ 13.9 72 27.1 32+ 43.5 23 75.9 84- 109+ 70— 13.7 73 26.8 32- 41.7 24 72.4 80+ 104+ 66+ 13.5 74 26.5 31+ 40 25 69.2 77 100 63 13.3 75 26.2 31— 38.5 26 66.3 ft 96 60+ 57+ 13.2 76 25.8 30+ 37 27 63.6 92+ 13 77 25.5 30— 35.7 28 61.3 69- 89- 55- 12.8 78 25.3 29+ 34.5 29 59.2 67— 86— 53- 12.7 79 24.9 29- 33.3 30 57.3 64H 83- 50+ 12.5 80 24.6 28+ 32.3 31 55.6 62- 80— 46+ 12.4 81 24.3 28+ 31.3 32 54 60- 77+ 12.2 82 24 28— 30.3 33 52.6 59— 75- 45— 12.1 83 23.7 27+ 29.4 34 51.2 57- 72H 43— 11.9 84 23.4 27- 28.6 35 50 55+ 70- 41+ 11.8 85 23.2 27— 27.8 36 48.7 54— 68- 40- 11.6 86 22.8 26+ 27 37 47.6 52+ 66- 38+ 11.5 87 22.6 26- 26.3 38 46.5 51 64- 37 11.4 88 22.4 26— 25.6 39 45.5 50— 63- 36— 11.2 89 22.2 25+ 25 40 44.6 48H 61 34- 11.1 90 22 25- 24.4 41 43.8 47- 59+ 33- 11 91 21.7 25- 23.8 42 43 46- 58- 32- 10.9 92 21.5 24+ 23.3 43 42.2 45- 56+ 55+ 31- 10.8 93 21.3 24- 22.7 44 41.4 44- 30- 10.6 94 21.2 24— 22.2 45 40.7 43- 54— 29- 10.5 95 21 23+ 23+ 21.7 46 40 42- 53— 28- 10.4 96 20.7 21.3 47 39.3 41- 5H 27- 10.3 97 20.5 23- 1 20.8 48 38.6 41- 50- 27— 10.2 98 20.4 23— I 20.4 49 37.9 40— 49- 26- 10.1 99 20.2 22+ 30 |50 37.3 39 48 25 10 100 20 22 PRACTICAL COTTON CALCULATIONS 07 Yards of Cloth per loom per day of ten hour* Picks per inch Picks per minute. 83.3 75.8 1.9.4 (54.1 59.5 5 r..<; 52.1 4tt.O 46.3 43.'.l 41.7 39. 7 37.9 3 c. 2 34.7 33.3 32.1 3H.0 29. X 28.7 27 1 I >2 104 L06 IDS no 12 1 14 L6 1 18 i ao 124 1 26 I2S 130 134 136 140 144 146 156 160 164 166 170 174 176 1 180 26.9 21',. 1 1 2:..:'. 24.5 23.x 23.1 22.5 21.9 21.4 2H..S 20.3 10.3 19.4 18.9 18.5 18.1 17.7 17.4 17.0 16.7 16.3 16.0 15.7 15.4 15.2 14.9 14.6 14.4 14.1 13.9 13.7 13.4 13.2 13.(1 12.X 12.4 12.3 11.9 11.6 11.4 11.1 1(1. X K).7 1(1.4 ld.2 l(i.(i 100 105 110 115 | 130 87.5 79.5 72.9 67.3 62.5 5S.3 54.7 51.5 48.6 46.1 43.7 41.7 39.8 3.X.O 36.5 .-.5.(1 33.7 32.4 31.3 3<>.2 2'l.2 28.2 27.3 2 6.5 25.7 25.(1 24.3 23.6 23..) 22. 1 21.9 21.3 2.0.X 20.3 19.9 19.4 19.0 18.6 18.2 17.9 17.5 17.2 16.8 16.5 16.2 15.9 15.6 15.4 15.1 14.X 14.6 14.3 14.1 13.9 13.7 13.5 13.1 12.9 12.5 12.2 12.(1 11.7 11.4 11.2 10.9 10.7 10.6 lo.3 10.1 9.9 9.7 61.1 57.3 53.9 50.9 4 8.2 45.8 43,. 7 11.7 39.9 38.2 36.7 35.3 34.0 32.7 31.6 30.6 29.6 28.6 27.8 27.0 26.2 25.5 24.X 24.1 23.5 22.9 22.4 21.8 21.3 2(1.8 20.4 19.9 19.5 19.1 18.7 18.3 18.0 17.6 17.3 17.0 16.7 16.4 16.1 15.8 15.5 15.3 15.0 14.8 14.6 14.3 14.1 13.7 13.5 13.1 12.7 12.6 12.2 11.9 11.8 11.5 11.2 11.0 10.8 10.5 K).4 10.2 79.9 73.7 68.5 63.9 59.9 56.4 53.2 50.4 47.9 45.6 43.6 11.7 39.9 38.3, 36.9 35.5 3 4.2 33.(1 31.'.) .-.('.9 29.9 29.0 28.2 27.4 26..; 25.9 25.2 24.6 24.0 23.4 22.; 22.3 21.X 21.3 20.x 20.4 211.0 19.6 19.2 18.8 18.4 18.1 17.7 17.4 17.1 16.8 16.5 16.2 16.0 15.7 15.5 15.2 15.0 14.7 14.3 14.1 13.7 13.3 13.1 12.8 12.4 12.3 12.0 11.7 11.5 11.3 11.0 10.9 10.6 loo.o 90.9 83.3 76.9 71.4 66.7 62.5 58.8 55.6 52.6 5(). O 47.6 45.5 43.: 41.7 40.0 38.5 37 35.7 34.5 333 32 31 30.3 29 4 28 6 2 7 X 27 O 26 3 25 6 25.0 24.4 23.8 23.3 22.7 2 21.7 21.3 2o.8 20.4 20 19.6 192 18.9 18.5 18.2 17.9 17.5 17.2 16.9 16.7 16.4 16.1 15.9 1 5.6 15.4 14 .9 14 7 14 13 9 13 7 13.3 13.1) 12 8 12.5 12.2 12() 11 X 11.5 11.4 111 104.2 94 7 86 80 74.4 69.4 65.1 61.3 57.9 54 52 49.6 47.3 45.3 43.4 41 7 40.1 38.6 37 2 35.9 34.7 33.6 32 6 31.6 3(). 6 29.8 28 28.2 27.4 26. 26.0 25.4 24.X 24 2 23 7 23 22 6 22 2 21 7 21 3 2(1.8 2(14 2().() 19 7 16.0 15.5 16 14 14.5 14. 13.9 13.5 13.4 13(i 12.7 12.6 12 12.0 11.8 11 6 1(18.3 98.5 90.3 83.3 77.4 72.2 67.7 63.7 60. 2 57.0 54.2 51.6 49,2 47. 45. 43.3 41.7 40. 34.9 33.9 32.8 31.9 31.0 30.1 29.3 28.5 27.8 27.1 26.4 25.8 25.2 24.6 24.1 23.6 2 3.o 22.6 22.1 21.7 21.2 2o.x 2(1.4 20.1 19.7 19.3 19.(1 18.7 18.4 18.1 17.8 7.5 13.5 112.5 102.3 93.7 86.5 80.4 75.0 70.3 66.2 62. 59.2 56.3 53.6 51.1 48.9 46.9 45.0 43.3 41,7 40.2 38.8 37.5 36 35.2 34, 33 32, 31.3 30.4 29.6 28.8 28.1 27.4 26.8 26.2 25.6 25.li 24 23.. 9 23.4 23. 22.5 22, 2 1 6 21.2 2(1.8 20.5 L'O.l 19.7 19.4 19.1 17.2) 17.9 6.9 16.7 16.2 15.9 15.5 15.0 14.8 14.4 14 1 13.9 13.5 13.2 13.1 12.7 12.5 12.3 12..) 17..; 17.3 16.8 16.5 16, 15.6 15.4 15..) 14.6 14.4 14.1 13.7 13.5 13.2 12.9 12.8 __ 12.5| 13.0 116.7 106.1 97. 89.7 83.3 77. 72.9 f.X.C, 64.8 61.4 58.3 55.6 53.0 50.7 48.6 46.7 44.9 43.2 41.7 403 38.: 37.6 3.6.5 35.4 34.3 33.3 32.4 3.1.5 293) 29.2 28.5 27.X 27.1 2< ',.5 25.9 25.4 24.8 24.3 23.8 23.3 22. 22.4 22.(1 21.6 21.2 20.8 20.5 20.1 19.8 19.4 19.1 18.8 18.5 18.2 17.9f 17.4 17 16.7 16.2 16. (I 15.6 15.2 15.(1 14.6 14.2 14.1 13.7 13.4 13.; xo.c, 75.5 7 67.1 6,3.6 6(1.4 57.5 54 52.5 5(13 48 3 46.5 4 18 43 2 41.7 403 39.0 37.8 36.6 35 5 34 33 6 32.7 31 8 .-,1 30.2 29.5 28.8 27.5 26.9 26.3 25 7 25 2 125.(. 113.6 K>4.2 96.2 89.3 83.3 78. 73.5 69.4 62.5 59, 56.8 54,3 52.1 50.0 48.1 46.3 44.6 43.1 41.7 40.3 39.1 37.9 3,6.8 35.7 34.7 33.8 32.9 32.1 31.3 30.5 29.' 2X.4 2-7. X 27.2 26, 26,.0 23.2J 24.0 22.X 22.4 22.o 21.6 21.2 20.: 20.5 20.1 19.8 19.5 19.2 18.9 18, 18.1, 17.8 17.3 16.8 16.6 16.1 15.7 15.5 15.1 14.7 14.6 14.2 13.9 13. 23 25.1 22.7 22.3 21.9 21.6 21.2 2(1.8 2(1.4 2. ). 1 19.8 19.5 19.2 18.7 18.4 17.9 17.4 17.1 16.7 16.2 16.0 15.6 15.2 15.1 14.7 14.4 14.2 13.9 PRACTICAL COTTON CALCULATIONS Yards of Cloth per loom per day of ten hours. Picks per Picks per minute. inch 20 155 160 165 133.3 137\5 170 175 180 150.( 1 185 1 190 154.2 158.3 195 162.E 200 205 1 20.2 141.7 145.8 100.7 170.8 22 117.4 121.2 125.0 128.8 132.0 130.4 140.21143.! 147.7 151.5 155.3 24 1(>7.( 111.1 114.0 118.1 121.5 125.( 128.6 131.0 13.5.4 138.0 1 12.4 20 00.4 ]02.< 105.8 100.( 1 1 2.2 115.4 '118. ( 121.8 125.1 128.2 13.1.4 28 112.3 05.2 08.2 101.2 104.2 1(17.1 110.] 113.1 110.1 1 19.0 30 80.1 88 '. 01.7 04.4 97.2 10().( 102.S 105.5 108.: 111.1 lT33l 32 80.7 83.3 85.0 88.5 01.1 03.'. 00, 00 () lol.l UI4.2 IOC. 8 34 70.0 78. 4 80.9 83.3 85.8 88.2 0O.7 03.1 05. ( 08. () 100.5 3(3 71.8 74.1 70.4 78.7 81.0 8:;.: 85. ( 88.0 oo.: 02 04.0 38 68.1 70.2 72.4 74.0 70.8 78.; 81.1 83.3 85.C 87.7 80.0 40 04.0 00.7 08.7 70.8 72.0 75.( 77.1 70.2 8i.: 83.3 85.4 42 01.5 03.5 05.5 07.5 00.4 71.4 73.4 75.4 77.4 70.4 81.3 44 58.7 00.0 02.5 04.4 00.3 08.2 70.1 72.0 73.: 75,x 77.7 41! 50.2 58.1 50.8 01.0 03.4 65.2 07.( 08.8 7o.7 72.5 74.3 48 53.8 55.0 57.3 59.0 0(1.8 02. f 04.'. GG.O 07.7 69.4 71.2 50 51. 7 53.3 55.0 56.7 58.3 C,ll.