S 1577 IN7 topy 1 Class XS_L2XT Book ■\\'^ Coppght]^" COPXRIGIIT DEPOSIT. COTTON SPINNERS con PAN ION PUBLISHED BY I. C. NOBLE NEW BEDFORD, MASSACHUSETTS, TJ. S. A. -^^^,',1 NEW BEDFORD THE A.E.COFFIN PRESS 'CI.A25J08 1^1??^ A The writer has often seen difficulties experienced in not having a small vest- pocket book handy for reference on Textile Machinery Calculations. In this book he has tried to fill this requirement, and at the same time to make the contents as simple and concise as possible, so that any person having charge of the machines can follow him in his explanation when he names the pulleys, gears and rolls. I am, Yours truly, I. C. NOBLE. I. C. NOBLE ALL KINDS OF New TextSe Machinery Erected. Old Machines Moved and Overhauled. Mules a specialty. 1649 Acushnet Ave. New Bedford, Mass. INDEX. PAGK Cotton 7 . Cotton (suitable for yarns) 11 Cotton Grading 12 Cotton Sampling 13 Cotton Mixing 14 Boilers 15 Steain Engine . . 17 Belting 20 Receipts for Machine Shop 23 Arithmetic 26 Table of Square Roots 42 Hopper Bale Breaker 44 Automatic Feeder 44 Opener 45 Breaker Lapper 46 Finisher Lapper 47 Carding 49 Sliver Lap Machine 51 Ribbon Lap Machine 51 Comber 51 53 Drawing Frame 54 Fly Frames 57 Wrapping Plivers, Roving and Yarn. 65 Setting Rolls 66 Self-Acting Mule 70 " (Hetherington's)... 78 " (Asa Lees) 82 " (Dobson & Barlow) 92 Turns of Spindle to one of rim 96 Ring Spinning Frame 98 Horse Power required 101 Howard and Bullough AMERICAN MACHINE CO., LD. PAWTUCKET, R. I. Builders of Bale Breakers, Feeders, Openers, Lattices, Brealier tappers, Interme- diaie and Finisher tappers^ Revolving FlatCards, Draw- ing Frames, Slubber, Inter and Roving Frames, Spin= ning Frames, Twisters and Cone Winders, COTTON. Cotton is grown in the United States of America, Egypt, China, Corea and South America. The cotton crop of the United States of America is larger than the wliole of the other crops combined. American varieties are classed in four qualities — good ordinary, low middling, middling and good middling. South American are classed in three^ middling fair, fair, and good fair. Egyptian, two — fair and good fair. East Indian, three — fair, good fair, and good. The names of the commonly used cot- tons are Sea Island, Egyptian, American. Brazilian, and Indian. There are several other varieties grown, but not generally used as the ones named. The Sea Island cotton is grown on islands off the coast of South Carolina and Georgia, namely, St. Helena, Port Royal, Edisto, John and James Islands, St. Simon and Cumberland Islands. It is also grown in the State of Florida from Sea Island seed. This cotton is the most valuable cotton grown on account of its length of staple, fineness, strength, smoothness, and clean- liness, also for the careful ginning it receives. The fibre is fine, soft, silky, long, and regular. The American varietv of Sea Island cotton is the best. The Fiji and Tahiti varieties of this cotton are uncertain in their staple. Lace and thread are made mostly from this cotton. The length of staple is from l^i to 2^4 inches. Egyptian cotton is next to Sea Island for the making of fine yarns. It is silky, strong, and tough. The brown Egyptian is generally soft, whilst the white Egyptian is hard and harsh. Gallini is the best of Egyptian cottons and is grown from Sea Island seed. The staple of Egyptian cottons ranges from 1% to 11/^ inches. American cotton is the staple cotton of the world. The vast territory covered by the culti- vation of this cotton gives us a number of varieties and grades; but we can divide them into four classes: Orleans, Texas, Upland, and Mobile. Orleans or Gulf cotton is the best of American cottons. It is grown on the banks of the Mississippi river and is known as Benders, Peelers, and Allan- seed. Peelers is a good cotton, regular in strength and staple, and is very soft and pliable. It mixes well with soft Egyptian. The length of the Gulf cotton staple is from 1 to iy2 inches. Mobile and Upland cotton is soft and clean, but rather short staple. Texas cotton is firmer in staple than the INTobile and Upland, but contains more leaf, and is not so bright in appearance. It is a cotton that will make 32s warp or filling. The staple is about an inch in length. Brazilian cotton has many varieties, as well as qualities, some being harsh, whilst otliers are soft. ir'eruvian mixes well with wool (the harsh or rough Peruvian), but the softer Peruvian, on account of its color, enables it to mix well with Orleans or Gulf cotton. Its staple Is a little longer than Ameri- can generally. It is from 1% to li/^. Indian cotton is generally dirty, some of it being low in character, and containing a large quantity of round and fiat fibres, and the fibres are not so uniformly twisted as in American cotton. The better classes, such as Hingunghat, can be mixed with American. The length of staple is % of an inch to 1^4 inches. China cotton is a short stapled cotton, rather harsh, but very white. It is used in China and Russia. Cotton is generally planted in April and picked in September or October. The average yield of lint cotton in India is about 75 lbs. per acre. American cotton Avlien picked and be- fore being ginned contains two -thirds its weight of seeds. So, if a man takes newly picked cotton to be ginned, and he has 1000 lbs., he receives 1000x2=2000, 2000-^3=666 2-3 lbs. of seed, and the re- mainder 333 1-3 lbs. cotton fibre. biobc ^■ ^- '-■^' C C cc cc yii cd !/3 '^'B ^ u u u > CCtpl^O o o o t, tH Gftft a 3 O ^ J-' ^5 f^ ^ ^ _ CC CC 03 CS > M w m m ^ .ooo la C:.P.>q^3(M.^ 'S P 13 O O O O (« OO a i^ft ft SSPPPP -< —4 ^H StSES ■ uu u . o o o g &&&ft ftftftft d c6 ce ^ Si U U Si dddd m m" m' . « » « « O OO w W W W M i^o coo oooo „^,--t- iaiTJi^ia o o o o CO O O ^-^■^-^ o,m 01 p. ft ftftft Pggp PPtJp ;^ J^^#^ 1— 1 1— 1 rH T-i lH o;^;5^#;^ o o_o o ;5^ :: ■ :o : ' § ^ S a • " ' 2 .-ft c6 gyptia allini bbasi rown Brazi era . ernam ariba aranh H0< m^ ' OO^CM^ 60 ^^ a SI >— 1 t— *■ F— *■ C "S ^^ ^ &| § da I ts rT W) tc c . in m &.Sg? > oo $sss o o M 02 a c I p-a PD ;^ ;^ s ;^. T-ll-l T- ■■-I BB^S ^o S^ ^ ? ^^ IH c • d C 5 p>.^ i ^^ > J .S S-, ;3 H W > (iiu i} -^ M SfLn a; 3 S-^ tr c t)§ h 02 w to m eg eg eg ca aaaa 02 02 02 02 02 522£2^| 32 J^: COTTON GRADING. There are twenty-six different grades, namely: Fair Barely Fair Strict Middling Fair Fully Middling Fair Middling Fair Barely Middling Fair Strict Good Middling Fully Good Middling Good Middling Barely Good Middling Strict Middling Fully Middling Middling Barely Middling Strict Low Middling Fully Low Middling Low Middling Barely Low Middling Strict Good Ordinary Fully Good Ordinarj^ Good Ordinary Barely Good Ordinary Strict Ordinary Ordinary Low Ordinary Inferior The Full Grades are Fair, Middling Fair, Good Middling, Middling, Good Ordinary, Ordinary. The Half Grades are termed "Strict." The Quarter Grades are termed "Bare- ly," coming between the half grade and the above full grade. The term "Fully" means between the half grade and the next full grade below it. The qualities to observe in sampling or grading cotton are: Length of Staple. 12 Regularity of length and diameter of staple. Fineness. Strength, Smoothness, Color, and Cleanliness; also see that the fibre has not been cut when ginning. The cotton becomes full of sand during wind storms; see that it is as free from sand as possible. COTTON SAMPLING. Take 100 lbs. of cotton, shake it well and the sand will drop out; weigh the sand and you -then get the percentage of loss through this source. During heavy rains it becomes stained with the earth. See that it is not stained, especially if you are going to spin filling; but if you are going to size the yarn, you do not require to be so particular, as there can be bought a cotton a little cheaper, of good staple, but stained a little, which can be covered by sizing. See that there is not too much leaf in the cotton, and that it is not dirty. Look out for dampness; it always con- tains a certain amount, absorbed from the atmosphere (about 89c). On one thing always be very particular. Always deal with reliable cotton brokers. Look at the brightness of your cotton or "bloom," as it is called. Bagging and Ties m.ust not exceed 22 lbs. per bale. The average allowance for loss of weight on any one mark of cotton shall not exceed three pounds per bale, with cotton in sound and dry condition. Cotton is valued according to its char- acteristics that best adapt it to the use for which it is intended. 13 COTTON MIXING. In mixing cottons be careful that you get equal length of staples. Do not mix a harsh and silky cotton together, except for special purposes. If you wish to imitate wool get rough Peru- vian. Always mix as large mixing as possible, as it keeps the drafts on your machines equal and saves time in the setting and resetting of rolls. Pay attention to the mixings, and picker room generally, as there lies a part of your foundation for an even yarn. The shorter stapled Sea Island mix well with Best Egyptian for 80s to 120s yarns. Peeler and Soft Egyptian also mix well to spin from 60s to 80s yarn. Gulf, Texas, and Soft Peruvian mix well for yarns of 40s to 60s. Rough Egyptian and Rough Peruvian incorporate well, and are suitable for spinning yarns from 40s to 50s. The better class of Indian cotton (Hingunghat) is mixed with the lower classes of American cotton — Georgia or Boweds. Mix also with Oomrawuttee, Broach, and others. If a mixing of bales — say, 24 bales has to be mixed — divide them as much as possible at the feeder. Say we have 8.X.Y.Z., 8.G.H.I. and 8.A.B.C. Spread one X.Y.Z. on a large floor space. On the top of this throw one G.H.I. Over the top of these spread one A.B.C. and keep repeating this until the 24 bales are finished. The mixings given here are only a few of the many different mixings made in our mills. 14 BOILERS. Rule for Calculating Strength of Cylinders and Boilers. The tenacity of the metal of which a boiler is constructed is about 60,000 lbs., or six- sevenths of that of good wrought iron, a bar one inch square being the standard. As the cylinder which constitutes the boiler is not whole, or in one piece welded together, but -is composed of a number of plates riveted together, the plates being cut away for the holes, it is necessary to diminish the number, which expresses the strength; therefore let the tenacity be put at 30,000 lbs. This boiler is 7 feet 6 inches diameter. Thickness of plates % of an inch. Multiply the numerator of the thickness by the tenacity of the metal, and multi- ply the denominator by half the diameter of the cylinder in inches, then divide the numerator by the denominator and the answer will be the strength, or bursting pressure. Example. The denominator of %: Dia. 7 ft. 6 in. 4-2=45 ins. 45 X 8=360 30000 tenacity of metal. 3 numerator of % plate. 360)90000(250 bursting pressure. 720 1800 1800 Then we get 250 lbs. bursting pressure. This is if the iron is good and all things in proportion. 15 INCRUSTATION OF BOILERS. 1. Potatoes, one-fiftieth of weight of water prevents adherence of scale. 2. Twelve parts salt, 2% caustic soda, % extract of oak bark, % of potash. 3. Pieces of oak-wood suspended in boilers, and renewed monthly prevents deposit. 4. Two ounces of mtiriate of ammonia in a boiler twice a week prevents incrus-- tation and decomposes scale. ^ 5. Molasses fed into a boiler prevents ' incrustation. 