,«^ ^^y ^•b-^ %<^'^ \^^' -^.- <'^ •'o .^^^ \:^7r::^\<^ o ° .0 \' . r- ,xV Jy^'^^ ^ tj- ,0'^ ^0 %, ^^ V " "^ " I 1 '' > ■*■ ^ " /■ C> - .- -. •» yfi ,1^ N>\-; dV ^^% ^vjc#*° '^:^^ '^_ y^-«^j|>^^ ^- ,j.V ^-^ -^-'l^^^^ .'■^ '^.. C^^' c'^'-'^'^' ■^aQ< .<^ •^c ^^ ■is. \^ <1^ ^ "V; " ^"^-^ ■• •^ y -K^i- « /, ,-" . , ^^.^ *0 NO- ^ X^^' ^^ ' O , X ^ .'\ '^/^^ffs^'^^ AV -^c ■. '^ ^' /■ ^^^■ ^^■^ s^ A> '^.. > 1' V / ^'^^ ^ o V^^''^^. 1, )^ v«'?*/< \0 o. > A^^ ^i « o .^ .^^' ''^: .S^ m MLLL-GEAErSTG. 13 210 5 1050 3 B . . . . 10)3150 B . . . . 5)315 A . . . 63)63 1 A. 63 = 63 Teeth in tlie first driven wheel. B. 10 X 5 = 50 Teeth in the second driven wheel. Answer. !N^.B. — It will be perceived, by a little reflection, that the driven wheels are found by first dividing the product of the double strokes per minute of the steam-engine, and the number of teeth in the driving wheels by the revolu- tions per minute of the upright shaft, and the quotient by as many numbers as will divide without a remainder. The last divisors are classed according to the number and size of wheels required, which is dictated by location and other circumstances. The product of the numbers in each class gives the respective wheels. From the particulars found in the preceding example, find the revolutions per minute of the upright shaft. 14 COTTON MANUFACTURE. Teeth in the first driven wheel 63 Teeth in the second driv- en wheel 50 60 Double strokes per mi- nute of the steam- engine. 210 Teeth in the first di'iv- ing wheel. .54 Teeth in the second driving wheel. Worked out hy Ccmcellation. 504 l-T-63 210-30 1-50 54-6 30 X 6 = 180 Answer. Hie sa/me without Ccmcellation. Dividend . . 50 x 210 x 54 Divisor ... 63 x 50 = 180 Answer. l^.B, — The product of all the terms on the left-hand side of the perpendicular line into the answer will equal the product of all the terms on the right-hand side of this line. Thus : 63 x 50 x 180=567000 ; 210 x 54 x 50 = 567000. Hence we have the following rule to find any of the above terms : Place all the terms classed with the one sought on the left-hand side, for a divisor (less the term sought), and all the rest on the right-hand side for a MILL-GEAEING. 15 dividend, and proceed by cancellation or multiplication : divide the product of the terms on the right-hand side by the product of the terms on the left-hand side, and the quotient will be the answer. This rule applies to all problems of this nature. From the particulars found in the preceding example, find the number of teeth in the driven wheels. Wo7'ked out hy Cancellation. 504 21(0 1-248(0 1-50 54:-6-3 21 X 3 = 63 Teeth in the first driven wheel. Answer. The same without Ca/ncellation. Dividend . . . 50 x 210 x 54 no = DO. Divisor .... 180 x 50 Answer. Worked out hy CoMcellation. 1-348(0 l-Y-63 5(0 210-30-10 54-6-1 10 X 5 = 50 Teeth in the second driven wheel. Answer. IG COTTON MA]SniFACTlIRE, The sa/me without Cancellation. Dividend . . . 50 x 210 x 54 ^ ^^ Divisor .... 180 x 63 Answer. From the particulars found in the preceding example, find the double strokes per minute of the steam-engine, and the number of teeth in the driving wheels. Worhed out hy CamjCellation. 180-20-10 1-21(0 63-3-1 1-2-6-54 5(0 10 X 5 = 50 Double strokes per minute of the steam- engine. Answer. The same without Cancellation. Dividend . . . 180 x 63 x 50 ^^ — = 50. Divisor .... 210 x 54 Answer. Worked out l)y Cancellation. 1-50 1-6-54 180-30 63-7 50-1 30 X 7 210 Teeth in the first driving wheel. Answer. MILL-GEAEESTG. 17 TTie same without Ca/ncellation. Dividend . . . 180 x 63 x 50 ^ ^lo Divisor .... 54 x 50 Answer. Worked out hy Cancellation. 1-50 18(0 1-21(0 63-3 50-1 18 X 3 == 54 Teeth in the second driving wheel. Answer. The same without Ca/ncellation. Dividend . . . 180 x 63 x 50 k. = 54. Divisor .... 210 x 50 Answer. MIXING COTTON. To mix together different qualities of cotton, so as to get the best possible combination for the purpose of mak- ing any given kind of yarn at the least possible expense, is an art of the very greatest importance. The way of mixing cotton most commonly practised is to take as many bales as the mixing-room will conveni- ently hold, and 8j)read them in layers on the top of each 18 COTTON MANUFACTURE. other, covering as large an area as tlie room will admit of. It is taken from top to bottom of the pile with a rake when wanted for use. Some cotton-spinners obtain the best results by keep- ing the different qualities of cotton separate until they have passed through the cards, a system that has many arguments in its favor. It is the most practicable way to make good, even yarn, to use one kind of cotton only, but this is not always the cheapest way; hence arises the necessity of mixing cottons. Suppose a mill to consume 40 bales of cotton per week, each weighing 500 pounds, one half at 42 cents, and the other half at 36 cents per pound : the total cost of cotton per week would be $T,800, while, if the whole was at 42 cents per pound, the cost per week would be $8,400, a difference of $600 per week, or $100 per day, in favor of mixing. THE WILLOW. The Willow is the first machine to which the cotton is subjected in its process of manufacture. The cylinder of a Bacon-Willow contains 1036 claws, and makes 500 revolutions, more or less, while the feed- rollers feed one pound of cotton, displaying 1036 x 500, 518000, claws in rapid motion. These tease the THE WILLOW. 19 cotton into as many loose tufts, and, as far as is practica- ble, undo what has been done for convenience in transpor- tation, free it from a superabundance of moisture and other impurities, and by the force of wind, created by the motion of the cylinder, carry it into a ventilated room convenient to the lapper. THE LAP PEE. As will subsequently be shown, the lapper is the machine at which the cotton first receives definite form and size. Some manufacturers contend tliat the size or decimal of a hank produced at a lapper cannot be depended upon as being positive ; that at best it is but an approximation and guess at the quantity of cotton spread on to the lat- tice, substituting an "evener" for the old system of spreading a definite weight on to a definite length. The Whiting Lapper is the one most generally appre- ciated in this neighborhood; being easy to manage, not liable to get out of order, and, with proper weighing, pro- duces good and truthful results, A lapper has three beaters. The first one makes 1800, the second 2000, and the third 2200 revolutions per minute. They are driven from an upright shaft, making 180 revolutions per minute by a train of tliree pairs of 20 COTTON MANTTFAOTUKE. pulleys, and one pair of wheels. The driving wheel has 96 teeth, and the respective diameters of the driving pul- leys are 40, 32, and 20 inches. How many teeth should there be in the driven wheel, and what should be the respective diameters of the driven pulleys, to drive the first beater at the speed above named? Revolutions per minute of the first beater, 1800 180 Revolutions per minute of the upright shaft. 96 Teeth in the driving wheel. 40, Diameter of the first driving pulley in inch- es. 32, Diameter of the second driving pulley in inch- es. 20, Diameter of the third driving pulley in inch- es. Worked out. 148(00 18(0-1 96 4(0 32 20 {Continued^ IHE LAPPER. 96 4 384 32 768 1152 12288 20 A . . . 2)245760 A . . 2)122880 A . . 2)61440 A . . 2)30720 A . 2)15360 A . 2)7680 B 2)3840 B 2)1920 B 2)960 B 2)480 B 2)240 C . 2)120 C . {Cont mv ed. 2)60 21 22 COITON MANUFACTURE. D . . 2)30 D . . 3)15 • • • 5)5 1 A. 2x2x2x2x2x2 = 64 Teeth in the driven wheel, B. 2x2x2x2x2 = 32, Diameter of the first driven pulley in inches. C. 2x2x5 = 20, Diameter of the second di-iven pulley in inches. D. 2x3 6, Diameter of the third driven pulley in inches, which is on the same axis with the first beater. Answer. The first beater of a lapper is driven fi'om an upright shaft making 180 revolutions per minute by a train of three pairs of pulleys and one pair of wheels. The driv- ing wheel has 96, and the driven wheel 64, teeth. The respective diameters of the di'iving pulleys are 40, 32, and 20, and of the di-iven pulleys, 32, 20, and 6, inches. How many revolutions per minute does the first beater make ? 180 Eevolutions per minute of the upright shaft. Teeth in the driven wheel 64 wheel. 96 Teeth in the driving THE LAPPEE. 23 Diameter of the first driven puUej in inch- es Diameter of the second driven pulley in inch- es Diameter of the third driven pnlley in inch- es 32 20 40, Diameter of the first driving pulley in inch- es. 32, Diameter of the second diiving pulley in inch- es. 20, Diameter of the third driving pulley in inch- es. Worked out hy GrniGellation. 180 9646-1 40-10 324 204 4-64 1-32 1-20 1-6 180 X 10 1800 The srnne without Ccmcellation. Dividend . 