( 61.7 03.3 05.( 00.7 08.3 52 49.7 51.3 52.0 54.6 50.1 57.7 50.3 OO.O 62.5 04.1 05.7 54 47. 8 40.4 50.0 52.5 54.0 55.0 57.1 58.0 60.2 01.7 63.3 66 40.1 47.6 40.1 5(1.0 52.1 53. ( 55.1 50.5 r>8.( 59 5 61.0 58 44.5 40.0 47.4 4S.8 50.3 51.7 53. l 54.0 5C,.( 57.5 58. :i 60 43.1 14.4 45.K 47.2 48.0 5( u 51.4 52.8 54.2 56.9 02 41.7 13.0 44.4 45.7 47.0 48.4 40.7 51.1 52.4 5 3'; 8 55 1 64 40.4 41.7 43.0 44.3 45.0 40.1 48.2 40.5 5(1.8 52.1 53.4 66 30.1 4(1.4 41.7 42.0 44.2 45.5 40.7 48.0 49.2 5(1.5 51.8 CM 38.0 39.2 40.4 41.7 42.0 44.1 45.3 40.0 47.8 40.O 5(1.2 -o 36.9 38.1 30.3 40.5 41.7 4 2.; 44.( 45.2 40.4 47.0 48.8 72 35.9 37.0 38.2 39.4 1(1.5 41.7 42.8 44. 45.1 40.3 47.5 74 34. o 36.0 37.2 :;.x.:: 30.4 4(i.5 41.7 42.8 43.: 45.() 40.2 70 34. (> :;.->. i 30.2 37.3 38.4 30.5 40.( 41.7 42.8 43.0 45.0 78 33.1 34.2 35.3 30.3 37.4 ::x.r. 3o.r 40.6 41.7 42.7 43.8 80 32.3 33.:'. ::i.t 35.4 30.5 37.5 38.: 39.6 40.1 41.7 4 2.7 82 3 1 .:■ 32.5 3.-',. 5 34.6 35.0 30.0 37.( 38.6 30.1 40.7 41.7 84 30.8 .-.1.7 32.7 :;::.7 34.7 35.7 30,.( 37.7 3X.7 30.7 4o.7 86 30.0 31.0 32.0 32.0 33.9 34.9 35.8 30.8 37., x 38.8 30.7 88 29.4 .".u..-', 31.3 32.2 33.1 34.1 35.1 30. o 36.1 38.x 90 2S. 7 20.0 30.6 31.5 32.4 33.3 34.3 35.2 30.1 37.(1 38.0 92 28.1 20.(1 20.0 30.8 31.7 3.2. 33.5 34.4 35.3 30.2 37.1 04 27.5 28.4 20.3 30.1 31.0 31.0 32.x 33.7 34.0 35.5 30.3 96 20.9 27. S 28.6 20.5 30.4 31.3 32.1 33.0 33.; 34.7 35.0 98 26.4 27.2 28.1 28.0 20.8 30.0 31.6 32.3 33.2 34.0 34.0 100 25.8 20.7 27.5 28.3 20.2 30.0 30.8 31.7 32.5 33.3, 34.4 102 25.3 20.1 27.0 27.8 28.0 29.4 30.2 3 1 .0 81.9 32.7 33.5 104 24.8 25.0 20.4 27.2 28.0 28.8 20.0 30.4 3 1 .3 32.1 32.0 106 24.4 25.2 25.0 20.7 27.5 28 3 20.1 20.0 30.7 31.4 32.2 108 23.0 2 1.7 25.5 20.2 27.(1 27.S 28.5 20.3 30.1 30.0 31.6 110 23.5 24.2 25.(1 25.S 20.5 27.3 2X.( 28.8 20.5 30.3 31.1 1 12 23.1 23. S 24.0 25.3 20.(1 20.8 27.5 28.3 20.O 20.8 30.5 114 22.7 23.4 24.1 24.0 25.0 20.3 27. 27.8 28.5 20.2 3O.0 116 22.:; 23.0 23.7 24.4 25.1 25.0 26.6 27.3 28.0 28.7 20.5 118 21.0 22.0 2:',..". 24.(1 24.7 25.4 26.1 20.8 27.5 28.2 29.0 ISO 21.5 22.2 22.0 23.6 24.3 25.0 25.7 26.4 27.1 27.8 28.5 L22 21.2 21.0 22.5 23.2 23.0 24.0 25.3 20.0 20.0 27.3 28.0 124 20.8 21.5 22.2 22.8 23.5 24.2 24.9 25.5 20.2 20.0 27.0 126 20.5 21.2 21.8 22.5 23.1 23.8 24.5 25.1 25,x 20.5 27.1 128 20.2 20.8 21.5 22.1 22.8 23.4 24.1 24.7 25.4 20.0 20.7 130 10.0 2(1.5 21.2 21.8 22.4 23.1 23.7 24.4 25.o 25.0 20.3 134 10.3 10.0 20.5 21.1 21.8 22.4 23.0 23.0 24.3 24.0 25.5 130 10.0 10.0 2().2 2d.8 21.4 22.1 22.7 23.3 23.0 24.5 25.1 140 18.5 10.0 10.0 20.2 20.8 21.4 22. o 22.0 23.2 23.8 24.4 144 17.0 18.5 10.1 10.7 2(1.3 2H.8 21.4 22.0 22.0 23.1 23.7 140 17.7 18.3 18.8 10.4 20.0 2(1.5 21.1 21.7 22.3 22.8 23.4 150 17.2 17.8 18.3 18.0 10.4 20.0 20.0 21.1 21.7 22.2 22.8 154 10.8 17.3 17.0 18.4 18.0 1 0.5 20.0 20.0 21.1 21.0 22.2 150 10.0 17.1 17.0 18.2 18.7 10.2 10.x 20.3 20.8 21.4 21.0 160 10.1 10.7 17.2 17.7 18.2 18.7 19.3 10.8 20.3 20.8 21.4 104 15.8 10.3 10.8 17.3 17.8 18.3 18.8 10.3 10.8 20.3 20.8 ICO 15.0 '16.1 10.0 17.1 17.0 18.1 18.0 10.1 1 0.0 20.1 20.0 170 15.2 15.7 10.2 10.7 17.2 17.0 18.1 18.0 10.1 10.0 20.1 174 14.8 15.4 1 5.8 10.3 10.8 17.2 17.7 18.2 18.7 10.2 10.6 170 14.7 15.2 15.0 10.1 10.0 17.0 17.5 18.0 18.5 18.0 10.4 180 14.4 14.8 15.3 15.7 16.2 16.7 17.1 17.6 18.1 18.5 19.0| CLOTH PRODUCTION. To Find Production of Cloth per Week of 56, 58, 60, or 66 Hours, at Any Desired % from 50 to 100, Running in 5's. Rule 82. Multiply the speed of the loom by the constant desired in the following list and divide by the number of picks per inch. Constant Constant Constant Constant Per Cent, of to us<> i'< >r to use for to use for to use for production. 56 hours. 58 hours. 60 hours. 66 hours. 50 46§ 48* 50 55 55 51* 53* 55 60.5 60 56 58 60 66 65 601 621 65 71.5 70 65* 67f 70 77 75 70 72* 75 82.5 80 74f 77* 80 88 85 79* 82* 85 93.5 90 84 87 90 99 95 88f 91* 95 104.5 100 93* 96f 100 110 Example. What is the production in yards per week of 60 hours of a loom running 160 picks per minute, weaving- a cloth with 120 picks per inch, at 80% ? 160 picks X 80 constant „_„ z~ — r~r— — : — ; = 106^ vards, Ans. 120 picks per inch * The preceding constants are based on the following: L0FC> 100 PRACTICAL COTTON CALCULATIONS 60 minutes X hours per week X % production 36 inches per yard The cloth production tables on pages 97 and 98 are based on 100% production for 10 hours, no allowance being made for stoppages. Owing to the tables being computed for 10 hours, they are very convenient when requiring To Find % Production of a Loom when Hours Run, Speed of Loom, Picks per Inch and Actual Production in Yards are Known. Rule 83. Multiply picks per inch by yards produced and by .6, and divide by speed of loom and number of hours run The .6 is obtained by dividing 36 inches per yard by 60 minutes per hour. Example. The actual production of a loom running 150 picks per minute, weaving a cloth with 80 picks per inch, is 23 yards, in 10 hours. What is the % of production? 80 picks per inch X 23 yards X -6 „ . 150 speed of loom X 10 " i6 ' b/ °' Am ' To Find Production of Cloth, in Yards per Loom, for Any Number of Hours, at Any Desired %. Rule 84. Multiply the production for 10 hours at 100% (see tables, pages 97 and 98) by the number of hours run and the % of production desired, and divide by 10. Example. A cloth with 60 picks per inch is desired to be woven on a loom running 160 picks per minute. What would be the production per week of 58 hours at 80% ? PRACTICAL COTTON CALCULATIONS ]01 According to the table the production for 10 hours at 100% would be 44.4 yards, therefore 44.4 vards X 58 hours X .80 ^ n . ^r^j — — — 20C) vds., Ans. 10 hours Rule 82 may be used To Find the Number of Cuts per Loom per Week by dividing the number of yards per week by the length of the cut. LOOM CALCULATIONS. To Find Constant to Use for Any Loom Take-Up Motion. Rule 85. Multiply all the driven gears to- gether and divide by all the drivers multiplied togt I her. The circumference of the sand roller in inches is considered a driver. If the motion takes up every two picks, the driven gears should be mul- tiplied by 2. It is customary to allow a certain % for the difference between the picks per inch in the cloth while