6. Carbonate of soda. 7. Chloride of tin. 8. Spent tanners bark. 9. Frequent blowing off. 10. Mahogany or oak sawdust in lim- ited quantities. The tannic acid attacks the iron, so this should be used with caution. BOILERS. Fuel — Average Evaporative Power. One pound of coke evaporates 9 lbs. off water. One pound of coal evaporates 9 lbs. off water. One pound of oak (dry) evaporates iVz •. lbs. of water. One pound of slack evaporates 4 lbs. of' water. (Feed water supplied at 212° for above.) Coal loses about one-third in coking (of its weight), but increases in bulk one- tenth. 1 STEAM ENGINES. ■ Horse power in engines is calculated as the power which would raise 33,000 lbs. a foot high in a minute, or 90 lbs. at the rate of four miles an hour. Always keep the cylinder hot and dry. Look to the mode of fitting the steam- pipes. A nominal horse power of an engine, as was mentioned before, is to move 33,000 lbs. one foot high per minute, or say 150 lbs. raised 220 feet per minute, which means the same thing, for if we multiply 150 by 220 it equals 33,000. For one horse power, multiply 220 by 22 circular inches. This gives 4840. Then multiply by the pressure 7 lbs. We get 33,880, and divide by 33,000 lbs., and the result is one horse power. Example: 220 440 440 4840 33000)33880(1 horse power. 33000 880 . Desaguliers figures that a horse walks 2% miles an hour against a resistance of 200 lbs; this is at the rate of 220 feet per minute. A horse power is therefore eoual to a force that will raise 44,000 lbs. one 'oot per minute when working eight hours 3er day. Mr. Watts found that a horse treading 17 a mill path at the rate of 2% miles an hour raised 150 lbs. by a cord hanging over a pulley, which is equivalent to raising 33,000 lbs. one foot high a minute. His steam engines were calculated to work at 44,000 lbs. per horse power, but he allowed 33,000 lbs. in his calculations, considering the difference due to friction. How Horse Power is Calculated. 1760 yards one mile, a horse walking 2% miles per hour against a force of 150 lbs. working 8 hours per day. Work this out, and we find it is equal to raising 33,000 lbs. one foot per minute. Example; 1760 yds. in a mile. 2.5 miles per hr. 8S00 3520 44000 3 ft. in a yard 132000 150 Hd. resistanc* 6600000 132000 Mins. in hour=:60)1980000.0(33000=l h. p. 180 180 180 18 1 I Horse Power of an Engine. Muiciply area of piston in square inches by mean effective pressure of the steam on the piston per square inch, and mul- tiply these by velocity of piston per min- ute, and divide by 33,000. Example: 45 dia. of piston. 45 225 180 2025 sq. in. in piston. 360 speed of piston. 121500 6075 729000 20 avg. pres. piston. ivide by 33000)14580000(441 h. power. 132000 138000 132000 60000 33000 How to Find a Pipe to Supply a 36-Inch Cylinder. Multiply the diameter of cylinder by .96; this will give area, from which you find diameter. 19 Example: 36 216 324 Decimal area .7854)345600(44 sq. inches. 31416 31440 31416 Find square-root of 44. 6)44(6.63 Answer. 36 126)800(6 756 1323)4400(3 3969 6.63 inch pipe required. BELTING. To Find Speed of Belt Per Minute. Rule: — Multiply circumference of thi pulley on which belt is running by th« revolutions of the shaft. Suppose your pulley is 24 inches or feet, and revolutions of shafting are 20( per minute. Proceed as follows: 2X3.1416X200=1356 feet per minute. 20 To Find Horse Power a Single Beit Will Carry from One Pulley to Another. Rule:— Multiply the width of the belt reduced to inches by 45 and by the feet the belt travels per minute, and divide the quotient by 33,000. Suppose a single belt travels 1356 feet per minute and the belt is 1 foot and 4 inches wide (equal to 16 inches). Example: 16X45X1356=976320 33000 = 33000 976320 divided by 33000=29.58 horse power To Find the Horse Power of a Double Belt. Rule: — Proceed exactly as you did in finding single belt, only multiply by 75 instead of 45. Example: 16X75X1356=1627200 33000 = 33000 1627200-^33000=49.3. To Find a Single Belt Required to Give a Certain Horse Power. Suppose you require 30 horse power and the belt will run 2000 feet per minute. Rule: — Multiply the 30 horse power re- quired by 33,000. Take this for the divi- dend. Then multiply the number of feet the belt travels per minute, 2000 by 45. Example: 30X33000=990000 2000X45 = 90000 990000 divided by 90000=11 inch single belt required. 21 To Find Double Belt Required to Give a Certain Horse Power. Rule: — Proceed exactly as when finding single belt, but use 75 instead of 45. Example: 30X33000=990000 2000X75=150000 990000^150000=6.6 inch double belt re- quired. In testing the horse power required to run the shafting alone, and then to run the whole load of the mill, I would say that a fair percentage is 25 per cent., or say a mill requires a hundred horse power to run the shafting and belts alone, it should not require more than 400 horse power to drive the whole mill load. If it does, look to your belts; a tight belt makes hot bearings, requires more power to drive, and runs the machine no quicker. A large quantity of coal can be saved by having the belts at a right tension. Tight belts ruin the bearings, cost more to run, and do not increase production. I RECIPES FOR MACHINE SHOP. 1. Mixture for welding steel is: One salammoniac and ten parts borax. Pound these together and fuse until clear; pour out, and when cool reduce to a powder. 2. Tempering Turning Tools. When the rature of the steel is un- known, it is a good plan to heat the tool and try with a file at the different shades of color, and when the file is felt to bite the least bit, quench the tool. This should be done by daylight, as pale straw color is difficult to see in artificial light. 3. Tempering Steel Springs. Wet the spring (hardened) with olive oil, turn it gently round on the fire till it catches a light. If it is a very par- ticular job, take a pan and boil in oil. 4. Hardening Tools. Heat the tool to a blood-red heat and plunge it into common oil, and it will be all right for turning purposes. 5. Solder for Brass. One-half lead and half tin, with a little resin. This solder will adhere to iron, but first rub the iron on a piece of tin. 6. Solder for Lead. Melt one part of block tin, and when fusing add two parts of lead. Use resin with this solder. -23 7. For Brazing Iron. Good brass and a little borax. 8. Uniting IVIetals. For uniting wrought and cast iron, or Fteel. Take 20 parts (by weight) of, wrought iron fillings. 10 of salammoniac, rr.d 5 of balsam of copaiba, melt together and beat until dry and hard. This will join metals and fill in holes, cracks, or other defects, in iron or steel plates. 9. Welding Cast Steel. One ounce powdered glass, one ounce salammoniac, and 16 narts borax. For mild steel, borax may be used alone 10. Cement. A strong glue is made by adding pow- dered chalk to common glue when melted and a srlue to resist warmth may be made by boiling one pound of common glue in two quarts of skimmed milk. 11. A Good Wheel-Grease, Twenty- five lbs. of tallow, 25 lbs. of tar, 15 lbs. of soda, and ZVz gallons of water Boil water and soda, th'^n add tallow and 12. Black Varnish. One pint of vitriol and two gallons o: gas tar. Apply after effervescence has nearly finished. 13. Lubricating Mixture. Sixteen ounces of good lard, 2 ounce; of bee's wax, 8 ounces of flour of sulphur, 4 ounces of black lead, 16 ounces of white soap. 24 I 14. To Keep Shafting Cool. Mix white lead and oil to the consist- ency of cream. 15. Dubbing. Two lbs. of black resin, 1 lb. of tallow, and 1 gallon of train oil. 16. Lacquering Brass. Boil the brass in a solution of potash and soda, after which dip them in aqua- fortis, 3 parts water. Wash them in 2 waters and rub in sawdust. Place on a gas stove; when warm brush them, then apply laccfuer. Put the work on the stove with brown paper over it. 17. Case Hardening. Place horn, hoof, bone dust, or shreds of leather, together with the article to be case hardened, in an iron box, heat to blood red, then dip article in cold water. Some engineers add white wine vine- gar and salt. 18. Case Hardening With Prussiate of Potash. Polish the article, then heat to a bright red; rub the surface over with prussiate of potash, and when a dull red, dip in water. 19. Case Hardening iVIixtures. Two of prussiate of potash to one of salammoniac mixed. Or 2 of salammoniac. 2 of bone dust and 1 of prussiate of potash. 20. Cold Soldering Without Fire. Bismuth 14 ounce, quicksilver 14 ounce, 25 block tin filings 1 ounce. Spirits of salt 1 ounce. Mixed together. 21. Cold Brazing Without Fire or Lamp. Floric acid % ounce, oxymuriatic acid % ounce, mix in lead bottle, put a chalk mark at each side you want to braze. This mixture will keep about six months in a lead bottle. ARITHMETIC. Before dealing with the drafts and twists in the machines, a few examples in arithmetic will help us. The signs used in calculation are: — ■ + meaning, add. = means equal to. — signifies subtraction. X means multiplied by. -=- meaning divided by. V signifies that the square root of the numter to which it is prefixed is required, V signifies that the cube root is re- quired. ' means feet. " meaning inches. Examples: If we write 20 + 4=24, vre mean 20 add 4 equals 24. Then 20 — 4=:=16 is 20 subtract 4 equal 16. 20x4=80. This meaning 20 multipliec by 4 equals 80. 2')-=-4=:5 signifies 20 divided by equals 5. >/16=4 meaning square of 16 equals 4. ^'27=3 signifies that cube root is re- quired 27 equals 3. 26 ad I Multiply 3 by 3 equals 9, which is square. Multiply 9 again by 3 and you have cube 9X3=27. 7'-6" means 7 feet 6 inches. CANCELLATION. If this is used when taking pulleys or gears as driver or driven and cancelled it makes what would be a very long sum short. If an 18 inch pulley was driving a 9 inch pulley, and on the same shaft with the 9 inch pulley was a 10 inch pulley, driving a 5 inch pulley, now w^e should place them thus: 18X10 meaning 18 multiplied by 10. 9X5 and 9 multiplied by 5. (Note the drivers are on the top or above the line, and the driven under.) Then we get 18X10=180 180^45=4 9X 5= 45 by multiplying 18 and 10 we get 180, and the 9 by 5 we get 45. Then divide the 180 by 45 and we find 4 revolutions. Thus meaning that if we turned the IS inch pulley round once, the 5 inch pulley would revolve 4 times, if there was no slippage. But this is not calculation. 27 What I was leading up to was this: If we were to cancel these figures it would make a very short sum, thus 2 2 1^ X ,10 = 4 Ans. p X .5 As you cancel one number in anothe draw a line through them. The 9 goes twice into 18, and the 5 goes twice info 10, so that you have only a 2 over the 18, and a 2 over the 10, and when mul- tiplying these you have: — Twice 2 are 4, which is the answer Never cancel one number in the bottom line figures with another number in th( bottom line. Always find a number h the bottom line that will cancel with on( in the top line, and vice-versa. Example: 7 3 6 1 /7p X U X ^4 x p^ I 10 X 1^ X 14 X P Now 10 will go into 70 seven times. 15 will go into 45 three times. 14 will go into 84 six times. 8 will go into 96 twelve times. Multiply the 7, the 3, the 6, and the 1 and the answer is 7X3X6Xl2=il512 Ans. Another example: 1 ] ? 