180 x 96 x 40 x 32 x 20 Divisor . . Answer. = 1800 64 X 32 X 20 X 6 Answer. The lattice-roller and lattice are, in effect, equal to a roller 4 inches in diameter. On the same axis with the 24 COTTON MANTJTAOTUEE. lattice-roller, there is a wheel that takes into a wheel with 9 teeth, on the feed-roller. On the feed-roller there is also a wheel that takes into a wheel with 42 teeth, on the under shaft. On the other end of the under shaft there is a wheel that takes into a wheel with 32 teeth, on the side- shaft. On the other end of the side-shaft there is a wheel that takes into a wheel with 32 teeth, on the clutch-shaft. On the clutch-shaft there is also a wheel that takes into a wheel with 100 teeth, on the calender-roller. On the other end of the calender-roller there is a wheel that takes into a wheel with 26 teeth, on the lap-roller. Sup- pose the wheels that have their dimensions given above to be driving wheels, what should be the dimensions of. the driven wheels and the lap-roller to produce a draught of 3? N.B. — The intermediate wheels are not taken into account in the above. 4, Diameter of the lattice- roller, including lat- tice, in inches. 9 Teeth in the wheel on the feed-roller. 42 Teeth in the wheel on the under shaft. 32 Teeth in the wheel on the side-shaft. THE LAPPEB. 25 32 Teeth in the wheel on the clutch-shaft. 100 Teeth in the wheel on the calender-roller. 26 Teeth in the wheel on the lap-roller. 3, Draught of the lapper. Worked out. 26 100 2600 32 5200 7800 83200 32 . 166400 249600 2662400 42 5324800 10649600 {Continued.) 2 26 COTTON MANUFACTURE. C D B . 111820800 9 1006387200 4025548800 3 13)12076646400 . 10)923972800 , 10)92897280 E F F G D E E E C 7)9289728 4)1327104 4)331776 4)82944 4)20736 4)5184 4)1296 {Continued.) . 3)324 . 3)108 . 3)36 . 3)12 THE LAPPEK. 27 C 2)4 D . . . . 2)2 1 A. 7 • 7, Diameter of the lap-roller in inches. B. 10 X 3 =^ 30 Teeth in the wheel on the lattice- roller. C. 13 X 3 X 2 78 Teeth in the wheel on the feed-roller that takes into the wheel on the undershaft. D. 10 X 4 X 2 80 Teeth in the wheel on the undershaft that takes into the wheel on the side-shaft. E. 4x3x3 36 Teeth in the wheel on the side- shaft that takes into the wheel. on the clutch-shaft. F. 4x4 = 16 Teeth in the wheel on the clutch- shaft that takes into the wheel on the calender-roller. Gr. 4x4 = 16 Teeth in the wheel on the calender- roller that takes into the wheel on the lap-roller. Answer, From the particulars found in the preceding example, find the draught of the lapper. Worked out hy Cancellation. 1-4 74 1-9 3(04 1-2-6-42 78-3 {Conti nued.) 28 COTTON MANUFACTURE. 1-2-32 8(04-24 1-2-32 3644 1(00 164 1-26 164 Answer. The sa/me without Ccmcellation. Dividend, 7 x 30 x Y8 x 80 x 36 x 16 x 16 ^^ ^ Divisor, 4 x 9 x 42 x 32 x 32 x 100 x 26 Answer. The lattice-roller and lattice of a lapper are, in effect, equal to a roller 4 inches in diameter ; and the lap-roller is 6.98Y5 inches in diameter. Suppose the lap-roller to be the driver of the lattice by- a train of six pairs of wheels ; the driving wheels to have respectively 9, 45, 32, 32, 100, 26, the driven wheels 30, 100, Y2, 32, 15, and 16 teeth. What would be the draught of the lapper ? Worlced out hy Cancellation. 14 6.98Y5-2.68T5 1-9 30-34 14545 1004 1-2-32 Y2-8-24 1-32 324 1400 154 1-2.6-26 164 2.68T5 Answer. THE LAPPER. 29 The same without Cancellation. • Dividend, 6.98Y5 x 30 x 100 x Y2 x 32 x 15 x 16 _g ^g^g Divisor, 4 x 9 x 45 x 32 x 32 x 100 x 26 Answer. The lattice and lattice-roller are, in effect, equal to a roller 4 inches in diameter; and the feed-roller is 1^ inches in diameter. The lattice-roller has on a wheel with 30 teeth, that, by means of an intermediate, takes into a wheel with 9 teeth on the feed-roller. Required the draught between the lattice and the feed- roller. WorJced out hj Cancellation. 1-4 I 1.5-.5 l-3'9 30-10-2.5 Answer. 2.5 X .5 = 1.25 The same without Cancellation. Dividend 30 x 1.5 _ ^ nfc Divisor 4x9 Answer. The calender-roller is 4, and the lap-roller 6.9875 inches in diameter. The calender-roller has on a wheel with 16 30 COTTON MAJSrUFACTUEE. teeth, that, by means of an intermediate, takes into a wheel with 26 teeth on the lap-roller. Required the di'aught between the calender-roller and the lap-roller. Worked out hy Cancellation. 1-4 1-6.5-26 6.98T54.075 1644 1.075 Answer. The same without Cancellation. Dividend 6.9875 x 16 _ ^^ ^^^ Divisor ...... 26 x 4 Answer. The draught between the lattice and the feed-roller is 1.25, and between the calender-roller and the lap-roller, 1.075. Required the draught between the feed-roller and the calender-roller, the total draught being 2.6875. Worked out 'by Cancellation. 14.25 14.075 2.6875-2.15-2 Answer. THE LAPPER. 31 The same without Ccmcellation. Dividend 2.6875 = 2 Divisor 1.0T5 x 1.25 Answer. From the particulars found in the preceding example, find the total draught of the lapper. 2 X 1.25 X 1.075 = 2.6875 Answer. On the same axis with the lap-roller there is a wheel with 26 teeth, that, by means of an intermediate, takes into a wheel with 16 teeth on the calender-roller. On the calender-roller there is also a wheel with 100 teeth, that takes into a wheel with 15 teeth on the clutch-shaft. On the clutch-shaft there is a pulley 25,92 inches in dia- meter, driven from a pulley on the first driven shaft. On the first driven shaft there is a pulley 20 inches in dia- meter that drives a pulley 6 inches in diameter on the same axis with the first beater. What should be the diameter of the pulley on the first driven shaft that drives the pulley on the clutch-shaft, to drive the lap-roller 5 revolutions per minute, the first beater making 1800 in the same time? 25,92, Diameter of the pul- ley on the clutch- shaft, in inches. 32 COTTON MANUFACTIEBE. Teeth in tlie wheel on the calender - roller that takes into the wheel on the lap- roller Teeth in the wheel on the clutch-shaft . . 16 15 Diameter of the pulley on the same axis with the beater, in inches 6 Revolutions per minute of the first beater, 1800 26 Teeth in the wheel on the lap-roller. 100 Teeth in the wheel on the calender - roller that takes into the wheel on the clutch- shaft. 20, Diameter of the pulley on the first driven shaft that drives the first beater, in inches. 5 Revolutions per minute of the lap-roller. Worked out hy Cancellation. 25.924.M-.24-.08-.02 1446 26 1-345 1(00 1-6 2044 148(00 5 26 X 5 X .02 : 2.6 inches. Answer. THE LAPPER. 33 The same without Cancellation. Dividend, 25.92 x 26 x 100 x 20 x 5 ^ ^ 6 Answer. Divisor, 16 x 15 x 6 x 1800 From the particulars found in the preceding example, find the revolutions per minute of the first beater. Worked out hy Cancellation. 5-1 1446 1-345 1-2.6 1-6 26-10 100 25.92-8.64:-l.M-.36 20-5 100 X 10 X 5 X .36 = 1800 Answer. The same without Ccmcellation. Dividend . . 5 x 26 x 100 x 25.92 x 20 _ ^g^^ Divisor . . 16 x 15 x 2.6 x 6 Answer. The fan that takes the dust fi-om a lapper is 1 yard in diameter, driven from an upright shaft making 180 revo- lutions per minute by a train of three pairs of pulleys and 2* 34 COTTON MANUFACTUBE. one pair of wheels. The driving wheel has 96 teeth, and the respective diameters of the driving pulleys are 40, 30, and 20 inches. How many teeth should there be in the diiven wheel, and what should be the respective diameters of the driven pulleys, to give the circumference of the fan a velocity of 1728 yards per minute ? Velocity of the circum- ference of the fan per minute, in yards, 1T28 180 Revolutions per mi- nute of the upright shaft. 96 Teeth in the driving wheel. 40, Diameter of the j&rst driving pulley, in inches. 30, Diameter of the sec- ond driving pulley, in inches. 20, Diameter of the third dri"^dng pulley, in inches. 1, Diameter of the fan, in yards. 3.1416, Circumference. THE LAPPEK. 3 Worked out. 18045 96-8 40 30 20 1 1-124M4728 34416-.2618 15 120 40 4800 30 144000 20 2880000 .2618 23040000 2880000 17280000 5760000 {Continued.) 36 COTTON MAJSTDFACTURE. A . . 4)Y53984.0000 A . . . . 4)188496 A . . . . 4)47124 D . . 2)11T81 B . . . . 2)5890.5 B . . . . 2)2945.25 B . . . 3)1472.625 B . . . . 3)490.875 D . . 7)163.625 C . 23.375)23.375 A. 4x4x4 = 64 Teeth in the di'iven wheel. B. 3x3x2x2 36, Diameter of the first driven pulley, in inches. C. 23.375 = 23.375, Diameter of the second driven pulley, in inches. D. 7x2 . 14, Diameter of the third driven pulley, in inches. Answer. From the particulars found in the preceding example, find the velocity of the circumference of the fan per minute. THE LAPPEE. 37 Worked out hy Cancellation. 