in the loom and after leaving the loom. This may be done by deducting a cer- tain % , varying from 1 to 2%, according to the motion used, from the circumference of the sand roller. To Find Change Gear or Picks per Inch on Looms where the Change Gear is a Driver, when Constant is Known. Rule 86. Divide the constant by picks per 102 PRACTICAL COTTON CALCULATIONS inch to find change gear. Divide constant by change gear to find picks per inch. When the change gear is a driver, the con- stant is always a dividend. To Find Change Gear or Picks per Inch on Looms where the Change Gear is a Driven Gear, when Constant is Known. Rule 87. Divide picks per inch, by constant to find change gear. Multiply change gear by constant to find picks per inch. The sand roller gear and every alternate gear from that are driven gears. All the remaining gears are drivers. SPEED CALCULATIONS. To Find Speed of Shafting, when Diameter of Driving Pulley, Diameter of Loom Pulley, and Speed of Loom are Known. P.ule 88. Multiply diameter of loom pulley by speed of loom, and divide by diameter of (hiring pulley. Example. What is the speed of shafting required to run a loom 145 picks per minute, with a 14-inch pulley on the loom and a 7-inch pulley on the shaft? 14-inch pulley on loom X 145 picks per minute 7-inch pulley on shaft = 290 revolutions per minute, Ans. PRACTICAL COTTON CALCULATIONS 103 To Find Diameter of Driving Pulley, when Speed of Shafting, Diameter of Loom Pulley, and Speed of Loom are Known. Rule 89. Multiply diameter of loom pulley by speed of loom, and divide by speed of shaft- ing. Example. What diameter of pulley will be required on a shaft running; 290 revolutions per minute to run a loom 145 picks per minute with a 14-inch pulley? 14-inch pulley X 145 picks per min. . diameter oi driving pulley, Ans 290 R. P.M. diameter of To Find Diameter of Loom Pulley, when Speed of Loom, Speed of Shafting, and Diameter of Driving Pulley are Known. Rule 90. Multiply speed of shafting by diameter of driving pulley, and divide by speed of loom. Example. A loom is required to run 145 picks per minute. The speed of the shaft is 290 R. P. M. and the diameter of the pulley on the shaft is 7 inches. What diameter of loom pul- ley will be required? 290 R. P. M. X 7 ins. driving pulley , t . — — — : — 5_j: ^- = 14 ms. 145 picks per mm. diameter of loom pulley, Ans. 104 PRACTICAL COTTON CALCULATIONS To Find Speed of Loom, when Speed of Shafting, Diameter of Driving Pulley, and Diameter of Loom Pulley are Known. Rule 91. Multiply speed of shafting by diam- eter of driving pulley, and divide by diameter of loom pulley. Example. What will be the speed of a loom with a 14-inch pulley, the speed of shafting being 290 R. P. M. and the diameter of the driv- ing pulley 7 inches? 290 R. P. M. X 7 ins. driving pulley ,,_ . . ... . =— „ — -= 145 picks 14-m. loom pulley per min ? Am The four preceding rules, 88 to 91, may be summarized in the following — Formula D. To Find Speed of Shafting, Diameter of Driving Pulley, Diameter of Loom Pulley, or Speed of Loom. Speed of shafting X diameter of driving pulley is equal to Diameter of loom pulley X speed of loom. Rule. Divide the product of the remaining items of the group containing the required item into the product of the other group. When the numbers found are too large for practical purposes, use smaller numbers that are in direct ratio with them. COST CALCULATIONS. To Find Weaving* Cost per Yard when Weekly Rate and Production are Known. Rule 92. Divide the weekly rate by the pro- duction in yards per week. Example. If the production of a loom is 150 yards per week, the weekly rate $9.75, and the looms per set 5, what would be the weaving price per yard of cloth? 150 yards X 5 looms = 750 yds. per week $9.75 weekly rate ., rt . , =— — - — 1.3c. weaving cost per yd., 750 yds. per week to F J A ' MS $9.75 M ._ or^-r; — — == $1.95 per loom 5 looms $1.95 , _ . , , — 1.3c. weaving cost per yd., 150 yards per loom j Lng To Find Weaving Cost per Cut when Weekly Rate, Length of Cut, and Production per Week are Known. Rule 93. Multiply the weekly rate by the length of cut and divide by the production per week. Using the preceding example what would be the weaving cost per cut of 100 yards? 106 PRACTICAL COTTON CALCULATIONS $9.75 weekly rate X 100 yds, cut length 750 yds. production per week weaving cost per cut, Ans. To Find Cost per Yard for Oversight when Pro- duction and Oversight per Loom per Week are Known. Rule 94. Divide the oversight per loom by the production. Example. If a plain loom produces 160 yards per week, and the oversight per loom per week is 31 cents, what would be the oversight cost per yard? 31c. oversight -, no ^r • w i — -^ — = .19375c. oversight per yard, 160 yards Am To Find General Expense per Yard when Produc- tion and General Expense per Loom per Week are Known. Rule 95. Divide the general expense per loom by the production. Example. If a loom produces 145 yards per week, and the general expense per loom is $1.74, what would be the cost per yard for general expense ? $1.74 — r^ 7- = 1.2c. general expense per yd., Ans. 145 yards To Find General Expense per Pound of Cloth when General Expense per Loom, Yards per Week per Loom and Number of Yards per Pound are Known. Rule 96. Multiply the general expense per PRACTICAL COTTON CALCULATIONS 107 loom by the number of yards per pound and divide by the number of yards per week. Example. If the general expense in a mill is estimated at $1.80 per loom per week, what would be the general expense per pound of a piece of cloth 5.3 yards per pound produced at the rate of 130 yards per week per loom ¥ $1.80 genl. expense per loom X 5.3 yards per lb. 130 yards per week = 7.338c. genl. expense per lb, Ans. To Find Cost of Stock per Pound of Cloth, in a Cloth Containing More than One Quality of Cotton and More than One Counts of Yarn when Cost of Cotton per Pound and % of Each Counts of Yarn are Known. Rule 97. Multiply the % of each yarn by the cost of cotton per pound. Add results. Example. A cloth contains 37% of 9c. cot- ton and 63% of 12c. cotton. What is the cost of stock per lb of cloth ? 