2 ^0 X 1^ ^ X U ^ '^ 1 1 /7 = 1 — = 1 An i X^ The 18 goes into the 36 twice. The 7 into 14 twice. The 6 into 12 twice. Then the two twos above the line and the two twos below the line cancel, thus leaving 1 for a divisor and 1 for a dividend. Ore in one is one, so one is the answer. If you did not use cancellation here, you would have to multiply the 36, 12 and 7 together, and then multiply the 6, 14 and 18 together, and divide one by the other. Never cancel a decimal and whole number. PROPORTION. Is the equality of two ratios. : :: : signifies proportion, as 2 : 4 :: 8 : 16. This meaning, as twice two are four, twice eight are sixteen. It can be writ- ten 2 is to 4 as 8 is to 16. When you see that your answer must be larger, multiply the two larger num- bers together and divide by the smallest number, but if the answer is to be smaller, multiply the largest and smallest number together and divide by the inter- mediate number. For example: 20 cards produce 3000 lbs. per day, what weight will 50 produce? We know 50 cards will produce more than 30 similar cards, so our answer will be greater. Then multiply the two larger numbers together and divide by the smallest. 50x3000=15000 and 15000^ 20= 7500 lbs. Answer. PERCENTAGE. This is very useful in mill business. The term per means by, or on the, and centum means a hundred. So Per- centage means on the hundred. Thus 6 per cent, means 6 of every hundred. Instead of writing per cent., the symbol is used %, or it may be placed by a fraction, as 6/100, or as a decimal, thus, .06. Example: A man has 60 ring frames, but they are only 20 per cent, of what he will have when the mill is fully furnished. How many will he have? Per cent. 20)60 percentage running. 100 300 Divide the percentage of the frames Tunning by the rate per cent., multiply by a hundred. 60 is the percentage of frames running and 20 per cent, of the whole number. When we say he has 20% of the whole running, we mean 20 of every 100, so he has 300, or 3 times 20=60, which proves the 303 to be correct. Instead of multiplying by the 100, add two ciphers. 60 H- 20=3 add 2 ciphers 300 When the principle and the rate per cent, are given, it is simple to find the interest. 30 A man borrows $500 at 7 per cent, per annum. What must he pay yearly? 500X7=3500 and 3500^100=35 dollars yearly. The better plan is to cross off the two last ciphers instead of dividing by the 100. Thus:— 500X7=35. A bale of cotton weighs 500 lbs., and after it has gone through the card- room processes, the roving made from it weighs 400 lbs. What percentage went to waste? 500 — 400=100 lbs. waste 100X100=10,000 and 10,000-f-500=20%. So we see that 20 per cent, went to waste. FRACTIONS. A Common Fraction is one in which the unit is divided into any number of equal parts. The Denominator is the number of equal parts into which the unit is divided. The Numerator tells us how many equal parts are taken. When we write 2/3, ask how many thirds? Why two, so it tells us how many of the figure under the line are taken. Take % for instance: — the 4 shows how many parts the unit is divided into, and we are taking 3, when we say %. An improper fraction is when the numerator, or the figures above the line are greater than the denominator or the figures below the line, 7/5, 9/4, 6/5. These are all improper fractions. 31 To reduce urits or mixed numbers to improper fractions. How manj^ thirds are there in 7 2/3? Multiply the 7 by the 3 and add the 2.7x3=21+2=23/3. To prove this divide the 23 by 3 and we get 7 with 2 over, which are thirds. To reduce improper fractions to mixed numbers. How many units are there in 28/4? Divide the 28 by 4, which equals 7 Addition of Fractions. How many eights are there in i^ and %? % is equal to 4/8, and % is equal to 6/8. 4/8 and 6/8 added equals 10/8, which is an improper fraction, 10/8-^8/8=1 2/8, and the 2/8 when cancelled equals a 1/4, so our answer is 1 1/4. Add 4/7 and 3/4 and 11/14. Rule: — Reduce the fractions to a com- mon denominator, add the numerators, and let the denominator or figures under the line remain as they are. Example: 4 3 11 — +— +— 7 4 14 You take the 4/7 and multiply both these figures by the denominators, or figures under the line, of the other two fracti-ins, this meaning by the 4 and the 14. 32 Do the same with tlie %, multiply the 3 and the 4 by the other two denomina- tors, the 7 and the 14. Now take the 11/14 and multiply these by 7 and 4, the denominators of 4/7 and 3/4. Take the denominators of the 4/7 and, 3/4 and 11/14. Multiply these, the 7, the 4 and the 14, which equals 392, and this is the least common denominator. 4X 4Xl4=r224 7X 4xl4=r392 3X 7X14=294 4X 7X14=392 11 X 7X 4—308 14X 7X 4=392 Now thej' all have a common denomi- nator, or, in other words, the three figures under the line are the same, and it now becomes a simple addition sum, by adding the numerators, which are 224 nd 294 and the 308, but we keep the de- nominator just the same. 224+294+308=826 or 826/392. 826/392 is an improper fraction, so we must divide 826 by 392. 392)826(2 42/392 784 42 The answer being 2 42/392, but the 42/392 can be cancelled by dividing the enumerator and denominator bv 14: we :et 3/28, making the answer 2 3/28. Subtraction of Fractions. Subtract 15/28 from 31/35. Now to do this we must have the frac- tions similar, so they must be reduced to a common denominator, or, in other words, the figures under the lines must be the same. To do this multiply the first fraction 15/28 by the denominator of the other fraction. 15X35=525 28X35=980 Follow this by multiplying the two numbers of the other fraction. Those are the 31 and 35 by the denominator of the first fraction; this is 28. 7 31 X 28 = 858 525 U^ = 7 35 X 28 = 980 980 ^^^ 20 20 Now both denominators are similar, and it becomes a simple subtraction sum. Subtract 525 from 868=343. Let the denominator remain as it was, then we have 343/980, and finding 49 will divide into the numerator and denomina- tor, thus bringing our answer H% 20 34 Multiplication of Fractions. Multiply 11/12 by 9. Multiply the 11 by 9, which equals 99. Let the denominator remain as it was and we get 99/12, which is an improper fraction, so divide the 99 by 12, which gives us 8 3/12, or, when cancelled, for the 3 will divide into 12 four times, we get the answer 8 14. Multiply 35/54 by 36/49. 5 2 r^ X n 10 — — = = — Answer. H X ^^ 21 3 7 By cancelling the 35 and 49, or, in other words, dividing each by 7, we get 5 and 7 instead of 35 and 49, and by dividing 36 and 54 by 18 we get 2 and 3. Multiply the 5 by the 2, we have 10 above the line; then multiply the 7 and 3, which equals 21, and our answer is 10/21. Division of Fractions. Divide 96/115 by 6. Divide the numeral anominator remains 96^6=16. 16/115. Answer. Divide the numerator 96 by 6 and the denominator remains the same. Divide 32/49 by 4/7. Multiply the dividend by the divisoi inverted. Or, in other v^^ords, place the 7 where the 4 is, and 4 where the 7 is, and mul- tiply. • 3^ X / 8 1 — — = — = 1 — Answer, ^^ X ^ 7 7 7 4 goes into 32 eight times. 7 goes into 49 seven times. "We get 8/7, which is an improper frac- tion; divide the 8 by the 7 and we get 1 1/7 for our answer. FRACTIONS (Complex). These are fractions that have theii numerators or denominators, or both, fractional. Example : 15 — 4 19 ;^ X J^ 4 1 45 ;^ X ^^ 3 3 3 76 Rule: — Invert the denominator and di- vide by the numerator. This is similar to dividing one fractioi by another. DECIMALS. A Decimal Fraction is a number of tenths, hundredths, thousandths, etc. A Decimal Fraction is shown by plac- ing a dot, or a point, before the numera- tor, and not expressing the denominator. If we were to write 1.5 in decimal frac- tions, we would express it in fractions as 1 5/10, or, when the 5/10 are cancelled, it is iy2. That is expressing a decimal fraction in tenths. When it is written 1.05 it means hundredths, as 1 5/100, and so on, as in thousandths 1.005=1 5/1000. The symbol of a decimal is termed decimal point. .25 = 1 4 To Reduce a Common Fraction to a Decimal. Reduce % to a decimal. Add ciphers to the numerator 3 and divide by the denominator. 3,00-^4=.75 Answer. It is exactly like saying $1 — 75 cents, meaning one whole dollar and 75 hun- dredths of another dollar, or %. In adding decimals write the numbers so that the decimal points come under each other: as, 24.33 + 146.33 + 63.175. White thus: 24.33 146.33 63.175 233.835 Answer. This written as a fraction, 233 835/1000 Subtraction of decimals is similar tc addition in keeping the points under eaci other. Subtract 123.25 from 212.758. 212.758 123.250 89.508 Multiplication of Decimals. ■ Suppose we multiply with the last two figures decimals, and the last two figures in the multiplicand decimals, then there are 4 decimals in the answer or product. Example: 4.25 2.25 21.25 85.0 .50 9.5625 Answer, or a little over 9^^. Division of Decimals. Is exactly similar to simple division, only the place for the points. Example: Divide 20.7888 hy 4.26. 4.26)20.7888(4.88 Answer. 17.04 3.748 3.408 3408 3408 Rule: — Deduct the two decimals in the divisor from the four decimals in the dividend. This leaves two, so we have two in our answer. SQUARE ROOT. In finding the square root of 92, mul- tiply a number by itself and the one that will come under f 2, but nearest to it. You could not say 10 times 10 because that w^ould be higher than 92, but you could say 9 times 9^ so you know the square root of 92 is between 9 and 10, or 9 and a fraction. Example: Extract square root of 92. 9)92(9.591 Answer 81 19181)31900(1 19181 In taking 92 for the number, you say 9 times 9 are 81. Commence by dividing 92 by 9, which gives 9 and 11 remaining; to the 11 add two ciphers, which wil make the 11 into 1100. Then multiply th< 9 which is in the answer by 2, whict will make it 18. This you put to divide in the 1100, but you must put anothei figure after the 18, and this figure must be the number of times 18 and the figure placed after it will divide into 1100. A good plan is to put a cipher afte; the 18, which makes it 180, divided int< 1100 would go 5 times. Then you plaG< the 5 after the 18 instead of the cioher making it 185 divided into 1100, which is 5 times with 175 remaining. You agair place two ciphers after the 175, making it 17500. The answer as far as you have gone is 9.5: multiply this by 2 and get your next divisor, 95 multiplied by 2 equals 190 But you must place another figure aftel this before dividing the 17500 by it. D( as 3'ou did before, place a cipher aftel the 190, making it 1900; now see ho^^ many times it will divide into 17500, anc you find 1900 will divide 9 times with remainder of 319. You repeat what 5^01 did to get the 5 and the 9. That is, yoi add two ciphers to the 319, making i 31900. Multiply the answer again by 2. Tha is 9.59X2=1918; add a cipher, makinj 19180; now see how many this will divide into 31900. You find it divides 1 time, S( take awav the cipher from 19180 an( make it 19181; divide this into 31900 am you get 1. 40 This is quite far enough to take it; in fact, for ordinary purposes, 2 decimals are far enough to go, but you see by our answer we have gone as far as 3 deci- mals, the answer being 9.591, which is the square root of 92. What is the square root of 10? 3)10(3.16 9 NUMBER WITH SQUARE ROOTS GIVEN. NO. S square No. Square No. Square Root Root Root .0625 .25 12 3.464 47 6.855 .125 .353 13 3.605 48 6.928 .25 .5 14 3.741 49 7.0 .375 .61 15 3.872 50 7.071 .5 .71 16 4.0 51 7.141 .625 .79 17 4.123 52 7.211 .75 .866 18 4.242 53 7.28 .875 .935 19 4.358 54 7.348 1. 