18045-3 1-8-64: 96-12 1-3-36 40-54 1-.9354.6T5-23.3T5 3040-5 1-2-14: 20 1 34416-3.36-48 3 X 12 X 5 X 20 X 48 1728 yards. Answer. The same without Cancellation. Dividend, 180 x 96 x 40 x 30 x 20 x 3.1416 ^ Divisor, 64 x 36 x 23.375 x 14 4728 Answer. CAKDING-ENGINE. What the Willow and Lapper perform in part, the carding-engine completes in a thorough cleansing of the cotton. The main cylinder of a common-sized carding-engine, when carding for medium numbers, makes about 120 revolutions per minute, and contains 22 sheets of cloth- ing, each 30 X 4 inches, containing 400 teeth to the square inch, and cards one pound of cotton every 20 minutes, more or less. Hence every pound of cotton is 6>i COTTON MANUFACTURE. picked from the feed-rollers, fibre by fibre, b}' 120 x 22 X 30 X 4 X 400 X 20 2534400000 diamond-pointed teeth, which by their traction and that of the top cards, or slats, untangles the fibres, and lays them more or less parallel to each other, and by suitable apparatus, delivers them formed into a " sliver." The main cylinder of a carding-engine is driven from an upright shaft, making 180 revolutions per minute, by a train of one pair of wheels and one pair of pulleys. The driven wheel has 96 teeth, and the driven pulley is 12 inches in diameter. How many teeth should there be in the driving wheel, and what should be the diameter of the driving pulley, to di-ive the main cylinder 120 revolu- tions per minute ? Revolutions per minute of the upright shaft 180 120 Revolutions per minute of the main cylinder. 96 Teeth . in the di'iven wheel. 12, Diameter of the driven pulley, in inches. Worked out. 1-348(0 12(0-2 96 124 {Cmitinued.) CAEDIN.G-ENGINE, 39 96 4 384 2 B . . 12)Y68 A. . . 64)64 1 A. 64 ^= 64 Teeth in tlie driving wheel. B. 12 ■ 12, Diameter of the driving pulley, in inches. Answer. From the particulars found in the preceding example, find the revolutions per minute of the main cylinder. Worked out by Ccmcellation. 180-15 1-12-96 142 64-8 124 15 X 8 = 120 Answer. Tfie same without Ccmcellation. Dividend .... 180 x 64 x 12 ^ -j^^o Divisor .... 96 x 12 Answer. 40 COTTON MANUFACTURE. The main cylinder makes 120 revolutions per minute, and drives the dothng-cylinder by a train of two pairs of wheels. The driven wheels have each 180 teeth. How many teeth should there be in each of the driving wheels to drive the doffing-cyhnder 9 revolutions per minute ? Revolutions per minute of the main cylinder, 120 9 Revolutions per minute of the doffing-cylin- der. 180 Teeth in the first driven wheel. 180 Teeth in the second driven wheel. Worked out. 142(0 9 180-15 18(0 18 15 90 18 2T0 9 {^Cooitmued.) CARDESTG-KNailSrE. 41 A 10)2430 A 3)243 B 81)81 1 A. 10 X 3 = 30 Teeth in the first driving wheel. B. 81 ■ 81 Teeth in the second driving wheel. Answer. From the particulars found in the preceding example, find the revolutions per minute of the doffing-cylinder. Worked out hy Ccmcellation. 12(04 145480 30-24 1-948(0 81-9 Answer. The same without Ccmcellation. Dividend . . . . . 120 x 30 x 81 Divisor 180 x 1-80 Answer. The lap-roller is 4^ inches in diameter, and has on a 42 COTTON MANUFACTUEE, wheel, that, by means of an intermediate, takes into a wheel with 10 teeth on the feed-roller. How many teeth should there be in the wheel on the lap-roller, and what should be the diameter of the feed-roller to produce a draught of 1.1 ? 4.5, Diameter of the lap- roller, in inches. 10 Teeth in the wheel on the feed-roller. 1.1, Draught. Worked out. 4.5 10 45.0 1.1 450 450 A .... . 3)49.50 A 11)16.5 B . . . . 1.5)1.5 1 A. 11 X 3=33 Teeth in the wheel on the lap-roller. CAKDING-ENGINE. 43 B. 1.5 = 1.5, Diameter of the feed-roller in inclies. Answer. From the particulars found in the preceding example, find the draught between the lap-roller and the feed- roller. Worked out l/y Crnicellation. 1-34.5 140 1.54 33414.1 1.1 The sa/me witliout Cancellation. Dividend 33 x 1.5 Divisor 10 x 4.5 Answer. 1.1 Answer. The doffing-cylinder is 15, and the drum at the railway that drives the belt (belt included) is 10, inches in dia- meter. They are connected by a train of four pairs of wheels and one pair of pulleys. Suppose the drum to be the driver, and the driving wheels to have respectively 100.70, 40, and 20 teeth, and the driving pulley to be 4 inches in diameter. How many teeth should there be in the driven wheels respec- tively ; and what should be the diameter of the driven 44 COTTON MANTJFACTUEE. pulley, to produce a draught of 1.04 between the doffing- cylinder and the di-um at the railway ? Worked out. 1(0 15 20 4 40 TO 10(0 1.04 1.04 10 10.40 70 T28.00 40 29120 4 116480 20 2329600 15 11648000 2329600 34944000 CAKDING-ENGINE, 45 E . . 10)34944000 D . . . 5)3494400 A 5)698880 A 2)139776 A 2)69888 E . . . 2)34944 E . . . 2)17472 E . . . . 2)8736 B 2)4368 B 2)2184 B 2)1092 B 2)546 D 3)273 C 91)91 1 A. 5x2x2 , 20 Teeth iu the first driven wheel. B. 2x2x2x2 16 Teeth in the second driven wheel. C. 91 = 91 Teeth in the third driven wheel. D. 5x3 15, Diameter of the driven pulley, in inches. 46 COTTO"N MANUFACTUKE. E. 10 X 2 X 2 X 2 wheel. 80 Teeth in tlie fourth di-iven From the particulars found in the preceding example, find the draught between the doffing-cylinder and the drum at the railway. Diameter of the doffing- cylinder, in inches, 15 Teeth in the fourth driv- ing wheel .... 20 Diameter of the driving pulley, in inches . . 4 Teeth in the third di'iv- ing wheel .... 40 Teeth in the second di'iving wheel . . . YO Teeth in the first driv- ing wheel . . . .100 10, Diameter of the di'mn, in inches. 80 Teeth in the fourth driven wheel. 15, Diameter of the driven pulley, in inches. 91 Teeth in the third driven wheel. 16 Teeth in the second driven wheel. 20 Teeth in the first di'iv- en wheel. Worlied out l)y CcmGellaUon. 1-15 104 1-20 8(0-.2 1-4 154 1-40 91434.3 l-Y-70 164 140(0 204 4 X 1.3 X .2 1 .r Answer. OAEDESra-ENGINE. 47 The same without Cancellation. Dividend, 10 x 80 x 15 x 91 x 16 x 20 _ Divisor, 15 x 20 x 4 x 40 x 70 x 100 " ^'^^ Answer. The feed-roller is driven from the doffing-cylinder by a train of two pairs of wheels. The driven wheels have respectively 60 and 50 teeth. How many teeth should there be in the driving wheels to produce a draught of 80 between the lap-roller and the railway-head, allowing a draught of 1.04 at the railway, and 1.1 between the lap-roller and the feed-roller, the feed-roller being 1|-, and the doffing-cylinder 15, inches in diameter? E".B. — In all cases where the draught of the carding- engine is mentioned in this work, the draught at the rail- way is included. Worked out. 14.5 1-8(0 154(0 60 50 1.1 1.04-.13 {Contmued.) 48 COTTON MANTIFACTURE. 60 60 3000 1.1 3000 3000 3300.0 .13 99000 33000 A . . . . 3)429.000 A 11)143 B . . . . 13)13 1 A. 11x3 33 Teeth in the first driving wheel. eheel. Answer. B. 13 = 13 Teeth in the second driving wheel. From the particulars found in the preceding example, find the draught of the card. Diameter of the feed- I 15, Diameter of the doflfing roller, in inches . . 1.5 | - cylinder, in inches. CAEDLNG-ENGINE. 49 Teeth in the first di*iv- ing wheel .... 13 Teeth in the second driving wheel . . .33 60 Teeth in the first driv- en wheel. 50 Teeth in the second di'iven wheel. 1.1, Draught between the lap-roller and feed- roller. 1.04, Draught at the rail- way. Worked otd hy CoAicellaiion. 14.5 1540 143 60-2 1-30-33 50 1.14 1.04-.08 50 X 10 X 2 X .08 80 Answer. The same without Cancellation. Dividend . . 15 x 60 x 50 x 1.1 x 1.04 . Divisor ... 1.5 x 13 x 33 Answer. The railway-head treated on below has four pairs of 3 60 COTTON MANUFACTURE. rollers with " Draper's Patent Evener " attached, adapted for 12 cards. The roller next to the front-roller is called the front- in iddle-roller, and the roller next to the back-roller is called the back-middle-roller. The front-roller is driven from the back-roller by a train of three pairs of wheels, and one pair of cones. The back-middle-roller and the front-middle-roller are each driven from the back-roller by an intermediate wheel. The tube throngh which the sliver passes, and the apparatus for moving the belt on the cones, are so adjust- ed, that, if the fleece delivered from one of the cards should break, they will cause the belt to move from the large end of the driving cone sufficient to reduce the speed of the front-roller -^ ; and, if the fleece should break from two cards, j^^, etc., etc., — thus keeping the sliver delivered of a uniform size. EAILWAT-HEAD. The front-roller is 1^ inches in diameter, and has on a wheel, that, by means of an intermediate, takes into a wheel with 80 teeth on the same axis with the delivering balls. How many teeth should there be in the wheel on the front-roller, and what should be the diameter of the delivering balls, to produce a draught of 1.02 ? draper's railway head. BAILWAT-HEAD. 51 Worked out. 1.02 1.25 80 B . 1.25 80 100.00 1.02 20000 100000 . 