37% or .37 X 9c. = 3.33 63% or .63 X 12c. = 7.56 10.89c. per It), Ans. To Find Cost of Yarns per Cut when Weight and Cost per Pound of Each are Known. Rule 98. Multiply the weight of each by the cost per pound. Add results. Example. A cloth contains 5 lbs. of warp and 4J lbs. of filling. If the warp costs 18c. 108 PRACTICAL COTTON CALCULATIONS and the filling 19c. per lb., what would be the cost of the yarns in the cloth ? 5 lbs. warp X 18c. = .90 4.5 lbs. warp X 19c. = .855 $1,755, Ans. To Find Cost of Yarns per Yard of Cloth when Total Cost of Cut and Length of Cut are Known. Rule 99. Divide the cost per cut by the length. Example. The yarn in a cut of cloth 100 yards long cost $3.80. What is the cost of the yarns per yard of cloth? = 3.8c. cost of yarns per yard, Ans. 100 vards To Find Cost of Yarns in a Warp when Counts, Length, Number of Ends and Price per Pound are Known. -KRule ioo. Multiply the length of fit? warp in yards by the number of ends in the warp and the price per pound and divide by 840 and the yarn counts. Iv\ ample. A cotton warp 1200 yards long contains 2700 ends of 35 's yarn. The yarn price is 26c. per pound. What is the cost of the warp ? 2700 ends X 1200 yards X 26c. _ 840 X 35 's warp counts " * - ' * PRACTICAL COTTON CALCULATIONS 109 To Find Cost of Filling in a Piece of Cloth when Length of Piece, Width in Reed, Pick, Counts and Price per Pound of Filling are Known. *Rule 101. Multiply length of pieee by width in reed, picks per inch and price per pound, and divide by 840 and the filling counts. Example. A cut of cloth 56 yards long is woven 30 inches wide in the reed with 70 picks per inch of 40 's filling'. The cost of the filling is 25 cents per pound. What is the cost of the filling per cut? 56 yards X 30 inches in reed X 70 pick X 25c. 840 X 40 's filling counts = 87.5c. cost of filling, Ans. COSTS OF CLOTH. In cloth mills the product from which the income is realized is cloth, therefore the most important branch of textile calculations in a cloth mill deals with cost. The cost of a piece of cloth, which is figured at so much per yard, or so much per pound, or both, is usually estimated in the office from items furnished by the various overseers. As all textile calculations enter either directly or indirectly into, and lead up to the final cost of the cloth, the rules in the earlier part of this book are given, although all of them are not necessary for any one piece of cloth. 110 PRACTICAL COTTON CALCULATIONS The preceding rules have been given so that any one item may be found with very little trouble, and it is intended in the succeeding pages to show how the cost of any cloth may be ascertained. As the methods of estimating costs vary in different mills, one method only will be ex- plained here; part of the items dealt with in explaining this, or other items calculated from them, are usually required in every mill. For convenience in dealing with mill calcu- lations it is customary to use what are termed blanks, upon which are printed various items. Against these items overseers of the various departments write out the necessary data. In the system to be explained here it will first be shown how the various items necessary to fill out the weave-room blank are obtained, then how the total cost per yard and per pound of cloth are estimated. In the following blank the words shown in italic type are supposed to be printed. The remaining figures and letters show the data nec- essary for the production of a certain piece of cloth, which will be taken as an example in ex- plaining the items and how they are obtained. PRACTICAL COTTON CALCULATIONS 111 System of Filling Out Blank with Weave Room Data for a Piece of Cloth. BLANK NUMBER 1. 1. Pattern number. 26. 2. Kind of cloth. Leno. 3. Sley. 56 L pick 8(X 5. Warp counts, No. of ends of each, and con- traction and size. 200 ends 4/32 's, 20% contraction. 300 ends 2/32's, 15% contraction. 2184 ends 50 's, 10% contraction and size. 6. Filling counts. 60 's. 7. Width of cloth. 28 inches. 8. Width in reed. 30 inches. 9. Yards per pound. 6.02. 10. Looms per set, 4. 11. Speed, 150. 12. Per cent, of production. 80. 13. Weekly rate. $10.00. 14. Yards per week {58 hours). 145. 15. Weaving cost per yard. 1.724c. 16. Counts and weight of yarn in 100 yards of cloth. Warp. 4/32 's, 3.56 pounds. 2/32's, 2.56 " 50 's 5 72 " 17. Filling. 60 's, 4.76 18. 16.60 pounds, Total weight in 100 yards of cloth. 112 PRACTICAL COTTON CALCULATIONS Explanation of Items in Weave Room Blank. 1. Pattern number. This item will readily explain itself. 2. Kind of cloth. Against this is placed leno, plain, bedford cord, etc., according to style made. 3 and 4. Sley and Pick. These are found from the cloth to be made by the designer, or by the weave room overseer, if the latter does the designing. The count of the cloth mentioned here is 56 X 80. The 128 shown under the sley reed represents the average sley, and is found from items 5 and 7 by Rule 51 as follows: 3584 total ends 28 ins. width of cloth = 128 average sley ' The average count of the cloth is 128 X 80. 5. Warp counts, No. of ends of each, and con- traction and size. The warp counts are usually found by comparison, as explained on page 12, or by weighing as in Rule 1. The number of ends of each counts are obtained by Rule 25. The amount to allow for contraction and size are estimated by the designer. Ply cotton yarns are not usually sized. 6. Filling counts. If the weight of the cloth is of secondary importance, which is usually the case in fancy cotton goods, the filling is varied, if necessary, until a counts is obtained that makes the appearance of the cloth satisfactory. When the counts of the filling is decided upon in this manner, the yards per pound, item 9, may be found by Rule 68, after finding item 18. See example after explanation of item PRACTICAL COTTON CALCULATIONS 113 9. If items 5 and 9 are found before the filling counts, the latter may be found from items 4, 8 and 17 by Rule 37. Example. 80 pick X 30 in. at reed X 100 yds. _ 840X4.76 lbs. of filling -^ filling. Note how the weight of the filling, item 17, is obtained. 7. Width of cloth. This is usually given to the designer by the superintendent. 8. Width at reed. This may be found from items 3 and 7 by Rule 63. Example. 