1.0 20 4.472 55 7.416 1.125 1.061 21 4.582 56 7.483 1.25 1.119 22 4.69 57 7.549 1 375 1.172 23 4.795 58 7.615 1.5 1.23 21 4.898 59 7.681 1.625 1.273 25 5.0 60 7.745 1.75 1.38 26 5.099 61 7.81 1.875 1.37 27 5.196 62 7.874 2 1.414 28 5.291 63 7.937 2.25 1.5 29 5.38i 64 8. 2.5 1.58 30 5.477 65 8.062 2.75 1.65 31 5.567 66 8.124 3 1.732 32 5.656 67 8.185 3.25 1.8 33 5.744 68 8.246 3.5 1.87 34 5.830 69 8.309 3.75 1.93 35 5.916 70 8.366 4 2.0 36 6.0 71 8.426 4.25 2.06 37 6.0S2 72 8.485 4.5 2.12 38 6.164 73 8.544 4.75 2.18 39 6.245 74 8.602 5 2.236 40 6.324 75 8.66 6 2.449 41 6.403 76 8.717 7 2.645 42 6.48 77 8.774 8 2.828 43 6 557 78 8.831 9 3.0 44 6.633 7^ 8.888 10 3.162 45 6.708 80 8.944 11 3.316 46 6.782 81 9 42 No. Square No. Square No. Square Root Rool Root 82 9.055 122 11.045 162 12.727 83 9.11 123 11.09 163 12.767 84 9.165 124 11 135 164 12.806 85 9.219 125 11.18 165 12.845 86 9.273 126 11.224 166 12.884 87 9.327 127 11.269 167 12.922 88 9.38 128 11.313 168 12.961 89 9.433 129 11.357 169 13 90 '.).486 130 11.401 170 13.038 91 9.539 131 11.445 171 13.076 92 9.591 132 11 489 172 13.114 93 9.643 138 11.532 173 13.152 94 9.695 134 11.575 174 18.19 95 9.746 135 11.618 175 13.228 96 9.797 136 1 1 . 661 176 13.266 97 9.846 137 11.704 177 13.304 98 9.89:0 138 11.747 178 13.341 99 9.949 139 11.789 179 13.379 100 10.0 140 11.832 180 13.416 101 10.049 141 11.874 181 13.453 102 10.099 142 11.916 182 13.49 103 10.148 143 11.958 lt:3 13.527 104 lO.lyS 144 12 184 13.564 105 10.246 145 12.041 185 13.601 106 10.295 146 12.083 186 13.638 107 10.344 147 12.124 187 13.674 108 10 392 148 12.165 188 13.711 109 10.44 149 12.206 189 13.747 110 10.488 150 12.247 190 13.784 111 10 535 151 12.2^8 191 13.82 112 10.583 152 12.328 192 13.856 113 10.63 153 12.369 193 13.892 114 10.677 154 12.4(i9 194 13.JJ28 115 10.723 155 12.449 195 13.964 116 10.77 156 12.49 196 14 117 10.816 157 12.529 197 14.035 118 10.862 158 12.509 198 14.071 119 10.908 159 12.609 199 14.106 120 10.954 160 12.649 200 14.142 121 11 161 12.688 43 Troy Weight. 24 Grains:=l Pennyweight. 20 Pennyweighls=l Ounce. 16 Ounces=il Pound. Avoirdupois Weiglit. 16 Drachms:=:l Ounce. 16 Ounces^l Pound. 28 Pounds=l Quarter. 4 Quarters=l Hundredweight. 20 Hundredweights! Ton. HOPPER BALE BREAKER. This machine is made in the Unite< States bj'- Messrs. Howard and Bullough of Pawtuclcet, Rhode Island. Its work is to brealc the cakes of cot ton, which are pulled from the newlj opened bales, without damage to th( fibres. It mixes waste with cotton evenly. I is a great improvement to opening oi* breaking the cotton by hand, and saves a great amount of labor, as one of these machines will open a lull sized bale of American cotton in from 6 to 10 minutes, or about 175,000 lbs. per week. AUTOMATIC FEEDER. The Automatic Feeder feeds the cotton evenly to the opener. The cotton is fed into the hopper and carried by a spiked lattice or apron to the Stripping Comb. The Stripping Comb knocks back the surplus cotton taken up by the vertical spiked lattice, so in case a heavier feed is required, the stripping roll is set further away from the lifting- apron, and if a lighter feed is required 44 it is set nearer, or the lifting apron may be made to run slower or quicker to feed heavy or light. The feed to the opener is controlled by a wood condensing roll. See that there is no slippage of the apron, and keep the machine clean, re- moving the sand, seeds, and dirt regu- larly. OPENER. Its duties are to open and clean the cotton and take out foreign matter. Some makes cut or chop the cotton and cause trouble. The revolutions of an 18 inch rigid beater are about 14.50 per minute; and a porcupine beater 550 R. P. M. The distance of the beater blades to the feed roll for working medium Ameri- can cotton is 5/16 of an inch. The beater blades should be sharp, but not sharp enough to cut the cotton. They should give the cotton a sharp, solid blow to knock out the dirt. If the beater knocks out the cotton in bunches there is not sufficient weight on the feed roll. If the laps vary much in weight the evener and feed roll are not working cor- rectly. The production of one of these ma- chines is anywhere from a 1000 to 7000 lbs. per day. 45 BREAKER LAPPER. The two machines mentioned before are generally connected to this machins In various ways. The Feeder and Opener are placed in another room and connected by conduct- ing trunks, or they can be directly con- nected to the Breaker Lapper. For stock 1% to 1% inch, a good speed for porcupine beater is 550 R. P. M. The rigid beater 1300 R. P. M. and the fan 1100 R. P. M., but these vary greatly according to the cleanliness of the cotton. Pay great attention to the setting of the bars. Set bars about i/^ inch and note re- sults. If you make too much waste close them, and if the dirt is coming along with the cotton open them. When working Sea Island spread the bars and run the rigid beater about 1100 R. P. M. But much depends on whether you are short of laps in card- room. The same applies to this machine in reference to the beater and feed rolls, as mentioned in the opener. A good speed for the fan with the other speeds given is 1100 R. P. M. But this depends largely on how they are dealing with the cotton in blowing it on the screens or cages. A good plan is to place a triangular piece of wood the whole length of the screens and near to where the screens meet, and divide the air current. This stops the cotton from being blown at the junction of the screens and prevents thick and thin places in the lap; it also, to a great ex- tent, does away with splitting or licking laps. See that the fan blows the cotton evenly on the screens or the lap will not be parallel from end to end, 46 FINISHER LAPPER. This machine is designed to double the laps from the breaker lapper, and in this way get a more even lap. The beaters and fans have been dealt with on tlie Breaker Lapper and Opener. The Pin Beater has not been mentioned. It is a beater with pins set in the blades, and for long staple cotton it works splendidly. For Sea Island a pin beater would do well at 1100 R. P. M. and the fans 1300. Always be well equipped for fires in the picker room. Keep the room and machines clean. The laps should be cylindrical, solid throughout, and have perfect salvages. Calculations on Lappers. To find speed of beater: — Speed of line shaft 230 R P. M. Pulley on line shaft 36 inches, which drives a 20 inch pulley on counter shaft, and an- other pulley on counter shaft 28 inches drives the pulley on the end of the beater shaft, which is 8 inches. Rule: — Multiply the driving pulleys and the revolutions of the line shaft together, namely, 230, 36, and 28. Then multiply the driven pulleys to- gether, which are the 20 and the 8, and divide the drivers bj^ the driven, then you have the revolutions of the beater per minute. 230X36X28=231840 20X8 = 160 231840h-160=1449 R. P. M. of beater. The fan is driven from the beater shaft; so for example take a pulley on the beater shaft 6 inches, driving a pul- ley on the fan shaft 8 inches diameter,' What vi^ould be the speed of the fan? Rule: — The beater revolves 1449 R. P. M. Multiply this by 6 and divide the product by 8. 1449X6=8694 8694^8=1086 R. P. M. of fan. To find percentage of waste: — Multiply weight of droppings by 100 and divide by weight of production and droppings added. To find the Hank Lap: — We must remember that 840 yards make one hank and 7000 grains 1 lb. So if 840 yards of lap, sliver, or yarn weigh 7000 grains, or 1 lb., then the counts must be Is. or one hank to the pound. If 840 yards weigh 1000 grains, then the sliver or yarn would be 7s. because we would require 7 times 840 yards to make 7000 grains or 1 lb. Find the Hank of a 12 ounce lap. Divide 7000 grains by 840. This gives 8.33, which means each yard weighs 8.33 grains. Now find how many grains there are in 12 ounces. There are 7000 grains in 1 lb. and there are 16 ounces in 1 lb. By dividing 7000 by 16 we get to know how many grains in an ounce; 7000 di- vided by 16 equals 437i/^ grs. in an ounce. Then multiply 12 by 437 1/4 and we get 4S 5250 grs. in 12 oz. Now divide the grains per yard (8.33) by 5250 and you have the Hank Lap. 8.33^5250=.00158 hank of lap. CARDING. Settings. Set Doffer, Licker-in, and Flats as near to the Cylinder as possible without touch- ing. Feed Plate to Licker-in 12/1000 of an inch. Cylinder screen to Cylinder 20/1000 of an inch. Licker-in knives to Licker-in 12/1000 of an inch. Back knife to Cylinder 15/1000 of an inch. Front knife plate to Cj^linder (lower edge) 15/1000 of an inch. The above settings are for a medium heavy production. When carding light, set all setting parts as near as possible without touching. Draft between Lap Roll to Calender Roll:— Multiply Lap Roll gear (59) by Feed Roll gear (154) and side shaft Bevel gear (32) and Doffer gear (180) and diameter of Calender roll 4 inches. Then multiply the following gears to- gether: Lap Roll driving gear (21). Draft bevel gear (20). Side shaft gear (26). Calender gear (28), and Diameter of Lap Roll 6 inches. 8 3 22 X&i 9 59 X l&JL X 3^ X 1^0 X ^ = 1038 ^X X 2p X ^0 X ^8 X ^ = 91- 7 13 J ^ 10384^S1=113 draft. To find constant for draft: Use the same gears as when findin the total draft, but leave out the draf gear (20). 10 23 16 3^ 59 X m y: 3;^ X X^^ X ^ = 207680 ?1 2^ X i^ X ^ = 91 7 13 J 207680^91=2282 constant. To get draft gear, divide the constant by the draft required. Say, for example, we want a gear to put in 113 of draft. 2282 (constant) divided by 113 (draft) equals 20. Then a 20 draft gear would give 113 draft. Length of Clothing required to cover cylinder and doffer. Diameter of cylinder 50 inches, and width of carding surface 40 inches, would reqviire 268 feet of clothing, 2 inches wide. A cylinder 50 inches diameter, and 45 inches wide, would require 297 feet of clothing 2 inches wide. A doffer 24 inches diameter, and 40 inches wide, requires 172 feet of 1% inch clothing. A doffer 27 inches diameter, and 40 inches wide, requires 194 feet of clothing iy2 inches wide. 50 A doffer 27 inches diameter, and 45 inches wide, requires 218 feet of 1% inch clothing. SLIVER LAP MACHINE. This machine converts the sliver from the card into a lap to be put on the rib- bon lap machine or on the comber direct. There are usually 14 to 20 slivers taken in behind to form the lap. A small draft of about 1.5 is generally- put in here. RIBBON LAP MACHINE. This machine dispenses with the first drawing frame. It doubles the laps (gen- erally six) from the sliver lap machine, and makes an evener lap for the comber. The draft is governed by the number of laps being doubled; it generally runs from 4 to 6 of draft. Spread the rolls according to the weight of laps behind, say from Vs to % of an inch wider than the staple of cotton being worked. COMBER. This machine takes out the short fibres, neps, and leaf by the needles in the half- lap combing the front ends of the fibres, whilst they are held by the nippers, and the top comb combing the rear ends by having the fibres drawn through it by the fiuted segment and the detaching rolls. This process makes a lot of waste, generally from 16 to 22%, but it makes a stronger, evener, and cleaner yarn, with a better lustre, as it combs the fibres parallel. 51 A single comber gives from 80 to 9! nips a minute. A good plan when starting a new ma chine is to commence slowly, then grad ually increase in speed untfi you find th( quality of the work deteriorating; thei stop right there. This applies to all ma chines. Roller Varnish Receipt. 