3)102.0000 . . . 34)34 1 A. B. 34 3 = = 34 Teeth in the wheel on the front-roller. 3, Diameter of the delivering balls, in inches. Answer. The front-roller is IJ, and the delivering balls 3, inches in diameter. The front-roller has on a wheel with 34 teeth, that, by means of an intermediate, takes into a wheel with 80 teeth, on the same axis with the delivering balls. Beqtdred the draught. 52 COTTON MANUFACTUKE. Diameter of the front- roller, in inches, 1.25 Teeth in the wheel on the same axis with the delivering balls, 80 3, Diameter of the deliver- ing balls, in inches. 34 Teeth in the wheel on the front-roller. Worlied out lyy Ccmcellation. 14.25 1-80 3-2.4-.03 34 Answer. 34 X .03 = 1.02 The same loithout Cancellation. Dividend ..... 3 x 34 = 1.02 Divisor ...... 1.25 x 80 Answer. The front-roller is driven from the back-roller by a train of 3 pairs of wheels, and one pair of cones. The driven wheels have respectively 100, 18, and 51 teeth ; and the driven cone is 3 inches in diameter at the small end. How many teeth should there be in the driving wheels respectively, and what should be the diameter of the large end of the driving cone, to produce a draught of 2 at the railway-head, allowing a draught of 1.02 between the RAILWAY-HEAD. 53 front-roller and the delivering balls, the front-roller being 1^, and the back-roller, 1 inch in diameter ? N.B, — The belt is always at the large end of the driv- ing cone, and, of course, at the small end of the driven cone, when the cards are utihziiig their maximum quan- tity. Worked out. 1-1.02 14.25 2 1 100 18 3 51-5040 10 3 120 18 960 120 2160 100 216000 2 432000 54 COTTON MANUFACTURE, A . 10)432000 B . 5)43200 B . 5)8640 A . . 2)1728 A . . . . 2)864 A . . . . 2)432 D. . . . 2)216 D. . . . 2)108 D. . . . 2)54 D. . . . 2)2Y B • • . . 3)13.5 C 1 1 • • . 4.5)4.5 1 A. 10 X 2 X 2 X 2 80 Teeth in the first driving wheel. B. 5x5x3 == T5 Teeth in the second di-iving wheel. C. 4.5 4^, Diameter of the large end of the di-iv- ing cone, in inches. D. 2x2x2x2 16 Teeth in the third di-iving wheel Answer. KAIL WAY-HEAD. 55 From the particulars found in the preceding example, find the total draught at the railway-head. Diameter of the back- roller, in inches . . 1 Teeth in the first driven wheel 100 Teeth in the second driven wheel ... 18 Diameter of the small end of the driven cone, in inches . . 3 Teeth in the third driv- en wheel .... 51 1.02, Draught between the front-roller and de- livering balls. 1.25, Diameter of the front- roller, in inches. 80 Teeth in the first driv- ing wheel. T5 Teeth in the second driving wheel. 4.5, Diameter of the large end of the driving cone, in inches. 16 Teetli in the third driving wheel. Worked out hy Ca/ncellation. 1.02-.02 1 1.25 1-5400 8044 1448 Y545-5 1-3 4.54 1-51 16 16 X 5 X 1.25 X .02 Answer. 56 COTTON MANUFACTDEE. The same witJiout Ccmcellation. Dividend, 1.02 x 1.25 x 80 x Y5 x 4.5 x 16 ^ ^ Divisor, 100 x 18 x 3 x 51 Answer. From the particulars given to find tlie di'aught be- tween the back-roller and the front-roller, and the parti- culars given to find the draught between the front-roller and the delivering balls, find the total draught. Worked out hy CcmcellaUon, 34 34-1 1.25-1 804 Y5-.75-.5 4.54 164 14.25 1-80 1 1400 1448 1-3 4.5-51 4 X .5 Answer. The same without Cancellation. Dividend, 3 x 34 x 1.25 x 80 x Y5 x 4.5 x 16 ^ ^ Divisor, 1.25 X 80 X 100 X 18 x 3 X 51 Answer. EAILWAT-HEAD. 57 From tlie particulars found in the preceding example, find tlie draught between the back and the front rollers. Worked out hy Cancellation. 1 1.25 1-5400 8044 1448 Y5-25-5 1-3 4.54 1-51 16-.3A 1.25 X 5 X .3 ^ 1.96A Answer. The same wiiliout Cancellation. Dividend, 1.25 x 80 x 75 x 4.5 x 16 ^-^^^^ Divisor, 100 x 18 x 3 x 51 ' ^^ Answer. The back and the back-middle rollers are each 1 inch in diameter. The back-roller has on a w^heel with 21 teeth. How many teeth should there be in the wheel on the back- middle-roller to produce a draught of 1.05 ? WorTced out hy Cancellation. 14.05 I 21-20 20 Answer. 68 COTTON MANUFACTUKE. From the particulars found in the preceding example, id the drai middle-roller. find the draught between the back-roller and the back- Worked out h/ Ca/ncellation. 1-20 I 21-1.05 1.05 Answer. The back-roller and the front-middle-rollers are each 1 inch in diameter. The front-middle-roller has on a wheel with 20 teeth. How many teeth should there be in the wheel on the back-roller to produce a draught of 1.25 ? 20 X 1.25 = 25 Answer. From the particulars found in the preceding example, find the draught between the back-roller and the front- middle-roller. Wm^hed out hy Cancellation. 1-20 I 25-1.25 1.25 Answer. From the wheels given to find the draught between the BAILWAT-HEAD. 59 back-roller and the back-middle-roUer ; and the wheels given to find the draught between the back-roller and the front-middle-roller, find the draught between the back-middle-roUer and the front-middle-roller. Worked out hy Ca/iicellation. 1-20 I 254. 1-21 204 1-20 I 254.19^'j- 'sT Answer. The same without Cancellation. Dividend 25 x 20 _.. ..q , Divisor 21 x 20 Answer. From the particulars given to find the total draught, and the particulars given to find the draught between the front-roller and the back-roller, find the draught between the front-roller and the delivering balls. Worked out hy Cancellation. 1.02 1 1.254 1400 804 148 754 1-3 4.54 {Conti nued.) 60 COTTON MANUFACTUEE. 1-51 1-1.25 1-80 1-75 14.5 146 164 1 1004 184 34 514 1.02 Answer. The same without Ccmcellation. 1.02 X 1.25 X 80 X Y5 X 4.5 X 16 X 100 X 18 X 3 X 51 100 X 18 X 3 X 51 X 1.25 x 80 x Y5 x 4.5 x 16 = 1,02 Answer. K.B. — The above result will be obtained by dividing the total draught by t]ie draught between the back-roller and the front-roller. See the following example. The draught between the back and front rollers is 1.96^, and the total draught is 2, Eequired the draught between the delivering balls and the front-roller. Worked out hy Cancellation. l^.B.— 1.96A 'TT 1 00 1400 2 51-.51 2 X .51 1.02 Answer. KAIL WAT-HEAD. 61 The same without Ca/ncellation Dividend 51 x 2 Divisor 100 =1.02 Answer. From the particulars given to find tlie total draught, the draught between the front-roller and the delivering balls, and the draught between the back-roller and the front-middle-roUer, find the draught between the front- middle-roller and the front-roller. WorTced out ly Cancellation. 1-1.25 1-80 1 1(00 1448 1-3 1-51 1-3 1-34 1-25 34 344 1.254 804 Y5-34 4.54 164 1.25 8(0-A 2(0 4 X 1.25 X 2 x^ 1.56M Answer. G2 COTTON MA2JUFACTUEE. The smne without Cancellation. 3 X 34 X 1.25 X 80 X 75 X 4.5 x 16 x 1.25 x 80 x 20 1.25 X 80 X 100 X 18 X 3 X 51 X 3 X 34 X 25 =1 .56ff Answer. The draught between the delivering balls and the front- roller is 1.02, and the draught between the back-roller and the front-middle-roller is 1.25. Required the draught between the front-middle-roller and the front-roller, the total draught being 2. Worked out hy Cancellation. 24.64.56tt 14.02 14.25 Answer. 1.56ii The sa/me without Cancellation. Dividend .... 2 _-, Divisor 1.25 x 1.02 ~ ' Answer. The draught between the back-middle-roller and the back-roller is 1.05. The di*aught between the back- middle and the front-middle-roller 1.19^\. The draught EAILWAT-HEAD. 63 between the front-middle-roUer and the front-roller is 1.56ff. The draught between the front-roller and the delivering balls is 1.02. Eequired the total draught. Iir.B.-1.19^V = ff 1.56M 80 Worked out hy Cancellation. 1.05-.05 1-21 1-51 25 80 1.02-.02 80 X 25 X .05 X .02 = 2 Answer. The sa/me without Cancellation. Dividend . . . 1.05 x 25 x 80 x 1.02 =2 Divisor .... 51 X 21 . Answer. The can that receives the sliver stands upon and revolves with the disc, and, in practice, it is found that the velocity of its circumference should be to that of the delivering balls as 1 to 8. The delivering balls are 3 inches in diameter, and drive the disc by a train of 2 pairs of wheels. The driven 04: COTTON MA.NUFACTUKE. .wheels have respectively 24: and 180 teeth. How many- teeth should there be in the driving wheels respectively, and what should be the diameter of the can, to give its circumference a velocity ^ of that of the delivering balls ? Worked out. 1-8 1 3 24-3 180 180 3 510 3 B . . . . 2)1620 C . . . ■ . 2)810 C. . . . 3)405 C. . . . 3)135 B 3)15 A 3)15 A ...... 5)5 1 KAIL WAY-HEAD. 65 A. 5x3 = 15 Teeth in the first driving wheel. B. 3x2 . 6 Teeth in the second driving wheel. C. 3x3x2 . 18, Diameter of the can, in inches. Answer. From the particulars found in the preceding example, find the ratio of velocity of the circumference of the delivering balls to that of the can, supposing that of the can to be 1 : Diameter of the can, in inches 18 Teeth in the first driv- ing wheel .... 