56 sley X 28 inches width of cloth 26.19 dents per inch in reed X 2 ends per dent = 29.93 inches, say 30 inches width in reed In the table on page 68 a 56 sley gives 26.19 dents per inch in the reed. In dealing with the contraction of a fancy cloth it is necessary that a person should have considerable practical experience before he can judge what to allow for contraction, and it is advisable that the notes on pages 62 to 66 be thoroughly understood and borne in mind. 9. Number of yards per pound. Cloths are sometimes made to a certain weight and the counts of yarns varied to make this weight; other cloths are made with given yarns and the weight figured from these. In both these methods item 5 is usually found in the same manner. 114 PRACTICAL COTTON CALCULATIONS If item 5 and the weight of the cloth are known, the filling, item 6, may be found from items 4, 8 and 17 by Rule 37. See example after explanation of item 6. If item 18 is known, item 9 may be figured from this by Rule 68. Example. Item 18 gives 16.60 lbs. of yarn in 100 yards of cloth. 100 yards . _ 16.60 lbs. =6.02 yards per ft Item 10. Looms per set; 11. Speed of loom; 12. Per cent, production; and 13. Weekly rate; are all estimated according to the width of cloth, quality of yarn, type of loom, and difficulty of pattern. It is while running a sample that any diffi- culties that are liable to be met with later in making an order of goods like the sample should be noted. The probable difficulties cannot always be noticed when making the sample, but should be when possible because the less the production, from any cause, the more the cost. If the actual production falls below that esti- mated, the margin between the cost and selling price gets smaller. Item 13 is mutually fixed by the head official and weave room overseer. 14. Yards per week. This may be found from items 4, 11 and 12 by Rule 84. 15. Weaving cost per yard. This may be found from items 10, 13 and 14 by Rule 92. Example. 145 yards X 4 looms = 580 yards per week from 4 looms. PRACTICAL COTTON CALCULATIONS 115 .+10 weekly rate -^580 yards = 1.724c. weav- ing cost per yard. 16. Con n Is and weight of warp yarns in 100 yards of cloth. The counts of warp are obtained as stated in explanation of item 5. The weight is obtained from item 5 and length by Rule 17. Example. 800 ends X 100 yards = g C)? = 3 56 810 X 32 's counts p(mnds of 4/32 > s ° r ' 8 !!n Dd ^ 12Qy ! rdS = 3.56 lbs. of 4/32 's 840 X 32 's counts Note. The length of 100 yards is taken instead of 1 yard because it does not deal with so many small amounts, and instead of any other number between 1 and 100 because fewer figures are dealt with. When multiplying by 100, it is only necessary to add 2 ciphers at the right of the multiplicand, or to move the point 2 places to the right if a decimal fraction. 17. Weight of filling in 100 yards of doth. This is figured out from items 4, 6 and 8 by Rule 34. Example. 80 pick X 30 ins. X 100 yds. - ... OAn w nfx , —=4.76 lbs. weight 840 X 60 s counts of fm^g. If item 6 is not known, item 17 may be found by deducting the combined weights of the warps from the weight of the cut, item 18. The loss by waste was not considered in the above examples when finding items 16 and 17. 116 PRACTICAL COTTON CALCULATIONS The waste item is usually added in the office when computing the cost. 18. Weight of cut. Say 100 yards. This may be found by adding items 16 and 17. together, or by dividing the length of cut by item 9, the number of yards per pound. Item 13 may be said to cover the weaving cost of cloth. To this must be added other costs which are necessary; these which are computed and arranged in the office are here numerically arranged as follows: 19. Oversight per loom per week. 20. Cost of stock. 21. Cost of labor in making yarn. 22. General expense per loom per week. Explanation of Items to be had in Office. 19. Oversight per loom per week. These are probable expenses in the weave room to pay for overseer, fixers, all day help other than weavers, and supplies. This is a fixed figure, estimated at so much per loom, based on previous reports, say for six months, and verified and corrected from time to time. The oversight varies] in different mills according to the time run, and efficiency of the help and management ; 42c. for fancy, and 31c. for plain looms will be consid- ered here for oversight. 20. Cost of stock. Against this is marked the prevailing price of raw material of the quality of cotton used. PRACTICAL COTTON CALCULATIONS 117 21. Cost of labor in making yarns. This is computed from production sheets, pay rolls and reports of the overseers of the various depart- ments from the picker to the spinning room, and is. stated at so much per pound. Items 20 and 21 may be shown together on a blank in the office, along with the counts of the yarns, as follows: BLANK NO. 2. Cost of Yarns per Pound. Stock ('or NTS. Quality. Pi: ice. Labor. Total. 4/32 A. 1J ins. 12c. 4.7c. 16.7c. 2/32 A. 1| ins. 12c. 4.9c. 16.9c. 50 's B. ljins. 14c. 6.2c. 20.2c. 60 's B. ljins. 14c. 7.35c. 21.35c The above blank only shows the items neces- sary for the cloth given here as an example. In the mill it would contain all the counts of yarn that they were making. Blank No. 2 takes in cost of spooling, slashing and warping, and represents the cost of the yarn delivered in the weave room. 22. General expense. This is an approxi- mate future expense estimated at a certain amount per loom per week, and is intended to cover all general expenses, beyond those already indicated, incurred before the cloth reaches the buyer. It includes costs for taxes, insurance, interest, salaries, supplies, sundries, engineers, yard help, watchmen, lighting, oil, power, office expenses, cloth room, etc., and varies in most 118 PRACTICAL COTTON CALCULATIONS mills. The general expense will here be as- sumed to be $1.80 per loom per week. With the data shown on blanks 1 and 2, and the price per week per loom for oversight and general expense known, the following method is adopted to arrive at the cost per yard and per pound of cloth. Rule 98 is first applied to find cost of yarns per cut, from items 16, 20 and 21. Example. 