1 lb. Gelatine Glue. 12 oz. Burnt Senna. 2 quarts of Acetic Acid. 4 oz. of Red Lead. 1 oz. of Origanum. Comber Setting. Feeds at 5 index Nipper knife touches cushion plate 9 to 9 1^ index Leather detaching roll touches segment ... 6% index Leather detaching roll leaves segment 9% to 9% index Delivery roll delivers. 6i/4 to GV2 index Top comb working 5 index Cushion plate to need es on halt - lap. .18 to 21 gauge Stop screw to nipper stand 14 step gauge Cushion to detaching roll 114 finger gauge Feed roll to detaching roll 1 13/16 finger gauge Top comb to segment.l8 to 21 gauge Angle of top comb 28 to 32 These settings vary according to length of staple, but for a 2.50 gr. lap. Egyptian the above settings are good. 52 Comber. Draught from Lap Roll to Calender delivery roll: — Multiplj^ the following driving gear together: — Lap roll gear 47. Bevel gear 55. Diagonal shaft gear 22. Feed Roll gear 38. Notch or star gear 5. Cylinder shaft gear 25. Front cross shaft gear 50. Gear 45. Front Roller gear (on opposite end of shaft) 20, and diameter of calender roll 2%", which we will call 11, as there are 11 quarters in 2%". Then multiply the following gears to-" gether: — Gear between Lap gears 37. Gear on diagonal shaft 20. Feed Roll gear 22. Change gear 16. Feed Peg 1. Front cross shaft gear 25. Gear on stud 45. Roller gear 42. Calender shaft gear 43. Diameter of lap roll 2%", or 11 quar- ters. Then we get t'he following: — • 47X55X22X38X5X25X50X45X20X11 37X20X22 X16X1X25X45X42X43X11 =22.97 draft. or alm.ost a draft of 23 we get by mul- tiplying the gears above the line, then multiplying the gears below the line, and dividing the product of the top line by the product of the bottom line. An easy way to get the draft is to mark a yard of the lap behind, putting a mark on the back of the comber. Set the first mark on the lap even with the mark on the machine, then break the sliver at the coiler. 53 start the comber, and when the yard of lap has gone to the stationary mark on the comber, again break the sliver at the coiler, and measure it. If there are 27 yards delivered for 1 yard fed at the back, then we have a draft of 27. To find amount of waste, break the sliver at the coiler and clean all the waste from behind the machine, run the comber a short time, break the sliver again and weigh the sliver that has come through also the waste made during this short time. Suppose the sliver weighs 60 penny- weights and the waste weighs 10 penny- weights. Multiply the weight of waste by 100 and divide by weight of sliver and waste added. 60 100 10 10 70)1000 14.28 percentage of waste. There is a weighing-machine made which gives the percentage of waste made, on a quadrant. DRAWING FRAME. As the name implies, this machine makes the slivers more uniform and the fibres more parallel by drawing them, 6 to 8 slivers from the card or comber being fed behind, and drafted so as to come out in front of the frame about the weight of one sliver fed behind. 54 Suppose there are 6 slivers fed behind, each weighing 60 grains, and there is a draft of 6 in the rollers. The one sliver in front of the frame will remain a 60 grain sliver. Constant for Draft between Back Front Rolls. Multiply Back Roll gear 70 by Crown gear 100, and by diameter of Front Roll 11 for a dividend. . Then multiply Front Roller gear 25 by diameter of Back Roll 9 for a divisor. 70X100X11=77000 25X9 = 225 77000^22.5=342 Constant. Divide Constant by draft, and this will give Draft Change gear. 342 Constant divided by 6 Draft=57. 57 Draft gear to give 6 of a Draft. Draft from Back Roll to Bottom Calen- der Roll. Multiply Calender Roll Compound gear 32, by Crown gear 100, by Back Roll gear 40, and by diameter of Calender Roll 16, for a dividend. Then multiply gear on Calender Roll 24, by Compound gear 45, by Draft gear 30, and by diameter of Back Roll 11, for a divisor. 32X100X40X16=5120 24X 45X30X11= 891 5120h-891=5.74 Draft. The above figures were cancelled. Note that the figures 16 and 11 are used for the Calender Roll and Back Roll. 55 The Calender Roll is 2 inches diameter* and the Back Fluted Roll 1% inches. These rolls are reduced to eighths of an; inch. There are 16 eighths into 2 inches, and there are 11 eighths into 1% inches. This rule is also used in the Draft from Back to Front Roll. Back Roll is IVs anql the Front Roll 1%, so we use the figures 9 and 11. Roller Varnish Receipt. 1^ lb. of Gelatine r,iue. V4 lb. of Pulverized Glue. 1 quart of Acetic Acid. 1 tablespoonful of Origanum Oil. 1 teaspoon ful of Brown Sugar. 56 FLY FRAMES. Slubbing, Intermediate, Roving and Jack Frames. These machines are built somewhat similar, excepting the slubber, which has no creel, it being the first machine after the Drawing Frame. The cans of sliver are placed behind the slubber and wound on a bobbin, whilst an actual twist is put in here, for the first time, so at this ma- chine the spinning really commences. Before, the Picker, Card and Comber have cleared the cotton of impurities and taken out short fibres. The Drawing Frame has made the slivers uniform or even, and now we want to diminish the slivers, and make the fibres still more parallel by drafting as fine as required, and as even as possible to prepare them for the Mule or Ring Frame. For the purpose of making the roving even, it is doubled at the Intermediate, Roving, and Jack Frames. Jack Frames are only used where fine counts are spun, as the bobbins required must be small and liglat, to draw off easily at the Mule or Ring Frame, with- out breaking the roving. The Jack Frame also makes the drafts smaller in the other Frames. For without this Frame it would be quite a task to make a 25 Hank Roving from an ordinary sliver, without having excessive drafts in the Slubber, Intermediate, and Roving Frames, and this wovild make roller-laps by the drafts being too high, and conse- quently waste. 57 The bobbins are run by the cone drums, which act exactly as tlie quadrant does to the spindle on the Mule. As the Bobbin becomes larger in diameter, and the rolls are delivering the same amount of roving, the Bobbins must run slower to wind on the roving deliv- ered. To do this the Cone-belt is inoving a little at evei-y change of the rail, just as the quadrant chain on the mule is shortening until the cop reaches the body or thickness. This, of course, is a Frame with a bobbin lead, or, in other words, v/hen the speed of the bobbin is in excess of the flyer, but when it is a Flyer Lead, the speed of the flyer is in excess of the bobbin, and so winds the roving on the bobbin. Then after doffing the bobbins run slowly and gradually increase in speed until the time for doffing. Constant for turns per inch, on Slub- bing Frame: — Multiply Front Roll gear 120, by Top Cone gear 35, by Driving Shaft gear 44 and by Spindle bevel gear on shaft 50 for a dividend. Then multiply gear on Cone Drum shaft 64, by gear on the end of Spindle shaft 44, by gear on the bottom of Spindle 25, and Circumference of Front Roll l'/4 inches or equal to 3.92. 120X35X44X50 =525 64X44X25X3.92=15.68 (The above figures have been cancelled before being multiplied.) 58 525^15.68=33 Constant. Divide Constant by turns per inch re- quired, and it will give you Twist gear. Suppose you w'ant to put in .777 turns per incli. Divide the Constant 33 by .777. (All the sevens being decimals we must add three ciphers to the 33.) (See Deci- mals.) 33.000^.777=42 Twist Gear. Constant for Draft in Slubbing Frame: Multiply Back Roll gear 60, by Crown gear 90, and by diameter of Front Roll. 11/4 inches (or 10 eighths) for a dividend. Then multiply Front Roller gear 24, by diam.eter of Back Roll 1 inch (or 8 eighths). 60X90X10=54000 24X8 = 192 54000^192=281 Constant. Constant divided by draft gives Draft gear. 281 (Constant) divided by 5 (Draft)=56 Draft gear. To find Lay or Lifter Gear. Suppose a 6 hank-roving requires a 14 lay gear, what lay gear will a 4 hank roving require? Rule: — Square 14 by multiplying 14 by 14, then multiply the product by 6 and divide by 4, and get the square root of the quotient. 59 Example: 4)1176 VI) 294(17 lay gear required. 1 27) 194 189 Another way to find Lay Gear, which is far simplier than the rule before given : — Multiply the 14 by the 6 hank roving and divide by the 4 hank roving, add the 14 to the answer and divide by 2. This gives lay gear. Example : 14 4)84 2)35 17.5 lay gear. 17 Lay or Lifter Gear required, GO To find change for Twist Gear: Suppose you are making a 6 hank rov- ing with a 30 twist gear on. What twist gear would you require to make a 4 hank roving? Rule:— Square the 30 twist gear. (This means multiply 30 by 30.) Then multiply by the hank roving you are making 6, and divide by the hank roving you are going to make 4, and the square root of the answer is the twist gear required. Example: 30 twist gear 30 900 6 hank you're making Hank to make 4)5400 V36) 1350(36.7 twist gear reqd 1296 727)5400(7 5089 .7 or almost 37 Twist Gear required. Another and easier rule. Multiply the 30 by 6 hank roving and divide by 4. Then add the 30 to your answer and divide by 2. This will give you Twist Gear required for a 4 hank roving, if a 6 hank roving requires a 30 Twist Gear. 61 Example: 30 twist gear 6 hank you're making Hank to make 4)180 45 30 twist gear added 2) 75 37 twist gear required. To find Tension or Rack Gear: Suppose you are making a 6 hank rov- ing with a 30 tension gear. Wliat ten- sion gear would a 4 hank roving require? Rule: — Multiply the tension gear on, by the square root of tlie hank roving being made, and divide by the square root of the hank roving j'ou are going to make. Example: Square Root of 6 is 2.4. 30 tension gear 2.4 square root of 6 120 Square root of 4=2)720 36 tension gear reqd. All the calculations given in regard to the Slubber apply exactly the same to the Intermediate, Roving and Jack Frames. To find Turns per inch required: — American and Low Egyptian. Slubber, Square Root of H. R. multi- plied by 1.16. Intermediate, Square Root of H. R. multiplied by 1.16. Rover, Square Root of H. R. multiplied by 1.25. Jacks, Square Root of H. R. multiplied by 1. Good Egyptian and Sea Island. SlublDer, Square Root of H. R. multi- plied by .7. Intermediate, Square Root of H. R. multiplied by .78. Rover, Square Root of H. R. multiplied by 1.1. Jacks, Square Root of H. R. multiplied by .95. These tvs^ists are changed according to the quality of the cotton and the condi- tion of the weather. To find the Draft Change Gear to put in a draft of 5.5 with the following gears : — Front Roll Gear 30 teeth. Crown Gear 100 teeth. Back Roll Gear 60 teeth. Diameter of Back Roll 1% Inches. Diameter of Front Roll 1^/4 inches. Multiply Front Roll Gear 30, by diameter of Back Roll l^/^ inches or 9 eigths, and by Draft required 5.5. Take these for a divisor. 63 Then multiply Crown Gear 100 by Back Roll Gear 60 and diameter of Front Roll 114 Inches, or 10 eights. Take these for your dividend. Example : lOOX 60X10=60000 30X5. 