15 Teeth in the second 1 Eatio of velocity of the circumference of the can. 3, Diameter of the deliv- ering balls, in inches. 24 Teeth in the first driv- en wheel. 180 Teeth in the second driving wheel ... 6 driven wheel or disc. Worked out hi 148 1-345 1-2-6 / Cam^Gellation. 1 3-1 24-8 180-10-5-1 Answer. GQ COTTON MANUTAOTUEE. The same without Ccmcellation. Dividend 3 x 24 x 180 = 8 Divisor 18 x 15 x 6 Answer. DBAWING-FBAME. As has been shown, the object attained by the previous processes in the carding department is a thorough cleans- ing of the cotton, untangling its fibres, laying them more or less parallel with each other, and forming them into a sliver. The object to be attained at the drawing-frame is to repeatedly double and draw the slivers until they mutually correct any unevenness that may have occurred in their formation, and lay the fibres perfectly parallel with each other and the sliver. The front-roller at the drawing frame is 1^, and the delivering balls 3 inches in diameter. The front-roller has on a wheel with 27 teeth, that, by means of an inter- mediate, takes into the wheel on the same axis with the delivering balls. How many teeth should there be in the wheel on the same axis with the delivering balls to pro- duce a draught of 1.08 ? Diameter of the front- roller, in inches . .1.25 3, Diameter of the deliv- ering balls, in inches. DEAWING-FBAME. 67 27 Teeth in the wheel on the front-roller. Draught .... .1.08 Worked out hy Crnicellation. 14.25 3 27-21.6-20 14.08 20 X 3 60 Answer. Tlie sa/me without Ccmcellation. Dividend 27 x 3 =60 Divisor 1.08 x 1.25 Answer. From the particulars found in the preceding example, find the draught between the front-roller and the deliver- ing balls. Worked out hy Cancellation. 14.25 1-20-60 34 27-21.64.08 1.08 Answer. The same without Cam^cellation. Dividend ..... 27 x 3 ^ -; ^^ Divisor 60 x 1.25 Answer. 68 COTTON MANUFACTURE. The front-roller is 1-|, and tlie back-roller is 1 inch in diameter. The fr-ont-roUer wheel has 27 and the change wheel 36 teeth. How many teeth should there be in the top-carrier and the back-roller wheel to produce a draught of 4 at the di-awing head, the draught between the front- roller and the delivering balls being 1.08 ? Diameter of the front- roller, in inches . . 1.25 Draught between the front-roller and the deliverino; balls . .1.08 1, Diameter of the back- roller, in inches. 2Y Teeth in the wheel on the front-roller. 36 Teeth in the change wheel. 4z, Total draught. Worhed out. 14.25 1 2r-25-20 36 14.08 4 36 20 T20 (Continued.) DKAWmG-FR.AME, Y20 4 B . . . 10)2880 A . .... 4)288 .... T2)Y2 69 A. T2 Y2 Teeth in the top-carrier. B. 10 X 4: = 40 Teeth in the back-roller wheel. Answer. From the particulars found in the preceding example, find the total draught at the drawing head. Worked out hy Cancellation. 1 1-36 1'2T 1.25 40 72-2 1.08-.04 40 X 2 X 1.25 X .04 = 4 The same without Ca/ncellation. Dividend . . 1.25 x40 x Y2 x 1.08 Answer. 4 Divisor ... 36 x 2Y Answer. 70 COTTON MANUFACTURE. BOBBIN AND FLY-FKAME, An upright shaft makes 180 revolutions per minute, and has on a wheel that takes into a wheel with 96 teeth on a lying shaft. On the lying shaft there is a pulley that drives a pulley 16 inches in diameter on a counter- shaft. On the countershaft there is a pulley that di'ives a pulley 10 inches in diameter on the first driven shaft of the fly-frame. How many teeth should there be in the wheel on the upright shaft, and what should be the diameter of the driving pulleys on the lying and the countershafts to drive the first driven shaft 288 revolu- tions per minute? Revolutions per minute of the upright shaft, 180 288 Revolutions per minute of the first driven shaft. 96 Teeth in the wheel on the lying shaft. 16, Diameter of the driven pulley on the coun- tershaft, in inches.. 10, Diameter of the pulley on the first driven shaft of the fly-frame, in inches. BOBBm AND FLY-FRAME. 71 Worked out. l-348(0 288-96 9646 16 1(0 96 16 676 96 1536 16 9216 A . . . 1536 . 8)24576 B . . . 6)3072 A ..... 8)512 B .... 4)64 C . . . . 16)16 1 A. 8 X 8 : 64 Teeth shaft. in the wheel on the nprigh 72 COTTON MANUFACTUKE. B. 6x4 == 24, Diameter of tlie di-iving pulley on the lying shaft, in inches. C. 16 == 16, Diameter of the diiving pulley on the countershaft, in inches. Answer. From the particulars found in the preceding example, find the revolutions per minute of the first driven shaft of the fly-frame. Worked out hy Cancellation. 18(0 1-8-96 64-8 146 24-2 1(0 164 18 X 8 X 2 288 Answer. The same witJiout Cancellation Dividend . . . 180 x 64 x 24 x 16 =288 Divisor ... 96 x 16 x 10 Answer. The first driven shaft of the fly-frame makes 288 revo- lutions per minute, and has on a wheel that takes into a wheel with 42 teeth on the sj)indle-shaft. On the spindle- sliaft there is a wheel that takes into a wheel with 24 BOBBIN AND FLY-FKAME. Y3 teeth on the spindle. How many teeth should there be in the wheel on the first driven shaft, and the driving wheel on the spindle-shaft, to drive the spindles 720 revolutions per minute? Revolutions per minute of the first driven shaft of the fly-frame, 288 720 Revolutions per minute of the spindles. 42 Teeth in the diiven wheel on the spindle shaft. 24 Teeth in the wheel on the spindle. Worked out. 1-24-288 720-60 42 24-1 42 60 A 10)2520 A 7)252 B 36)36 1 A. 10 X 7 = 70 Teeth in the wheel on the first driven shaft of the fly-frame. 4 74 B. 36 spindle shaft. COTTON MANUFACTURE. 36 Teeth in the di'iving wheel on the Answer. The first driven shaft makes 288 revolutions per minute, and has on a wheel with TO teeth that takes into a wheel with 42 teeth on the spindle-shaft. On the spindle-shaft there is also a wheel with 36 teeth that takes into a wheel with 24 teeth on the sphidle. How many revolutions per minute does the spindle make ? Teeth in the driven wheel on the spindle- shaft ...... 42 Teeth in the wheel on the spindle .... 24 288 Revolutions per minute of the first driven shaft. 70 Teeth in the wheel on the first driven shaft. 36 Teeth in the driving wheel on the spindle- shaft. WorTced out hy Cancellation. 288-48 1-642 1-2-24 48 X 5 X 3 7040-5 36-3 T20 Answer. BOBBIN XSD FLY-FRAME. TO The same without Cancellation. Dividend . . . 288 x YO x 36 _ ^^q Divisor .... 42 X 24 Answer. In treating on the epicyclic train of wheels, or what is technically called the differential coupling, it has been thought best to name each wheel and its use. The object to be obtained by the differential coupling is gradually to increase the speed of the bobbin at the same rate as its diameter increases, since it is essential that the bobbin and the front-roller have equal surface velocities. The train of wheels in the differential coupling are 5 in number, 3 of which are on the same axis with the first driven shaft. The first wheel is made fast to the first driven shaft, and is called the fast internal wheel. The second or middle wheel revolves loose upon the first driven shaft, and is called the differential wheel. The third wheel is made fast to a hollow cylinder that revolves loose upon the first driven shaft, and is called the loose internal wheel. The other two (only one of which is necessary) are intermediate or carrying wheels, connecting the fast and loose internal wheels : they are fast to, and have their axis in the plane of the differen- tial wheel. The fast and loose internal wheels are both of the same dimensions, and need not be taken into ac- 70 COTTON MAJSrUFACTUKK. count ; but there is a wheel outside of the difibrential coupling, called the external wheel, that is made fast to the same hollow cylinder as the loose internal wlieel, which, with the differential wheel, will be fomid in the following examples, and will answer every purpose for calculating anything pertaining to the differential coup- ling. It is obvious that if the differential wlieel were lield fast, the external wlieel and the fast and loose internal wheels would all revolve at the same speed, and that, if it were made to revolve at the same speed as the fast inter- nal wheel, the external wheel would stand still. Hence it is by having the differential wheel revolve in the same direction as the fast internal wheel, but at a slower rate, equal to the difference in speed between the flyer and the bobbin, that the surface velocity of the bobbin is made to keep pace with that of the front-roller. !N.B. — In the following example, the differential wheel is supposed to stand still. The external wheel makes 288 revolutions per minute, and takes into a wheel with 42 teeth on the bobbin-shaft. On tlie bobbin-shaft there is a wheel that takes into a wheel with 40 teeth, to which tlie bobbin is made fast. How many teeth should there be in the external wheel, BOBBnsr AND FLY-FEAME. YT and the driving wheel on the bobbin-shaft, to drive the bobbin 720 revohitions per minute? Revolutions per minute of the external wheel, 288 T20 Revolutions per minute of the bobbin. 