3.56 lbs. 4/32 at 16.7c. = .59452 2.56 lbs. 2/32 at 16.9c. = .43264 5.72 lbs. 50's at 20.2c. =1.15544 4.76 lbs. 60's at 21.35c. = 1.01626 16.60 lbs. total weight $3.19886 total cost per 100 yds. of yarns per 100 yds. of cloth This would be considered as $3.20. Rule 99 is next applied to find cost of yarns per yard of cloth. Example. $3.20 cost per cut . AO _ , . — — — ^— - = $.032 or 3.2c. cost of yarns 100 ^ ds - per yard of cloth. Rule 94 is next applied to find cost per yard for oversight. Example. 42c. oversight per loom per week ODn „ — = = .2896c. over- 145 yards per loom per week { M d PRACTICAL COTTON CALCULATIONS 119 Rule 95 is next applied to find cost . per yard for general expense. Example. $1.80 genl. expense per loom per week = 1.24c. 145 yards per loom per week g-eneral expense per yd. Although the cost per yard for oversight and general expense may be found in one problem by adding the amount per week for each to- gether and dividing by the number of yards per week, the above method is usually adopted so that either one may be referred to again if re- quired. It is now only necessary to add the various costs per yard together. Summary of Costs per Yard of Cloth. Weaving, 1.724c. Yarns, 3.2 Oversight, .2896 General expense, 1.24 6.4536c. cost per yard. The cost per pound of cloth may now be found by multiplying the cost per yard by the number of yards per pound. Example. 6.4536c. cost per yard X 6.02 yards per pound = 38.85c. cost per pound of cloth. 120 PRACTICAL COTTON CALCULATIONS In a cloth mill where the yarn is bought on warp beams and cops or bobbins, the counts and price per pound would be required instead of blank No. 2. If the yarn is bought in cone or skein form, the costs entailed during the various processes necessary before it reaches the loom must be considered. There is no extra cost entailed on filling yarn from the time it leaves the spinningpframe or mule to the time that it reaches the weaver, beyond the cost of handling it. Yarn intended for warp must undergo several processes before it can be made into cloth, the principal of which are spooling, twisting, if for ply yarns, warping, slashing and drawing-in. ^ ct •»o © "t-4 o *>■»* V) z v3 ^ Q Ho CO ^ ^ •*o 4^ •*o CO £> CO o pa cia ha c •»o CO °Q ^ •»o *3 So ft. tt ft* •»o « s « *> Q I 121 ) INDEX RULE NUMBER PAGE Average counts of cloth ... 53 Average counts of filling in cloth contain- ing 2 or more counts of filling - 41 50 Average counts of yarn in a set of warps containing different counts of yarn 20 36 Average counts of yarn in cloth, from ends in warp, pick, width in reed and yards per pound - - - - 42 51 Average counts of yarn in cloth from sley, pick, width and yards per pound - 43, 44 52 Average counts of yarn in cloth from sley, pick, counts of warp and filling - 45 53 Average counts of yarn in cloth with only one counts of warp in a cramped stripe - 54 Average counts of yarn in cloth containing more than one counts of warp - 46, 47 54 Average counts of yarn in cloth from per cent, warp, percent, filling, and counts of warp and filling - - - 48 56 Average counts of yarn from a small piece of cloth - - - - - 49, 50 57 Average pick when check pegs are used 53, 54 59 Average sley from ends in warp and width of cloth ----- 51 58 Average sley in an unequally reeded stripe, from sley and warp layout • - - 52 58 Beam yarn and warp calculations - - 31 Beam, counts of yarn on a, from length, weight and number of ends Beam, weight of yarn on a . Beam, ends on a, from counts, weight and length ----- Breaking weights of American yarns 6 31 7 32 9 35 95 123 Cable yarns - - - - Change gear to give a certain number of picks per inch - Check peg patterns, calculations for Check pegs to use per pattern Cloth analysis - Cloth calculations - Cloth contraction - Cloth, yards per pound of - Cloth, ounces per yard of - Cloth production - Contraction, percentage of, in length from warp to cloth - Constants or constant numbers Constant to use for loom take-up motion Cost calculations Cost of filling in a piece of cloth - Cost of a piece of cloth Cost of oversight per yard - Cost of stock per pound of cloth - Cost of weaving per yard - Cost of yarns per cut Cost of yarns per pound ... Cost of yarns per yard of cloth Cost of yarn in a warp Costs per yard of cloth, summary of Cotton yarn, table of counts and lengths of Counts of cloth, average Counts, length or weight of cotton yarn (formula "A") Counts, number of hanks or weight (formula "B") Counts, weight, length or ends on a beam (formula "C") RULE NUMBER PAGE 24 86,87 56, 57 )-71 72 58 85 101 94 97 92 98 99 100 101 60 61 71 51 62 77 78 99 64 8 101 105 109 109 106 107 105 107 117 108 108 119 33 58 30 31 35 RULE UMB ER 3 AGE 12 13 10 14, 29 3 14 14 30 20 20 124 Counts, comparing yarns for Counts, weighing short lengths of yarn for Counts, from length and weight - -1, Counts, from number of leas and weight Counts, from weight and number of hanks Counts, systems of numbering yarns of various materials for ... Counts, equivalent - Counts, equivalent, of cotton to a given counts of other materials - 21 Counts, equivalent, of raw silk (yards per ounce system), spun silk, worsted, woolen and linen to a given cotton counts ----- 4 20 Counts, equivalent of raw silk (denier and dram systems) to a given cotton counts ----- 23 Counts of twisted, or ply and cable yarns 24 Counts of single yarns equal to a ply yarn composed of 2 or more single yarns of unequal counts - - - - 5, 6 25 Counts of yarn to twist with a given yarn to produce a required ply yarn Counts of spun silk ply yarns Counts of yarn on a beam from length, weight and number of ends Counts of yarn in a set of warps - Counts of yarn, from the weight of a few inches ----- 29 41 Counts of warp or filling required to give a certain number of yards per pound 37 46 Counts of filling required, from sley, pick, warp and average counts - - 38 48 Counts of filling required, from sley, pick, width, warp and yards per pound - 39 49 Counts of filling required in a cloth con- taining 2 different counts of filling yarn ----- 7 26 28 16 31 20 36 40 49 INDEX. 