5X 9=1485 60000^1485=40 Draft Gear. We are making a 8 hank roving with a 31) draft gear. What Draft Change Gear is required to make a 6 hank roving? Rule: — Multiply Change pinion on, (30) by hank roving being made (8) and divide by hank roving (6) we are going to make. 30 8 6)240 40 draft change gear required. To find turns per inch on Interme- diate: — Multiply gear on driving shaft 52, by Spindle shaft bevel gear 57, and by Top cone gear 55, and by Front Roll Gear 140. These gears taken for a dividend. Then multiply End Spindle Shaft gear 50, by Spindle gear 25, and by Twist gear 52, and by gear at the opposite end of cone 78, and by diameter of Front Roll 11/4 inches or 3.927. These gears use for a divisor. 64 52X57X55X140 =1463 50X25X52X 78X3.927=1276.275 (The above numbers were cancelled be- fore multiplied.) 1463 — 1276.275=1.14 Turns per inch. To get a constant for Twist Gear: — Rule: — Proceed exactly as in the exam- ple given to find turns per inch, but leave out the Twist Gear 52. Example : 52X57X55X 140=22822800 SOX 25 X 78 X 3.927=382882.500 22822800-^382882.5=59 Constant. 59 Constant divided by 1.14 Turns per Inch equals 52 Twist Gear. These Twists and Drafts apply also to Rover and Jack Frames. WRAPPING OR SIZING SLIVERS, ROV- INGS, AND YARNS. In finding the Hank of Slivers weigh a yard of Sliver, and suppose it weighs 58 grains, divide this in 8.33. 8.33^58=.14 Hank Sliver. The reason for dividing one yard on sliver in 8.33 is because there are 8.33 grs. to one yard of Is.: to get this divide 7000 grains by 840 yards. 7000-^840=8.33 grs. per yard. 65 1 Wrapping or Sizing Roving. Wrap 12 yards of Roving, and divide weight in grains in a hundred. Suppose 12 yards weigh 50 grains. 100-=-50=2 Hank Roving. The reason we divide the weight of 12 yards into lOQ is because 12 are 1/70 part of 840 yards, or 1 Hank, and 100 is 1/70 part of 7000 grs., or 1 lb. Wrapping or Sizing Yarn. Wrap or Reel 120 yards and divide the weight in grains into 1000. Suppose 120 yards or 1 Lea weighs 50 grains. 1000 divided by 50=20s Yarn or Counts. The reason for dividing the weight of 120 yards into 1000 grains is that 120 yds. are 1/7 of 840 yds. and 1000 grs. are 1/7 of 7000 grs., or 1 lb. SETTING ROLLS. It is very difficult to give a fast rule for the Setting of Rolls, as the Front Roll running slowly, or at an excessive speed, also the feed being heavy or light, govern the settings to a great extent. Drawing Frame Rolls. For Combed stock set Front and 2nd Roll 1/16 of an inch further apart from centre to centre than the length of the staple of the cotton being worked. And from centre of 2nd Roll to centre of 3d Roll set Vs of an inch further apart than length of staple. And from centre of 3d Roll to centre of Back Roll set 3/16 of an inch further than length of staple. Drawing Frame. Suppose, for example, you are work- ing combed stock 1% inch staple. Distance from centre to centre of Front and 2nd Roll 1 7/16 of an inch. From centre to centre of 2nd and 3d Roll 1 1/2 inches. From centre of 3d Roll to centre of Back Roll, set 1 9/16 of an inch. For Carded work you may set the rolls % of an inch. Front and 2nd % of an inch, 2nd and 3d and % of an inch 3d and Back Rolls, further apart than length of staple. Note result after setting rolls, and if the sliver comes through not properly drawn, or in tufts, spread the rolls a little more. SLUBBER ROLLS. Set from centre of Front Roll, to centre of 2nd or middle roll, 1/16 of an inch wider than the staple you are working, and from centre of middle roll, to centre of Back Roll % of an inch longer than staple. INTERMEDIATE ROLLS. Set these similar to Slubber Rolls. ROVER AND JACK FRAMES. Set Front and Middle Roll a little fur- ther apart than length of staple, from centre to centre, and from centre of mid- dle roll to centre of Back Roll Vs of an inch. 67 MULE AND RING FRAME. Set Front and Middle Roll from centra to centre slightly Wider than staple. Always take in consideration, whei setting rolls, whether the feed is heav] or light. For a heavy feed, set rolls furJ ther apart, for a light feed set nearer. Watch your drafts when setting rolls If a small draft, set your rolls furtht apart, and, if a large draft, set rol nearer. Look to your Roving when setting roWi If it is hard twisted, set the rolls furth€ apart. If the roving is soft, set near. With Self-weighted rolls on Fly Framesr set Back and Middle Rolls a little further apart. Never have Top Leather Roll the same diameter as the fluted roll, for if they are, the leather will become fluted. Keep the leathers on the rolls in good condition. Loose Boss Front Rolls are best. Varnish for Drawing Frame Rolls. 11/^ lbs. Fish Glue. V^ lb. of Gum Arabic. 1/4 lb. Powdered Alum. 2 lbs. Acetic Acid. 4 lbs. Water. Add together, dissolve over slow fire, and when cold, it is ready for use. Circumference of Rolls. 1 inch diameter, circumference is 3.1416. 1 1/16 inch diameter, circumference is 3.3379. 1 1/8 inch diameter, circumference is 3.53. 1 3/16 inch diameter, circumference is 3.73. 1 1/4 inch diameter, circumference is 3.92. 69 SELF-ACTING MULES. Good Drafts for Mules spinning Ameri- can Cotton range from 7 to 10, but these are often exceeded. In spinning good Sea Island Cotton, 14 of a draft is common. Suppose you were going to spin 50s. yarn from a 10 hank roving double. The 10 H. R. being double, would be twice as heavy, so it would equal a 5 H. R., and you require what is termed 10 of a draft, or, in other words, draw the 5 H. R. ten times finer. You see this by saying 10 times 5 are 50. To find Draft Gear, to give a draft of 10. We will suppose you have a Back Roll gear on 54. Multiply this by Crown Gear 120, and by diameter of Front Roll 1 inch. Take these for a dividend. Then multiply Front Roll gear, which we will suppose to be 18, by the Draft required 10, and by diameter of Back Roll 1 inch. Take these for a divisor. Example : B.R.G. C.G. D. ofF.R. 54 X 120 X 1 =6480 10 X 18 X 1 =180 Draft. F.R.G. D. of B. R. 6480-^180=:36 draft gear required. 70 If the Front Roll diameter is 1 1/16 of an inch, and the Back Roll 1 inch, reduce them to sixteenths. There are 16 six- teenths in one inch, so there must be 17 in 1 1/16 inch. Place your terms thus: 54X120X17=110160 lOX 18X16= 2880 110160^2880=38 draft gear required. If the diameter of the Front Roll is 1^ inch, reduce to eights. There are 9 eighth in 1% and 8 eights in 1 inch. 54X120X9=58320 lOX 18X8=1440 5832:)^1440=40 draft gear required. To find Constant for Draft. Rule: — Proceed exactly as when finding Draft Gear, but leave out the draft. Example: 54X120X1=6480 18X1 = IJ 6480^18 = 360 Constant. 71 The Constant divided by the Draft re- quired will give you Draft Gear. 360 (Constant) divided by 10 (Draft re- quired)=36 Draft Gear. Suppose you require 9 of a draft. 360 divided by 9 equals 40 Draft Gear. If you take the rule given before, the Counts vi'ould come a little lower than 50s. The reason for this is that 1/15 is generally taken up with the twist, which would make the numbers of the yarn heavier. You must also watch the drag or gain in the carriage, for this is equal to putting in more draft. For if the Rolls only deliver 62 inches and the Stretch of the Mule is 64 inches, you are drawing the yarn finer. A good rule to find the Numbers of the Yarn, from the hank roving, is the fol- lowing: — We will suppose the Roving in the Creel is 8 hank doubled. This would equal 4 hank, and you are going to put in 9 of a draft, and the Front Roll delivers 62 inches, and the length of stretch is 64 irches. Now find the Counts or Numbers of the Yarn. Rule:— Multiply the H. R. 4, by the Draft 9, and the length of stretch 64 inches, and divide the product by the length delivered by the Front Roll 62 inches. Then deduct 1/15 from your answer for twist and you will have the Counts or Numbers of the Yarn. 72 Example : 4 H. R. 9 draft 36 64 L. of stretch 144 216 L..D. byF. R. 62)2304(37.16 186 444 434 100 62 380 372 Taken up by twist 1/15)37.16(2.47 7.1 6.0 1.16 1.05 37.16 2.47 84.69 yarn you get. Answer. 73 To find the Draft Gear, from one nui ber of yarn to another, without changii Ro-ving: — Suppose you have on a 45 Draft Gea and spinning 40s yarn, and you wish make 45s yarn out of the same roving. Rule: — Multiply the 45 Draft Gear you have on, by the numbers you are spinning. 40s, and divide the product by the num- bers you wish to spin 45s. 45 40 45)1800(40 draft gear required for 45s yarn 180 To find the Twist or Turns per inch re- quired for the Numbers of Yarn you are going to spin: — Suppose you are going to spin 36s Fill- ing. Rule: — Multiply the standard used for filling, which is 3.25 or 314,, by the square root of the numbers you are going to spin. Example: — Square root of 36 is 6, and 3.25 multipliefd by 6 equals 19.50 or IdVz turns per inch for 36s filling. When spinning warp yarns on mules: — Multiply square root of Counts by 3.75. This gives turns per inch required. 74 i The 3.25 and 3.75 are often left and standards of the overseer's used, as much depends on the quality of the cotton, and whether a hard or soft twisted yarn is required. Sometimes a standard of 2 is used for very soft hosiery yarn. This makes quite a difference to the turns per inch for the same numbers of yarns. Take for example, you are spinning 16s hosiery yarn and using a standard of 2. You would say the square root of 16 is 4 and multiplied by 2 equals 8 turns per inch required to spin very soft hosiery yarn, and in using the standard 3.25 we get 13 turns per inch for exactly the same numbers of j^arn. To find Constant for Twist, or Turns per inch on Messrs. Hetherington's Rim at Back, or Ordinary Mule: — Rule: — Multiply Front Roller Box Bevel gear 38, by gear 35, and by gear 58, and diameter of Rim Pulley IS inches, and diameter of cylinder 6 inches, or 97 six- teenths. Take these for a dividend. Then multiply the bevel gear 17, by the gear 28, and by diameter of Cylinder Pulley 12 inches, and by the diameter of spindle whirl % of an inch or 13 six- teenths, and circumference of Front Roll 3.1416. 38X35X58X18X97 = 134686440 17X 28 X 12 X 13 X 3.1416=233282.6496 134686440.0000^233282.6496=577 constant. 75 Note. — Having 4 decimals in the divisoi we must add 4 ciphers to the dividend. 35 190 114 1330 58 10640 6650 77140 18 617120 77140 1388520 97 9719640 12496680 233282.6496)1346864400000(577 constant. 11664132480 18045115200 16329785472 17153297280 16329785472 3.1416 13 94248 31416 408408 12 4900896 28 39207168 9801792 137225088 17 960575616 137225088 233282.6496 Note. — The writer would refer you to Arithmetic (Cancellation), as this exam- ple could be shortened considerably by cancelling the numbers. The turns per inch required to be put in the yarn, divided into the Constant 577, give you the size of Speed Gear. Suppose you want 20 Turns per inch. Example: 577 divided by 20 equals 28 Speed Gear at the end of Rim Shaft. The gears 38, 17, 35, and 28 are not generally changed, but the gear 58 is a change gear. With a 40 gear instead of a 58, the Constant is 398. Note. — That 97 is used for diameter of cylinder, and 13 for diameter of whirl. 