42 Teeth in the driven wheel on the bobbin- shaft. 40 Teeth in the wheel to which the bobbin is made fast. Worked out. 1-2-24-288 720-60-5 42-21 40 21 5 105 40 A 10)4200 A. . . . . 10)420 B 42)42 1 78 COTTON MANUFACTURE. A. 10 X 10 100 Teeth in tlie external wheel. B. 42 ■ 42 Teeth in the driving wheel on the hob- bin-shaft. Answer. N.B. — In the following example the differential wheel is supposed to stand still. The external wheel makes 288 revolutions per minute, has 100 teeth, and takes into a wheel with 42 teeth on the bobbin-shaft. On the bobbin-shaft there is also a wheel with 42 teeth that takes into a wheel with 40 teeth, to which the bobbin is made fast. How many revolutions per minute does the bobbin make ? 288 devolutions per minute of the external wheel. 100 Teeth in the external wheel. Teeth in the driven wheel on the bobbin- shaft 42 Teeth in the wheel to which the bobbin is made fast .... 40 42 Teeth in the driving wheel on the bobbin- shaft. Woi'Tced out hy Cancellation. 288-Y2 1-42 1-4(0 10(0 424 T2 X 10 T20 Answer. BOBBIN AND FLT-FEAME. 79 The same without Cancellation. Dividend . . . 288 x 100 x 42 Divisor . 42 X 40 :720 Answer. The first driven shaft makes 288 revolutions per minute, and has on a wheel with 20 teeth, that takes into a wheel on the grooved shaft. On the other end of the grooved shaft there is a wheel with 100 teeth, that takes into a wheel on the front-roller. How many teeth should there be in the wheel on the grooved shaft, that takes into the wheel on the first driven shaft, and the wheel on the front-roller, to drive the front-roller 96 revolutions per minute ? Kevolutions per minute of the front-roller . . 96 288 Revolutions per minute of the first driven shaft. 20 Teeth in the wheel on the first driven shaft. 100 Teeth in the wheel that takes into the wheel on the front- roller. 80 COTTON MANUFACTURE. Worked out. 1-8-96 288-24-3 20 100 A A 20 3 60 100 10)6000 .... 10)600 B 60)60 1 A. 10 X 10 100 Teetli in tlie wheel on tlie front- roller. B. 60 60 Teeth in the driven wheel on the grooved shaft. Answer. The first driven shaft makes 288 revolutions per minute, and has on a wheel with 20 teeth that takes into a wheel with 60 teeth on the grooved shaft. On the other end of the grooved shaft there is a wheel with 100 teeth, that takes into a wheel with 100 teeth on the front-roller. How many revolutions per minute does the fr*ont-roUer make? BOBBIN AND FLY-FBAME. 81 Teeth in the driven wheel on the grooved shaft 60 Teeth in the wheel on the front-roller . . 100 288 Revolutions per minute of the lii'st di'iven shaft. 20 Teeth in the wheel on the first drive!i shaft. 100 Teeth in the driving wheel on the grooved shaft. Worked out l)y GcmcellaUon. 28848 1-6(0 2(0 1400 1004 48x2. 96 Answer. TJie sa/me without Ccmcellation. Dividend .... 288 x20 xlOO _ q^ Divisor 100x60 Answer. The front-roller is 1^ inches in diameter, and makes 96 revolutions per minute, and the spindle makes Y20 revolu- tions per minute. How many turns of twist per inch is there in the roving ? 82 COTTON MAJfUFACTUKE. Revolutions per minute Y20 Revolutions per minute of the front-roller . . 96 of the spindle. Diameter of the front- roller, in inches . .1.25 Ratio of circumference to diameter . . . 3.1416 Worked out hy Cancellation,. 1-8-96 'r20-60-7.5-6-1.9 1-1.25 1-3.1416 1.9 The same without Cancellation. Dividend .... 720 Answer. 1.9 Divisor 96 x 1.25 x 3.1416 Answer. The spindle makes 720 and the front-roller 96 revolu- tions per minute. How many revolutions does the spindle make while the front-roller makes 1 ? Worked out hy Cam^cellation. 1-8-96 I 720-60-7.5 7.5 Answer. BOBBIN AND FLY-FRAME. 83 N.B. — If it is admitted that the diameter of the empty bobbin is equal to that of the front-roller, the spindle making T|-, while the front-roller makes 1 revolution, it will be evident that the bobbin will have to make 1 revo- lution less than the spindle in the same time, in order to wind on the roving as fast as it is delivered by the front- roller (making no allowance for shrinkage in twisting), until the first layer is wound on to the bobbin; there- fore the bobbin will make 6|, while the spindle makes 7^ revolutions. If the bobbin makes 6^, while the spindle makes Y^ revolutions, how many revolutions per minute will the bobbin make, if the spindle makes 720 ? Worked out hy Ccmcell^ition. 720-2400 1-.34.5-7.5 6.54.3-.26 2400 X. 26 = 624 The same without Ccmeellation. Dividend 720x6.5 Answer. 624 Divisor 7.5 Answer. The bobbin makes 624 revolutions per minute, while winding on the first layer of roving. The wheel to which 84 COTTON MANUFACTUKE. the bobbin is made fast has 40 teeth, and takes into a wheel with 42 teeth on the bobbin-shaft. On the bobbin- shaft there is also a wheel with 42 teeth that takes into the external wheel, which has 100 teeth. How many revolutions per minute does the external wheel make ? 624 Revolutions per minute of the bobbin. 40 Teeth in the wheel to Teeth in the wheel on the bobbin-shaft that takes into the wheel to which the bobbin is made fast, 42 Teeth in the external wheel 100 42 which the bobbin is made fast. Teeth in the wheel on the bobbin-shaft that takes into the external wheel. Worked out hy CcmcellaUon. 624 142 140(0 4(0-.4 424 > 624 X. 4: 249.6 Answer. The 80/nie without Cancellation. Dividend 624 x 40 x 4 2 Divisor 100x42 = 249.6 Answer. BOBBIN AND FLY-FRAME. 85 The first driven shaft makes 288, and the external wheel 249.6 revolutions per minute, while winding the first layer of roving on to the bobbin. How many revo- lutions per minute has the external wheel been retarded, admitting that it would have revolved at the same speed as the first driven shaft, if the differential wheel had stood stiU? 288.0 249.6 38.4 Answer. The wheel to which the bobbin is made fast has 40 teeth, and takes into a wheel with 42 teeth on the bobbin- shaft. On the bobbin-shaft there is also a wlieel with 42 teeth that takes into the external wheel, which has 100 teeth. The differential wheel retards the external wheel 38.4 revolutions per minute. How many revolutions per minute is the bobbin retarded ? 38.4 Revolutions per minute that the external wheel is retarded. Teeth in the wheel on 100 Teeth in the external the bobbin-shaft that wheel, takes into the exter- nal wheel .... 42 {Continued.) 86 COTTON MANUFACTURE. Teeth in the wheel to which the bobbin-shaft is made fast ... 40 42 Teeth in the wheel on the bobbin-shaft that takes into the wheel to which the bobbin is made fast. Worked out hy Cancellation. 38.4 142 10(0-2.5 14(0 424 38.4 X 2. 5 96 The same without Cancellation. Dividend . ... 38.4 x 100 x 42 Divisor 42 x 40 Answer. = 96 Answer. K.B. — It will be observed from the above that the bob- bin, while winding on the first layer of roving, is retarded exactly the same number of revolutions per minute as the front-roller makes, which is right (making no allowance for shrinkage in twisting), because the empty bobbin and the front-roller are both of the same dimensions, and the winding on is effected by the bobbin falling behind the spindle. BOBBEST AND FLT-FKAME. 87 The first driven shaft makes 288 revolutions per minute, and has on a wheel with 20 teeth that takes into a wheel with 60 teeth on the grooved shaft. On the grooved shaft there is a pulley 5 inches in diameter that drives tlie cone at the small end. On the same axis with the cone there is a wheel with 54 teeth that takes into a wheel on a short shaft. On the other end of the short shaft there is a wheel with 32 teeth that takes into the differential wheel. How many teeth should there be in the driven wheel on the short shaft and the differential wheel, and what should be the diameter of the small end of the cone, to drive the differential wheel 38.4: revolutions per minute ? l^.B. — The belt is always at the small end of the cone at the commencement of the bobbin, when the winding on is effected by the bobbin falling behind the spindle ; and every time the differential wheel makes one revolu- tion, it reduces that of the external wheel the same. Revolutions per minute of the differential wheel 38.4 Teeth in the wheel on the grooved shaft . 60 288 Revolutions per minute of the first di'iven shaft. 20 Teeth in the wheel on the first driven shaft. 5 Diameter of the pulley on the grooved shaft, in inches. 88 COTTON MANUFACTURE. 54 Teetli in the wheel on the same axis with the cone. 32 Teeth in the wlieel that takes into the differ- ential wheel. 1-3.2-38.4 288-24-8 1-3-60 204 5 54 3240 54 10 540 5 2700 8 . . . 