125 Denier system of counts in raw silk com- pared to dram silk and IT. S. cotton counts systems - Dents per inch in reed to produce a given sley - Dents per inch in reed, table of Dents, number of, occupied by an equally reeded warp - Diameter of driving pulley Diameter of loom pulley Diameters of yarns - Dram system of counts in raw silk com- pared to denier silk and U. S. cotton counts systems Ends on a beam, from counts, weight and length ----- Ends, number of, in an equally reeded warp ----- Ends* number of, in an unequally reeded pattern, from sley, width and warp layout ----- Equivalent counts - - - - Equivalent counts in various systems, short methods to find - Expense per yard of cloth, general Expense per pound of cloth, general Filling calculations, warp and Filling calculations - Filling, weight of, per cut from per cent, of filling . . . . Filling, required per day, weight of Filling, hanks of, in a piece of cloth Filling, per cut, weight of - Filling, counts of, required to give a cer- tain number of yards per pound Filling, counts of, required from sley, pick, warp counts and average counts RULE NUMBER PAGE 23 60 67 68 64 71 89 103 90 103 80,81 92 23 19 35 21 36 25 38 20 20 95 106 96 106 41 43 30 41 31 42 32 43 34 44 37 46 38 48 126 INDEX. RULE NUMBER PAGE Filling, counts of, required from sley, pick, width, warp counts and yards per pound - - - * - 39 49 Filling, counts of, required in a cloth con- taining two different counts of rilling yarn ----- 40 49 Filling, average counts of, in a piece of cloth containing 2 or more counts of filling ----- 41 50 Filling, percentage of 73—77 82 Filling, cost of, in a piece of cloth - 101 109 Gear, change, to use to give a certain number of picks per inch - - 86, 87 101 Glossary of technical words and terms - 5 Ground picks per inch, from average pick, number of teeth used per pattern and picks per pattern - - - 55 60 Hank of roving, number of Hanks, from weight and counts - Hanks of warp yarn in a piece of cloth Hanks in a warp, from ends and length ■ Hanks of rilling, from pick, width in reed and length - - - - 32 43 Hanks of yarn, warp or rilling, in 100 yards of cloth, table of - - 80 Length for cotton, standard of - - 11 Length and weight standards - - 11 Length, weight or counts of cotton yarn (formula "A") - - - 30 Length, weight, counts or number of ends on a beam (formula "C") - - 35 Length and counts table - 33 Length, from counts and weight - - 11 29 Length of yarn on a beam, from weight, counts and number of ends - - 18 34 * 14 15 31 22 37 23 37 INDEX. 127 RULE NUMBER PAGE Length of yarn on a warp, from number of hanks and number of ends 24 38 Length of cloth that can be woven with a given counts and weight of filling - 33 43 Length of warp required for a given length of cloth in lenos, lappetts, etc. - 59 65 Loom calculations - 101 Metric system compared to U. S. cotton counts system - 20 Numbering cotton yarn, standard for - 16 Numbering yarns of various materials, systems of 20 Ounces per yard, from yards per pound - 65 74 Ounces per yard, from a small piece of cloth - - - 72 79 Oversight per yard, cost of - - 94 106 Patterns, number of, in an unequally reeded cloth - 26 39 Percentage of contraction in length from warp to cloth - 58 64 Percentage of warp or tilling in any cloth 73 82 Percentage of warp or filling in cloth, from ends, pick, warp, rilling and width ----- 74 84 Percentage of warp or filling in cloth, from sley, pick, warp and filling counts ----- 76 85 Percentage of warp or rilling in cloth, from weight of warp and weight of cut - - - 75 85 Percentage of warp or filling in cloth, from sley, pick, average counts and warp - - - - 77 86 Per cent, of production of a loom - - 82-84 99 Pick, average, when check pegs are used - 53, 54 59 128 Picks per inch, ground, from average pick, number of teeth used and picks per pattern ----- Ply and cable yarns, counts of twisted or, Ply yarns, counts of, composed of 2 or more single yarns of unequal counts Ply yarn, counts of a yarn to twist with a given yarn to produce a required Ply yarns, counts of spun silk Production tables, cloth ... Production of cloth per week Raw silk calculations Raw silk counts compared to cotton counts ----- Reed calculations - Reed to use for unequally reeded patterns Reed, width in, from sley and width of cloth ----- Reed, dents per inch in, for a given sley - Reed table ----- Reeling yarns Size, per cent, of, on warp yarns - - 27 40 Sley that would be woven with a reed of a given number of dents per inch - 61 69 Sley. average, from ends and width of cloth ----- 51 58 Sley, average, in an unequally reeded stripe from sley and warp layout - 52 58 Speed calculations - 102 Speed of shafting - - - 88 102 Speed of loom - - - - 91 104 Spun silk ply yarns, counts of - - 28 Square root of numbers 1 to 140 - - 90, 91 Square yards in a cut of cloth - - 78, 79 87 RULE NUMBER PAGE 55 60 24 5,6 25 7 26 28 97 98 82 99 22 23 65 62 69 63 70 60 67 73 14 INDEX. 129 RULE NUMBER PAGE Standards of lengths and weights for textile materials ... 11 Systems of filling out blank with weave room data for a piece of cloth - 111 Tables for counting cotton yarn, from weight in grains of 120 yards - - 16-20 Tables of cloth production - 97, 98 Table of dents per inch in reed to produce any even numbered sley from 48 to 132 68 Table of dents per fa inch (1 to 20) to weave cloths with from 48 to 112 sley ground ----- 73 Table of lengths and counts - - 8 Table of length and weight : - 8 Tables of hanks of yarn, warp or filling, in 100 yards of cloth - 80, 81 Table of yards of yarn per pound in counts from 1 to 250 - - - - 33 Take-up in length from warp to cloth - 58 64 Technical words and terms, glossary of - 5 Testing yarns for counts by comparison - 12 Testing yarns for strength - 93 Twisted or ply and cable yarns, counts of 24 Twists per inch in yarns ... 