77 The reason is that we want to add 1/16 of an inch for thickness of spindle band, j To do this reduce the cylinder to six-^ teenths of an inch. The cylinder being 6' inclies diameter, and there are 16 six- teenths in 1 inch. Then multiply 16 by 6 and you get 96; add 1/16 for thickness of- band and you get 97. If there are 16 sixteenths in 1 inch, there must be 12 sixteenths in 3/4 of an inch whirl, and 1/16 added for thickness of band gives 13. This accounts for using the 97 and 13 for diameter of cylinder and whirl of spindle. Also note that when the Front Roll is 1 inch diameter, the circumference is 3.1416. This is used in the example. But suppose the Front Roll is 1 1/16 inches diameter, you must use 3.338 instead of 3.1416. The reason is that the larger the diameter of the Front Roll the more it delivers at each revolution. Consequently you get less turns per inch with a thicker roll than you do with a thinner one when using the same gears. This rule applies to all mules. Constant for Drag or Gain of Carriages over Front Roll on J. Hetherington's Mule: Rule: — Multiply length of stretch 64 inches, by Gear on Front Spindle 60, and by small Gear on Drag Gear 25, and by diameter of Scroll on Back Shaft and Band reduced to eights of an inch. This is the dividend. 78 Then multiply Back Shaft gear 75. by diameter of Front Roll reduced to eights of an inch. Diameter of Front Roll 1 inch, or equal to 8 eights. r Example : I 64X60X25X45=4320000 75X8 = 600 432000-=-600=7200 constant. Divide Constant by length of stretch and Drag required and you get Drag or Gain Gear. Suppose length of stretch is 64 inches and you want a gain or drag of 3 inches. 64" add 3" equals 67". 7200^67=107 drag gear. To find Constant for Turns per inch on Messrs. Hetherington's Rim at Side Mule: Rule:— Multiply Front Roll Gear 90, by the gear 70, and by second change gear 70, by diameter of Rim Pulley 18 inches, and by diameter of cylinder 6 inches, or 97 (see Constant Rim at back). Then multiply the gear 45, by the gear 50, and by the diameter of the Cylinder Pulley 12, and by the diameter of the whirl % of an inch or 13 (see Constant Rim at back), and by circumference of Front Roll 3.1416. 90X70X70X18X97 =142590 45 X 50 X 12 X 13 X 3.1416=204.2040 (The above numbers were cancelled be- fore being multiplied.) 142590.0000-^204. 2040=698 constant. Constant divided by turns per incl give speed gear. The above Constant is witli a 70 secon( change gear on. With a 50 second chang gear, the Constant w^ould be 498.5. Suppose you want to put 20 turns pe inch in the yarn. 698 (Constant) ^20=34 Speed Gear. To find revolutions of Spindle to on revolution of Rim: Suppose an 18 inch Rim is driving a 1 Inch Cylinder Pulley, and a 6 inch Cylin der is driving a % inch vv^hirl on Spindle Rule: — Multiply 18 inch Rim by the inch cylinder for a dividend. Then mul tiply the 12 inch Cylinder Pulley by th % inch whirl, for a divisor. Example: 18X 6 =108 12X. 75=9.00 108-^9.00=12 revolutions of spindle. Note that decimal 75 is used for the ^ whirl. The reason is that .75 is % of 100 You can also place the terms thus: 18X6X4=432 12X3 = 36 432-4-36=12 revolutions of spindle to on- of rim. If it is a % whirl place thus: 18X6X8=864 12X7 = 84 864-4-84=10.28 revolutions. If it is one inch whirl: 18X6=108 12X1= 12 108^12= 9 revolutions. To find Twist Gear when putting Twist in on the Catch or Latch. Commonly called "Head Twist" on Hetherington's Mule: Suppose you are going to put 30 turns per inch in, and the length of stretch is 57 inches, and 3 inches added if you have roller motion on. This would equal a 60 inch stretch. The diameter of cylinder 6 inches and the spindle whirl % of an inch. Then there is the gear 20, driving the finger gear 68, and an 18 inch Rim, driving a 12 inch cylinder pulley. Rule:— Multiply length of stretch 60 inches, by the turns per inch 30, and by gear 20 and diameter of cylinder pul- ley 12 and of whirl % of an inch. Take this for your dividend. Now multiply the finger gear 68 by the 18 inch rim, and by diameter of cylinder 6 inches. Example: 60X30X20X12X3=1296000 68X18X6X4 = 29376 1296000^29376=44 Twist Gear required. 81 ( Asa Lees & Go's Mule ) Draft Gear and Drafts are found actly as explained on the Hetheringtoi Mule. To find Constant for Speed Gear, oi Rim at Back: Rule: — Multiply diameter of Rim, whicl we will suppose to be 19 inches, by diany eter of cylinder 6 inches, and by Rolld Box Gear 48. Take this for a dividend. Then multiply Cylinder Pulley, whicii we will suppose to be 11 inches, by spiir die whirl % of an inch, and by Rim Pin' ion 22, and by Bevel Gear 24, which geamj with Roller Box Gear, and by circum ference of Front Roll 3.1416. Example: R C B C 19 X 97 X 48 " = 88464 11 X 13 X 22 X 24 X 3.1416=237203.3664 C.P. S.W. R.P. B.G. F.R. 88464-=-237203.3664— 372 constant. When dividing 88464 by 237203.3664 add 4 ciphers to the 88464, as there are i decimals in 237203.3664, and the 3 figures? in the Constant are decimals (.372 Con- stant). The turns per inch required divided hy the Constant will give you Speed Gear. !* Note. — As the Constant is 3 decimals add 3 ciphers to your turns per inct, before dividing. j 82 J Suppose you wanted to put in 30 turns per inch, and the Gears and Pulleys were the same sizes as we have used to find the Constant .372. Proceed as follows: [turns per inch. .372)30.000(80 speed gear required for 30 2976 .240 Note. — In these examples there is no allowance for slippage of bands. Note.— Why the 97 and 13 are used for diameters of cylinder and spindle whirl is fully explained on the Hetherington Mule. In finding Constant for Speed Gear, you may use 7/22 instead of 3.1416, if the Front Roll is an inch diameter, and you get the same result, as: R. C. E.G. F.R. 19 X 97 X 48 X 7 .372 Constant. 11 X 13 X 22 X 24 X 22 C.P. S.W. R.P. E.G. F.R. If the Front Roll is 1 1/16 diameter place the terms as follows: 19X97X48X16X7 11X13X22X24X17X22 or you can place them as follows, with exactly the same result, using 3.338 in- stead of 3.1416: 19X97X48 11X13X22X24X: If the Front Roll is IVs inches place asl follows : 19X97X48X8X7 11X13X22X24X9 X22 19X97X48 11X13X22X24X3.53 If your mules are "Rim at Side" the^ Constant works out the same, the only; change being the two gears from the' Roller Box; on "Rim at Side" these gears are 60 and 30; on "Rim at Back" they are 48 and 24. Constant for "Rim at Side" Mule with 1 inch Front Roll. 19X97X60X7 :.372 Constant. 11X13X22X30X22 To find Twist Gear. Asa Lees's mule differs from the Del son and Barlow's and Hetherington" Mules, as the Worm for the Twist Gear is on the Cylinder Shaft and not on the Rim Shaft. So in finding the Twist Gear we haA'e not to deal with the Rim Pulley or Cylinder Pulley. Suppose the Cylinder is 6 inches and Spindle Whirl % of an inch, and the two Gears cast together, which generally are 45 and 15. 84 Now suppose, for example, you are going to spin 100s and put in 30 turns per inch, and you wish to put % of the twist in as the carriage is coming out, and the other Vs whilst the carriage is on the latch or holding out catch, and suppose the length of the stretch is 57 inches, and a roller motion on delivering 3 inches, which makes the length of stretch equal to 60 inches. Rule: — Multiply the length of stretch with Roller Motion added, 60 inches, by the turns per inch 30, and by diameter of spindle whirl % of an inch and the gear 15, which drives the Twist Gear. Take this for your dividend. Then multiply the diameter of Cylinder 6 inches by the Worm Gear 45. Take this for divisor. E.xample: 60X 30X 13 X 15=351000 97X45 = 4365 351000 -f- 4365=80 twist gear required. Constant for Twist Gear. Rule: — Proceed exactly as when finding Twist Gear, but leave out the Turns per Inch 30. Example: 60X13X15=11700 97X45 = 4365 11700^4365=2.68 Constant. 85 Constant multiplied by turns per Incli will give Twist Gear. 2.68X30 turns per inch=80 twist gear. Note.— There is no allowa.nce for slip- ping of bands. The overseer must make his own allowance with these calculations. Now we have got the Twist Gear, we want to put in % of the 30 turns per inch, until the carriage comes on the latch. Multiply 30 by 7 and divide by 8 and we have 26.22 turns per inch to put in during' outward run of carriage and the other Ys when the carriage Isj on the latch. Take the Constant .372 and divide the turns per inch 26.22 by it, and you get the Speed Gear. Example : .372)26.220(70 speed gear. 26.04 .180 To change from, one Number or Count to another without changing speed gear, but to change Rim. Suppose you are spinning 50s with an 18 inch Rim Pulley and you want to change to 45s by changing your Rim and keeping on the same Speed Gear. Rule: — Square the Rim Pulley 18 (that means multiply 18 by 18) and then mul- tiply this by the numbers you wish to spin 45s, and divide by the numbers you are spinning, and the square root of the answer is the Rim required. Example 18 18 144 18 324 45 1620 1296 5 0)14580(291 100 458 450 80 50 Square root for 45s. of 291 is 17. Rim required Here is another and simpler M'ay the Rim: Multiply the 18 Rim by 45 and by 50, add IS (Rim) and divide by to get divide 2_ Example "18 45 90 72 50)810 16 18 2) 34 17 rim required To change from one Number to anoth< without changing your Rim, but i change Speed Gear. Suppose you are spinning 50s with a I Speed Gear, and you wish to spin il without changing your Rim. Rule: — Square the Speed Gear you hav on 55, and multiply by the counts or num bers you wish to spin 45, and divide b the counts you are spinning and ge square root of quotient. Kxample : 275 275 50)136125(2722 100 361 350 112 100 125 100 Square root of 2722 is 52. required for 45s. Speed Gear Another and easier way to find one Speed Gear from another: Rule: — Multiply the Gear 55, by the counts 45s, and divide by the counts 50s, add the gear 55, and divide by 2. Example : 53)2475 49 55 2)104 52 speed gear required. Note. — If the speed gear is a driver, instead of being larger for finer numbers it will be smaller. To find Drag Gear for 64 inch draw. Rule: — Multiply revolutions of Front Roll per stretch, which we will say for example are 20, by gear on Front Roll 47, and by small gear on Drag Gear 25. Take these for a dividend. Then multiply turns of Back Shaft per stretch or draw 3.6 by Back Shaft Gear 72. Example: 20X47X25=23500 3.6X72 =259.2 23500.0^259.2=90 drag gear. To Find Shaper Gear. For 1% inch gauge of spindle, or, in other words, when the spindles are 1% inches apart, and the Shaper screw is Pitch 4. This meaning 4 threads to the inch. Then multiply the numbers you are going to spin by .7. Suppose you are going to spin 30s. Example: — 30 multiplied by .7= 210; strike off the cipher, as it was decimal 7 you multiplied by. Then we get a 21 Shaper Gear for 30s yarn. If your spindles in the mule are 1% inches apart, and a Shaper screw, pitch 6, your Shaper Gear will be similar to the numbers you are spinning. Suppose you are spinning 40s, your Shaper Gear will be about 40. A fast rule cannot be given for the Shaper Wheel, as much depends on the weight on the Counter or under Faller, and the tightness of the winding, also the length of chase. If you have a long chase, the cop will be thinner than with a short chase, although you use the same Shaper Wheel. Production of Mule. Suppose a mule contains 90D spindles and it is running 4 stretches or draws a minute. Length of draw is 64 inches and 3 inches added for roller motion equals 67 inches. Find how many hanks per spindle, and the weight turned off in 56 hours, deduct 3 hours for doffing and other stoppages, and the numbers of the yarn being spun is 40s. Rule: — Reduce the 53 hours to minutes by multiplying the 53 by 60, then multiply 90 this by draws per minute 4, and by length of draw 67. Take this for your dividend. Then multiply 840 (1 hank) by 36 inches (1 yard). Example: 53X60X4X67=852240 840X36 =30240 852240-=-30240=28 hanks per spindle. Now we will find the weight per week. Rule: — Multiply the number of spindles 900, by the hanks per spindle 28, and divide by the number of yarn 40s. Example : 900 28 7200 1800 40)25200(630 lbs. per week. 240 120 120 To find the average Numbers or Counts being spun. Suppose you have spun 1000 lbs. of 80s, and 1000 lbs. of 70s, and 1500 lbs. of 50s, and 2000 lbs. of 40s, and 2000 lbs. of 36s, and 5000 lbs. of 28s. Now what is your average number or count? Rule: — Multiply each weight by counts and add them together. 