10)21600 B. . . . 10)2160 A .... 2)216 C . . B. . . {ConUnued.) . . 2)108 . . 2)54 BOBBm AJSTD FLT-FEAME, 89 B 3)27 C 3)9 C 3)3 1 A. 2 ^= 2 Diameter of the small end of the cone, in inches. B. 10 X 2 X 3 :^= 60 Teeth in the driven wheel on the short shaft. C. 10 X 2 X 3 X 3 180 Teeth in the differential wheel. Answer. The first driven shaft makes 288 revolutions per minute, and has on a wheel' with 20 teeth that takes into a wheel with 60 teeth, on the grooved shaft. On the grooved shaft there is a pulley 5 inches in diameter, that drives the cone at the small end, which is 2 inches in diameter. On the same axis with the cone there is a wheel with 54 teeth that takes into a wheel with 60 teeth, on a short shaft. On the other end of the short shaft there is a wheel with 32 teeth, that takes into the differential wheel, which has 180 teeth. How many revolutions per minute does the differential wheel make ? 90 COTTON M^ySTUFACTURE. Teeth in tlie wheel on the grooved shaft . 60 Diameter of the small end of the cone, in inches 2 Teeth in the di*iven wheel, on the short shaft 60 Teeth in the differen- tial wheel . . . .180 288 Revolutions per minute of the first driven shaft. 20 Teeth in the wheel, on the first driven shaft. 5 Diameter of the pulley on the grooved shaft, in inches. 54 Teeth in the wheel on the same axis with the cone. 32 Teeth in the wheel that takes into the differ- ential wheel. Worked out hy Cmicellation. 1-3-60 1-2 1-5-60 1-5-20480 288-24-84-1 204 54 54-6 32-6.4 6.4 X 6 38.4 The same without Cancellation. Dividend . . 288 x 20 x 5 x 54 x 32 Divisor . . . Answer. = 38.4 60 X 2 X 60 X 180 Answer. BOBBESr AJSTD FLY-FKAME. 91 The first driven shaft makes 288 revolutions per minute, and has on a wheel with 20 teeth that takes into a wheel with 60 teeth, on the grooved shaft. On the grooved shaft there is a pulley 5 inches in diameter that drives the cone at the small end, which is 2 inches in diameter. On the same axis with the cone there is a wheel with 54 teeth, that takes into a wheel with 60 teeth, on a short shaft. On the other end of the short shaft there is a wheel with 32 teeth, that takes into the diiferential wheel, which has 180 teeth. The external wheel has 100 teeth and takes into a wheel with 42 teeth, on the bobbin shaft. On the bobbin shaft there is also a wheel with 42 teeth, that takes into a wheel with 40 teeth, to which the bobbin is made fast. How many revolutions per minute is the bobbin retarded ? ]Sr.B. — The above includes the whole train of wheels, pulley, and cone leading from the first driven shaft through the differential coupling to the bobbin. 288 Revolutions per minute of the first di'iven shaft. Teeth in the wheel, on 20 Teeth in the wheel, on the grooved shaft . 60 the first driven shaft. Diameter of the small 5 Diameter of the pulley end of the cone, in on the grooved shaft, inches 2 in inches. 92 COTTON MANUFACTUEE. Teeth in the driven wheel, on the short shaft 60 Teeth in the differen- tial wheel . . . .180 Teeth in the driven wheel, on the bobbin shaft 42 Teeth in the wheel to which the bobbin is made fast . . .- . 40 54 Teeth in the wheel, on the same axis with the cone. 32 Teeth in the wheel that takes into the differ- ential wheel. 100 Teeth in the external wheel. 42 Teeth in the di'iving wheel, on the bobbin shaft. Worked out hy Cancellation. 288-24-6-3 1-6(0 20-1 1-2 5-1 1-5-60 54-9-1 1-20480 32 1-42 1(00 1-4(0 42-1 32 X 3 96 Answer. The same without Cancellation. Dividend 288 x 20 x 5 x 54 x 32 x 100 x 42 Divisor . = 96 60x2x60x180x42x40 Answer. BOBBIZSr AJSTD FLY-FKAME. 93 From the revolutions per minute of the front-roller, and the train of wheels, and the pulley and cone leading from the front-roller to the bobbin, find how many revolu- tions per minute the bobbin is retarded. Worhed out by Cancellation. 96 1400 1004 1-2 64 1-240-60 54-64 1-248(0 32-16-4:-2-l 142 1(00 14(0 42-1 96 Answer. The same without Canoellat/ion. Dividend 96 x 100 x 5 x 54 x 32 x 100 x 42 . Divisor . 100x2x60x180x42x40 96 Answer. ]N".B. — ^Every time the bobbin is retarded or falls behind the spindle one revolution, it laps the roving once round the bobbin ; consequently, the front-roller and empty bob- bin both being of the same dimensions, the front-roller making 96 revolutions per minute, and the bobbin falling Oi COTTON MANUFACTUKE. behind tlie spindle 96 revolutions per minute, the roving will be wound on to the bobbin as fast as it is delivered from the front-roller (making no allowance for slirinkage in twisting). The front-roller wheel has 30 and the change-wheel 32 teeth, and the back-roller is one inch in diameter. How many teeth should there be in the top-camer and the back-roller wheel, and what should be the diameter of the front-roller to produce a draught of 7 ? Worked out. 30 32 8 = I of an inch. 32 30 960 T680 7 A. . . 10)53760 B . . {Contmued.) . 2)5376 BOBBIN AND FLY-FKAME. 95 B . . . 2)2688 B .. . . 2)13M B . . . 7)6Y2 C . . 96)96 1 10 Diameter of the fr of an inch. B. 7x2x2x2 56 Teeth in the back-roller wheel. C. 96 == 96 Teeth in the top-carrier. Answer. The front-roller is 1^ and the back-roller one inch in diameter. The front-roller wheel has 30, the top-carrier 96, the change-wheel 32, and the back-roller wheel 56 teeth. Required the draught. Diameter of the back- roller, in eighths of an inch 8 Teeth in the change- wheel 32 Teeth in the front-roll- er 30 10 Diameter of the front in eighths of an inch. 56 Teeth in th? back-roUer- wlieel. 96 Teeth in the top-carrier. 96 COTTON MAJfUFACTUEE. Worked out l>y Cancellation. 1-8 14-32 1-3(0 1(0 56-7 96-12-3-1 Answer. The same without Cancellation. Dividend 10 x 56 x 96 Divisor 8 x 32 x 30 Answer. What slioiild be the draught between the middle and front rollers, if 19 is drawn into 20 between the back and middle rollers, the total draught being Y? WorTced out hy Cancellation. 7 1-4-20 19-3.8-.95 7 X .95 = 6.65 TTie same without Cancellation. Dividend 19 x 7 Answer. = 6.65 Divisor 20 Answer. BOBBIN AND FLY-FRAME. 97 The front-roller is 1:^ and the middle-roller one inch in diameter. The front-roller wheel has 30, and the change- wheel 35 teeth. How many teeth should there be in the top-carrier and the middle-roller wheel to produce a draught of 6.65 between the middle and the front rollers? Worked out. 3(0 i^ of an inch 1(0 35 6.65 4 of an inch. 6.65 B B 53.20 35 26600 15960 1862.00 3 2)5586-00 3)2T93 7)931 {Continued^ 5 98 CO'lTON MAIfUFACTUBE. A. 19 X 3 = B. 7x7x2 B ..... 7)133 , 19)19 1 = 57 Teeth in the middle-roller wheel. 98 Teeth in the top-carrier. Answer. The front-r. Her is 1^ and the middle-roller one inch in diameter. The front-roller wheel has 30, the top-carrier 98, the change-wheel 35, and the middle-roller wheel 57 teeth. Required the draught between the middle and the front-rollers. Diameter of the middle- roller, in eighths of an inch 8 Teeth in the change- wheel 35 Teeth in the front-roller wheel 30 10, Diameter of the front- roller, in eighths of an inch. 57 Teeth in the middle-rol- ler Avheel. 98 Teeth in the top-carrier. Worked out hy Cancellation. 1-8 1-7-35 1-3(0 1(0 5741.4-3.8 98-12.25-1.75 3.8 X 1.75 6.65 Answer. BOBBIK AND FLY-FKAIrlE. 99 The same without Cancellation. Dividend 10 x 57 x 98 . Divisor 8 x 35 x 30 6.65 Answer. From the particulars given, to find the draught between the back and the front, and the middle and the front rollers, die rollers. Find the draught between the back and the mid- WorTced out hy Ga/nGellation. 1(0 84 1-1.9-5.Y41.4-5Y 35-54 1-749-98 30-1 1-8 1(0 14-32 56-8-2-1 1-30 96-12-6-24.05^ 1.05tV Answer. The same without Ca/ncellation. Dividend . 8x 35 x30xl0x 56x96 _ Divisor . . 10x57x98x8x32x30 'fF Answer. 100 COTTON MANUFACTURE. The draught between the back and the fi'ont-rollers is Y, and the dranght between the middle and the front- rollers is 6.65. Required the di'aught between the back and the middle rollers. 1-6.65 I 7-lM^ ^T? Answer. A Fly-Frame is making coarse roving with a one-inch back-roller, a 1^ inch front-roller, a 32 front-roller wheel, a 96 top-carrier 40 change-wheel, and a 64 back-roller wheel. Eeqnired the dranght. Worked out hy Cancellation. 1-8 1-32 1-24(0 1(0 96-48-6 64-2-1 6 Answer. The same without Ca/ncellation. Dividend 10 x 96 x 64 _ ^ Divisor 8 x 32 x 40 Answer. BOBBIN AND FLT-FEAME. 