88 Twist tables - - 90, 91 Warp calculations, beam yarn and - 31 Warp, length of, from number of hanks and number of ends - - - 24 38 Warp and filling calculations - - 41 Warp required per day, weight of - 31 42 Warp, counts of, from sley, pick, filling and average counts - - - 38 48 Warp, length of, required for a given length of cloth in lenos, lappetts, etc. Warp, percentage of Weaving, cost of - 73-77 82 92, 1)3 105 9 27 12 29 13 30 30 31 35 28 '40 130 INDEX. RULE NUMBER PAGE Weight and length standards - - 11 Weight required of each count for a given weight of ply yarn 8 26 Weight required of each counts in a group of warps, from counts, number of ends of each and total weight - Weight, from counts and length - Weight, from counts and number of hanks Weight, counts or length of cotton yarn (formula "A") Weight, counts or number of hanks of yarn (formula "B") - Weight, length, counts or number of ends on a beam (formula "C") Weight of warp in ounces per yard of cloth Weight of warp per cut from per cent. warp ----- 30 41 Weight or number of yards per pound and ounces per yard - 74 Weight of yarn on a beam, from length, number of ends and counts - - 17 32 Weight of warp yarn on beams in the looms ----- 34 Weight of warp yarn in a piece of cloth - 17 32 Weight of each separate color of filling required for colored check fabrics - 35 44 Weight of each count or kind of filling required for embossed fabrics - - 36 45 Weight of filling required for stop peg checks ----- 44 Weight of fillin j required per cut - - 34 44 Weight or yards per pound - - 74 Width in reed, from sley and width of cloth ----- 03 70 Yards per pound of a cloth containing different counts of yarns or patterns that are unequally reeded - - 67, 68 75 131 Yards of cloth per pound, from ounces per yard Yards of cloth per pound, from sley, pick, width and average counts Yards of cloth per pound, from sley, pick, width, warp and filling counts Yards of cloth per pound from a small piece of cloth - Yarn, counts of, from any number of yards reeled or measured Yarn calculations - Yarn standard - - - Yarn, weight of, from counts and hanks Yarn, counts, length or weight of (formula "A") Yarn, length of, from counts and weight Yarn, weight of, from counts and length Yarn, counts of, from length and weight Yarn, counts of, from weight and hanks Yarn and warp calculations, beam Yarn on a beam, counts of Yarn on a beam, weight of Yarn on a beam, length of Yarn, counts of, from weight of a few inches - Yarns, cost of, per yard and per cut Yarns, cost of, in a warp - Yarns, diameters of - Yarns, reeling - Yarns, testing, for strength Yarns, testing, for counts by comparison Yarns, testing, for counts by weighing short lengths ... Yarns, twists per inch in - Yarns of various materials, systems of numbering - rule NUMBER 65 69 '0, 71 66 1,2. 13" 11 12 10 14 16 17 18 29 - 98, 99 - 100 PAGE 74 77 14 11 11 30 30 29 29 29 30 31 31 32 34 41 107 108 92 14 93 12 13 88 20 Howard & Bullough American Machine Company, Ltd. PAWTUCKET, R. I. COTTON MACHINERY * O Hopper Bale Openers, Feeders, Openers, Breaker, Intermediate and OEND for our Illustrated Finisher Lappers, Revolving Flat Cards, Drawing Frames, Slabbing, Intermediate and with list of Roving Frames, Users Improved Spinning Frames, New Model Twisters, Cone Winders, I Warpers, Slashers WE INVITE YOUR INVESTIGATION AND COMPARISON SACO & PETTEE MACHINE SHOPS Main Office NEWTON UPPER FALLS, MASS., U. S. A. Cotton Machinery Revolving Flat Cards, Railway Heads, Drawing Frames, Stubbing, Interme- diate and Roving Frames, Spinning Frames, Spoolers and Reels Works BIDDEFORD, ME. NEWTON UPPER FALLS, MASS. Southern Agent A. H. WASHBURN, CHARLOTTE, N. C. { L33 I WEBSTER'S INTERNATIONAL DICTIONARY A LIBRARY IN ONE ROOK. Besides an accurate, practical, and scholarly- vocabulary of English, with 25,000 NEW WORDS, the International contains a History of the English Language, Guide to Pronunciation, Dictionary of Fiction, New Gazetteer, New Bio- graphical Dictionary, Vocabulary of Scripture, Greek and Latin Names, English Christian Names, Foreign Quotations, Abbreviations, Etc. 2.380 PAGES. 5000 ILLUSTRATIONS. SHOULD YOU NOT OAVN SUCH A ROOK? WEBSTER'S COLLEGIATE DICTIONARY. Largest of our abridgments. Regular and Thin Paper Editions. 1110 PAGES AND llilO ILLUSTRATIONS. Write for "The Story oflTBook"— Free. G. & C. MERRIAM CO., Springfield, Mass. Jacquard Card Machinery THE ROYLE LINE INCLUDES— PIANO MACHINES for cutting the card ; AUTOMATIC LACERS for lacing them in packs ; and REPEATERS for duplicating sets. These machines are widely used for the economical preparation of the Jacquard card for the loom. Write for catalogue. JOHN ROYLE & SONS PATERSON, N. J. ( 135 i IJYY/E manufacture improved cotton machinery at Hopedale, Mass." DRAPER COMPANY FRANK C. LITCHFIELD, Pres. GEO. M. CHENEY, Treas. H. L. LITCHFIELD, Clerk Established 1843 Litchfield Shuttle Co. SOUTHBRIDGE, MASS. Manufacturers of SHUTTLES Shuttle Spindles Shuttle Springs Shuttle Eyes Thompson Eyes Leveling Screws Shuttle Tips Shuttle Catches Spiral Springs The Cheney Tube Holder The Truesdell Spring AND ALL KINDS OF SHUTTLE FITTINGS The Whitin Machine Works WHITINSVILLE, MASS. Builders of Cotton Machinery Cards Railway Heads Combing Machinery Drawing Frames Spinning Frames Spoolers Twisters Reels Long Chain Quillers Looms STUART W. CRAMER, Southern Agent Trust Building, CHARLOTTE, N. C. Equitable Building, ATLANTA, GA. ( 138 ) American Wool and Cotton Reporter The Leading Textile Weekly of the United States We challenge contradiction of our statement that the WOOL AND COTTON REPORTER has a larger bona fide circulation among cotton, woolen, worsted, hosiery and carpet mills than any other paper in the United States. The REPORTER is the only paper in the United States devoted to all the materials, processes and products of textile manufacture, from the farm and the field, through the loom and the cloth perch to the counter of the merchant, and the back of the con- sumer. It has imitators in some departments, but is practically without competition in its scope and cir- culation. Our mailing list is always open to the inspection of our customers, and all other information will be fur- nished upon addressing us at either of our offices. 530 Atlantic Avenue, Boston 757 Broadway and 31 Nassau Street, New York 308 Chestnut Street, Philadelphia 930 Monadnock Block, Chicago 208 Corcoran Building, Washington, D. C. Agents and correspondents in every section of the United States and in every country of the world. I should be pleased to supply you with any textile books you may require, at publishers' prices, or to ad- vise you where the same may be obtained. Discounts allowed on price of Practical Cotton Calculations when ordered in quantities of six or more. Ernest JVhitworth, Southbridge, Mass. MEMORANDA. MEMORANDA MEMORANDA. MEMORANDA. HAY 24 190T