91 Then a,dd all the weights sspun and divide the total into the weights multi- plied by counts. Example: Weight Spun. Counts. 1000 ms. multiplied by 80 equals 80000 1000 n3s. multiplied by 70 equals 70000 1500 lt3S. multiplied by 50 equals 75000 2000 ItjS. multiplied by 40 equals 80000 2000 rbs. multiplied by 36 squals 72000 5000 lbs. multiplied by 28 equals 140000 12500 517000 517000-^ 12500=41s average numbers of yarn. To find Constant for Speed Gear on D. & B. Mule. We will suppose the Rim Pinion is 19, driving a 48 gear on Compound, and the small gear on Compound 35, driving Speed Gear (which you omit when find- ing Constant for Speed Gear), and on opposite end of Side Shaft is a Bevel Gear 40, driving another Bevel Gear 40 on Front Roller Catch Box. The Rim 18 inches diameter, driving a Cylinder Pulley 12 inches, and a 6 inch Cylinder, driving a % inch whirl on spin- dle, and Front Roll 1 inch diameter. Rule: — Multiply Bevel Catch Box Gear 40, by gear on Compound 48, and diam- eter of Rim Pulley 18 inches, and diam- eter of Cylinder 6 inches. Take these for your dividend. Then multiply Bevel Gear on Side Shaft 40, by small Gear on Compound 35, and Rim Shaft Pinion 19, and diameter of Cylinder Pulley 12 inches, and diameter of Whirl % of an inch, and Front Roll 92 1 inch (here you can use 7/22, or 3.1416 for Front Roll). E\'ample: 40X48X18X 6X 4X 7= 5805080 40X35X19X12X 3x22=21067200 5805080-=-21067200=:.275 constant. Note. — The three figures in the Con- stant are decimals, so when you divide the Turns per Inch by them always have three declrr.al places. The Turrs per Inch divided by Constant will give you Speed Gear. Suppose you want to put in 19.3 turns per inch, you must add 2 ciphers after the 19.3, so as to have as many decimals as there are in the Constant. Example : .275)19.300(70 speed gear reciuired. 19.25 .50 If you wish to add 1/16 of an inch for thickness of Spindle bands, place your terms as follows: 40X48X18X97X 7 • =Constant. 40X35X19X12X13X22 If a 7/8 whirl and 1 1/16 front roll, place as follows: 40X48X18X 6X 8xl6X 7 ;=Constant. 40X35X19X12X 7X17X22 If a 3/4 whirl and 1 1/8 front roll, place as follows: 40X48X18X 6X 4x 8X 7 =Constant. 40X35X19X12X 3X 9X22 9:i All these examples will give Constant for Speed Gear. Note. — If you have not the Speed Gear required, you can overcome the difficulty by changing the 35 gear on the Com- pound. To Find Twist Gear. Suppose the length of stretch is 57; Inches, and a Roller Motion delivering 3 Inches. This would equal 60 inch draw. You wish to put in 30 turns per inch, and you have an 18 inch Rim driving a 12 inch Cj^linder Pulley, and a 6 inch Cylinder driving a % whirl on spindle. Rule: — Multiply length of draw 60 Inches, by Turns per inch 30, and by Cylinder Pulley 12 inches, and diameter of Whirl on Spindle % of an inch. Take this for your dividend. Then mviltiply the Rim 18 inches by Cylinder 6 inches. Take this for your divisor. Example: 60X30X12X 3=64800 18X 6X 4 = 432 64800-^432=150. 150^2=75 twist gear. Note. — Always divide your answer by 2 on the D. & B. Mule, as it always works out twice the size of Twist Gear required. The reason you divide by 2 is: The Twist Gear revolves twice each draw, and on the Asa Lees's Mule the Twist Gear only revolves once each draw. 94 To Find Drag Gear. Suppose the Front Roll makes 19 revolu- tions per draw, and the Front Roll Spur Gear is 51, and Drag Gear Pinion is an 18, and Back Shaft Gear 68, and revolu- tions of Back Shaft 3.5 for a 64 inch draw. Rule:— Multiply Rev. of Front Roll 19, by Front Roll Spur Gear 51, and by Drag Gear Pinion 18. Take these for your dividend. Then multiply Back Shaft Gear 68 by Rev. of Back Shaft 3.5. Take this for your divisor. Example: 19X51X18=17442 68X3.5 = 238 17442-=-238=73 drag gear. Note. — For 60 inch draw use 3.28 in- stead of 3.5 for Rev. of Back Shaft and for 54 inch stretch use 2.95. To Find Draft. Suppose you have a 120 Crown Gear on, and 54 Back Roll Gear, and an 18 Front Roll Gear, and 40 Change Gear. Find the Draft. Example: 120X54=6480 18X40= 720 6480-=-720=9 of a draft. 95 TURNS OF SPINDLE TO ONE OF RIM Diam- eter of Rim 10 incn Cylinder 11 inch Cylinder Pulley Pulley Inches 6 in.Cyl. 6 in.Cyl. 6 in.Cyl. 6 in.Cyl ^whirl 1 iu.whirl! i X whirl 1 in. whir 12 8.95 1 6.84 1 8.14 6.22 13 9.70 7.41 8.81 6.73- 14 10.44 7.99 9.49 7.26. 15 11.19 1 8.55 10.17 1 7.77 16 11.93 9.12 10.84 8.29 17 12.68 9.70 11.52 8.81 18 13.43 10.27 12.20 9.33 19 14.19 • 10.84 12.90 9.85 20 1 14.92 11.41 1 13.56 10.37 12 inch Cylinder 13 inch Cylinder Pulley Pulley 12 1 7.46 5.70 6.88 5.26 13 8.14 6.17 7.46 5.70 14 8.70 6.65 8.02 6.14 15 9.32 7.12 8.60 6.57 16 1 9.94 J 7.6-) 9.17 7.01 17 1 10.56 ^ 8.08 9.75 7.46. 18 1 11.19 8.56 10.33 7.90' 19 1 11.82 9.03 10.91 8.32: 20 1 12.43 9.50 i 11.47 8.77 When finding turns of spindle to one o Rim, there is 1/16 of an inch added foi thickness of spindle band, to the Cylinde; and Whirl. The 6 inch Cylinder is reduced to six teenths. This is got by multiplying 1 by 6, which equals 96, and 1/16 added fo thickness of band equals 97. 96 There are 12 sixteenths in 3/4 of an inch, and 1/16 added equals 13. There are 16 sixteentlis in 1 inch, and 1/16 added equals 17. Suppose you have on an 18 inch Rim, ind a 12 inch Cylinder Pulley, a 6 inch Cylinder, and a % inch Whirl. Place them as follows: 18x97=1746 1746^156=11.19 turns. 12X13= 156 Suppose the whirl was 1 inch instead of 3/4. Place as follows: 18X97=1746 12X17= 204 1746^204=8.56 turns of spindle to one Df rim. NUMBERING YARNS. For every revolution of Reel handle, the Reel revolves twice ard winds on 1% vards at each revolution of Reel. If the landle has made 40 i evolutions, the Reel las made 80 revolutions, and SO times IV2 yards equals 120 yards or 1 Lea. Suppose 12 J yards of yarn weighs 25 grains. You divide the 25 into 1000 and his gives the Number or Count of the Yarn. j Example: 1000-^25 grs.=40s. yarn. 1 The reason for dividing 1000 by the ;veight (in grains) of 120 yards is because 1-20 yards is eoual to 1 '7 of 840 yards, or ■:. hark, and 1000 equals 1/7 of 7000 grains, )r 1 lb. 97 RING SPINNING FRAME. To Find Draft. Suppose you have on an 84 Back Roll Gear, and a 40 Change Gear, a 120 Crown Gear, a 30 Front Roll Gear, and the Back Roll is % of an inch diameter, and the Front Roll 1 inch diameter or 8 eights. Rule: — Multiply Back Roll Gear 84, by Crown Gear 120, and by diameter of Front Roll 1 inch, or 8 eights. Take this for a; dividend. ; Then multiply Change Gear 40 by Front- Roll Gear 30 and diameter of Back Roll' 7 eights. ". Example : 84X120X8 ==9.6 draft. 40X 30X7 To Find Constant for Draft Gear. Rule: — Proceed exactly as when finding draft, but leave out the Draft Gear. Example.: 84X120X8 =384 constant. 30X7 Constant divided by draft required gives Draft Change Gear. Example: 384 (constant) -=-9.6 draft=40 change gear. To Find "Turns per Inch" on the Whitin Spinning Frame. Rule:— Multiply Front Roll Gear 108, by Stud Gear 74, and by diameter of Cylin- der 7 inches. Take these for a dividend. Then multiply Twist Gear (which we will suppose to be) 40. by Cylinder Gear 36. and diameter of whirl % inch and circumference of Front Roll 3.1416. Example: 108X74X7 ^1^16.48 turns per inch. 40X36X.75 X3.1416 ! Deduct 117c for slippage and thickness lof bands. 16.48 less 119f=14.65. Actual turns per 'inch. To Find Constant for Twist Gear on Whitin Frame. Rule: — Proceed as when finding "ti;rns per inch," but omit the Twist Gear. Example: 108X74X7 =659 36X. 75X3. 1416 Deduct ll^'f from 659=586 Constant. Constant divided by '"turns per inch" gives Twist Gear. Constant 586 divided by 14 turns per inch equals 42 Twist Gear. To Find Turns Per Inch on the H. and B. Frame. Rule:— Multiply Front Roll Gear 84, by Jack Gear 72, and diameter of Cvlinder 7 inches. Take these for a dividend. Then multiply Twist Gear (suppo.sed to be) 40. by Cylinder Gear 21. and bv diam- eter of Whirl "s of an inch, and circum- ference of Front Roll 3.1416. 99 Example: 84X72X7X8 =1 8.33 40X21X7X3.1416 Deduct 15% from 18.33 on H. and B. Frames. 18. 33X. 85=15. 58 actual turns per inch. Constant for Twist Gear on H. and B Frame. Rule: — Proceed as when finding turns per inch, but omit Twist Gear. Example: 84X72X7X8 =733 21X7X3.1416 Deduct 15% from 733. 733 X. 85=623 Constant. Constant divided by turns per inch gives Twist Gear. (Constant) 623-:-15.58 (turns per inch)= 40 T. G. A fixed rule cannot be given for the weights of travellers, as an inferior grade of cotton, a large draft, and a larger ring, requires a lighter traveller. Whilst good stock, and more twist in the yarn, also the spindles running quicker, re- quires a heavier traveller, although spin- ning the same Counts or Numbers. 100 To Find Average Counts Being Spun. Rule: — Proceed exactly as when finding average numbers given on the Mule. Keep the spindle rail and roller beam level, the spindle perfectly upright, or vertical and in the centre of the ring, when the rail is at the highest and lowest point of traverse. The guide wires should be set exactly over centre of the spindle (with spindle band on). HORSE POWER REQUIRED. Spin- I.H.P. dies. Hopper Bale Breaker 2 Automatic Feeder li/^ Opener 2 Picker (Single Beater) 4 Picker (Double Beater) 8 Flat Card 1 Sliver Lap Machine V2 Ribbon Lap Machine 1 6 Head Single Nip Comber... % 8 Head Single Nip Comber... 1 Drawing Frame (12 Deliveries) IVz Slubbing Frame 1 45 Intermediate Frame 1 65 Roving Frame 1 85 Jack Frame 1 105 Fine Mule 1 130 Coarse Mule 1 115 Ring Spinning Frame 1 75 WOONSOCKET MACHINE AND PRESS CO. =WOONSOCKET, R. I.^= Builders of Fly Frames, Cloth Presses,Cloth Trim= mers, Woolen Card Feeds, Transmission Machinery, and Yarn Gassing Aiach= ines. DRAPER COMPANY HOPEDALE, MASS. Makers of the celebrated NORTHROP LOOM And all kinds of Ring Spinning Spindles, Rings etc., Twisters, Spoolers, Banding Machines, Warpers, Balling Mach- ines, and Reels. SACO AND PETTEE Builders of Revolving Flat Card, Railway Heads, Drawing Frames, Roving Frames, Spinning Frames, Spoolers and Reels, MAIN OFFICE: NEWTON UPPER FALLS, MASS., U. S. A. WORKS : NEWTON UPPER FALLS, AND BIDDEFORD, ME. SOUTHERN AGENT: A. H. WASHBURN, CHARLOTTE, N. C. The Whitin Machine Works WHITINSVILLE, MASS., U. S. A Builders of Revolving Flat Cards, Spoolers, Sliver Lap Machines, Quillers, Ribbon Lap Machines, Reels, Comb- ing Machines (high speed). Twisting Frames, Railway Heads, Plain Looms, Drawing Frames, Drop Box Looms, Roving Machines, Dobbies, Spinning Frames, and all com- ponent parts. Southern Offices : Charlotte, N. C. and Atlanta, Ga. Stuart W. Cramer, Southern Agt. // you are contemplating building, or ctianging over your old macliinery, write to the . . . METALUC DRAWING ROLL COMPANY for prices and advantages of ttieir METALLIC ROLLS 25 to 33 fo more production guaranteed, tlian can be re= ceived from any leattier roil, INDIAN ORCHARD, MASS. LIBRARY OF CONGRESS illlilliililllilllillliil 018 533 836 8 •