101 The first layer of roving on the bobbin is 6 inches long, containing 30 laps per inch ; consequently, the coppiug- rail will have to traverse 6 inches, and the bobbin make 30 X 6 = 180 revolutions, while winding on the layer, and, as has been shown in preceding examples, the empty bobbin and the fi'ont-roller are both of the same dimen- sions, and in eifect, both move at the same speed, while winding on the first layer of roving. The rack to which the copping-rail is made fast is driven from, the cone- shaft by 5 pairs of wheels, and the wheel that takes into the rack. The driven wheels contain respectively, 90, 100, 60, 80, and 80 teeth, and the rack 4 teeth per inch. From the above particulars and the train of wheels, and the pulley and cone leading from the front-roller to the cone, find driving wheels that will make the copping-rail traverse 6 inches, while the fi'ont-roUer makes 180 revo- lutions. JRevolutions of the front- roller 180 Teeth in the wheel on the front-roller , . 100 Diameter of the pulley on the grooved shaft, in inches .... 5 100 Teeth in the wheel on the grooved shaft. 2, Diameter of the small end of the cone, in inches. 90 First driven wheel from the cone. 102 COTTON MANUFACTURE. 100 Second di-iven wheel from the cone. 60 Third driven wheel from the cone. 80 Fom'th driven wheel from the cone. 80 Fifth driven wheel from the cone. 4: Teeth per inch in the rack. 6 Length of the first lay- er, in inches. WbrJced out. 1-2480 1400 1-5 1004 24 904 100-20 60 80 80 4 6 BOBBESr AJSnO FLY-FRAME. 103 24 1920 80 153600 60 9216000 20 B 10)184320000 E . . 10)18432000 C . . . . . 10)1843200 A 10)184320 E . . . , 2)18432 D 2)9216 D 4)4608 D 8)1152 A 3)144 3(48 F . . . . 16)16 1 104 COTTON MANUFACTURE. A. 10 X 3 30 Teetli ia the wheel on the same axis with the cone or first driving wheel. B. 10 = 10 Teeth in the second driving wheel. 10 X 3 =: 30 Teeth in the third driving wheel. 8x4x2 = 64 Teeth in the fourth driving C. D. wheel E. F. rack. 10 x 2 == 20 Teeth in the fifth driving wheel. 16 ■ 16 Teeth in the wheel that takes, into the Answer. From the particulars found in the preceding example, find the length of the first layer of roving on the bobbin. Worked out ty Cancellation. 18(0-6 1-100 100-1 1-2 5-1 1-3-90 30-1 1(00 1(0 14-12-60 3(0-1 1(0-80 64-8-2-1 1-20-80 20-1 1-4 16-4-1 6 inches. Answer. BOBBIN AND FLT-FEAME. 105 Dividend, Divisor, The same without Cancellation. 180 X 100 X 5 X 30 X 10 X 30 X 64 X 20 X 16 = 6 100 X 2 X 90 X 100 X 60 X 80 X 80 X 4 Answer. From the particulars found in the preceding example, find how many revolutions the front-roller makes while the first layer of roving is being wound on to the bobbin. Worked out hj Ga/ncellation. 6-2-1 14-16 4-1 1-20 80-4-1 1-24-8-64: 80-10-24 1-30 60-2-1 1(0 1(00 1-3(0 90 1-5 2 1400 1004 90 X 2: 180 Answer. The 8a/me without Cancellation. Dividend, 6 x 4 x 80 x 80 x 60 x 100 x 90 x 2 x 100 _ ^g^ Divisor, 16 x 20 x 64 x 30 x 10 x 30 x 5 x 100 Answer. 5* 106 COTTON MANUFACTURE. From the particulars found in tlie preceding example, find how many teeth there is in the reversing wheels. l!*f.B. — The reversing wheels take into the wheel with 10 teeth. They are two in nimiber, only one of which is in operation at a time. Worked out hy Cancellation. 180-24 1(00 100 1-2 54 1-90 3(0-1 1(0 14-20-60 30-54 1-240-80 64-8-2-1 14-80 20-1 14 16-4-1 1-6 100 Answer. The same without Cancellation. Dividend, 180 x 100 x 5 x 30 x 10 x 30 x 64 x 20 x 16_ Divisor, 100 X 2 X 90 X 60 X 80 X 80 X 4 x 6 100 Answer. SPINNING-FEAME. 107 SPINNING-FKAME. An upright shaft in a spinning-room makes 180 revolu- tions per minute, and has on a wheel that takes into a wheel with 64 teeth, on a lying-shaft. On the lying-shaft there is a pulley that drives a pulley 12 inches in diame- ter, on a counter-shaft. On the counter-shaft there is a pulley that drives a pulley 8 inches in diameter, on the same axis with the cylinder of the spinning-frame. How many teeth should there be in the wheel on the upright shaft, and what should be the diameter of the driving pulleys on the lying and counter shafts, to drive the cylin- der 900 revolutions per minute ? Revolutions per minute of the upright shaft. 180 900 Revolutions per minute of the cylinder. 64 Teeth in the wheel on the lying shaft. 12, Diameter of the driven pulley on the counter- shaft, in inches. 8, Diameter of the pulley on the same axis with the cylinder, in inch- es. 108 COTTON MANUFACTUKE. Worked out. l-3-18(0 90(0-30 12-2 C B B C 30 1920 2 3840 8 10)30Y20 2)3072 6)1536 4)256 . 8)64 . 8)8 1 A. 10 X 8 shaft. 80 Teeth, iii the wheel, on the upright SPESTNING-FKAME. 109 B. 6x4 = 24, Diameter of the pulley on tlie lying shaft, in inches. C. 8x2 =r 16, Diameter of the driving pulley on the counter-shaft, in inches. Answer. From the particulars found in the preceding example, find the revolutions per minute of the cylinder. Worked out hy Cancellation. 180-45 1-2-8-64 8040 1-12 24-24 1-8 16-2 45 X 10 X 2 900 The same without Ca/ncellaUon. Dividend ... 180 x 80 x 24 x 16 Answer. = 900 Divisor .... 64 x 12 x 8 Answer. The cylinder makes 900 revolutions per minute, and the spindle-warls are one inch in diameter. What should be the diameter of the cylinder to di-ive the spindles 6300 revolutions per minute ? 110 COTTON MANUFACTURE. Worked out hy Cancellation. 1-900 I 6300-Y 7 Answer. The cylinder makes 900 revolutions per minute, and on the same axis there is a pulley that drives a pulley 15 inches in diameter, on a stud. On the same axis with the pulley on the stud, there is a wheel that, by means of an intermediate, takes into a wheel witli TO teeth on the front-roller. What should be the diameter of the pulley on the same axis with the cylinder, and how many teeth should there be in the wheel on the same axis mth the pulley on the stud, to drive the front-roller 60 revolutions per minute ? Revolutions per minute of the cylinder . . 900 60 Revolutions per minute of the front-roller. 15, Diameter of the pulley on the stud, in inches. TO Teeth in the wheel on the front-roller. Worked out. l-3-9(00 6(0-2 15-5 T(0 {Continued^ SPmNING-FKAME. Ill 5 35 2 A . . . Y)YO A . . . 2)10 B . . . 5)5 1 A. 7x2 = 14 Teetli in the wheel on the same axis with the pulley on the stud. B, 5 = 5, Diameter of the pulley on the same axis with the cylinder, in inches. Answer. From the particulars found in the preceding example, find the revolutions per minute of the front-roller. Worked out hy CanoellaUon. 900-60 145 i44:-ro 54 144 60 Answer. 112 COTTON MAITOFACTUKE. The sa/me witJiout Ca/ncellation. Dividend 900 x 5 x 14 60 Divisor 70 x 15 Answer. The front-roller is one incli in diameter, and makes 60 revolutions per minute, and the spindles make 6300 revo- lutions per minute. Required the number of tm-ns of twist per inch in the yarn. Worked out hy CetnceUation. 1-6(0 I 630(0405-8.Y5-33.42 1-.2618-3.1416 I 33.42 Answer. The same without Cancellation. Dividend 6300 33.42 Divisor 3.1416 x 60 Answer. The cylinder is 1 inches in diameter, and on the same axis there is a pulley 5 inches in diameter that drives a pulley 15 inches in diameter, on a stud. On the same axis with the pulley on the stud, there is a wheel with 14 teeth SPrNTNING-FKAME. 113 that, by means of an intermediate, takes into a wheel with YO teeth, on the front-roller. Kequired the number of tm-ns of twist per inch in the yarn, the front-roller being one inch in diameter. Diameter of the front- roller, in inches . . 1 Circumference . . 3.1416 Diameter of the pulley on the same axis with the cylinder, in inches 5 Teeth in the wheel on the same axis with the pulley on the stud 14 7, Diameter of the cylin- der, in inches, 16, Diameter of the pulley on the stud, in inches. YO Teeth in the wheel on the front-roller. Worlced out hy Ca/riGellation. 1-.4488-3.1416 1-5 144 1-1 15-33.42 Y0-.144 33.42 Answer. The, same without Cancellation Dividend . . . . Y X 15 x YO Divisor 3.1416 x 5 x 14 = 33.42 Answer. 114 COTTON MANUFACTURE. The heart or traverse motion makes one revolution while two layers of yarn are being wound on the bobbin. On the same axis with the heart there is a wheel with 72 teeth driven by a worm. On the same axis with the worm there is a pulley 9 inches in diameter, driven from a pulley on a stood. On the same axis with the pulley on the stood there is a wheel with 32 teeth that takes into a wheel on the front-roller. How many teeth should there be in the wheel on the front-roller, and what should be the diameter of the pulley on the stood, to make each layer of yarn 15 yards long, the front-roller being one inch in diameter, making no allowance for shrinkage in twist- ing? Layers wound on while the heart makes one revolution .... The worm is equal to one tooth, in effect . 1 Kevolutions of the heart. 72 Teeth in the wheel on the same axis with the heart. 9, Diameter of the pulley on the same axes with the worm, in inches. 32 Teeth in the wheel on the same axis with the pulley on the stud. SPINNING-FEAME. 115 Indies in one yard 36 Length of one layer of yarn, in yards ... 15 1, Diameter of the front- roller, in inches. 3.1416 Ratio of circnmfer- ence to diameter. Worked out. 1-2 1 1 Y2-6-24 9-3 32 1-3-36 1 3.1416'.62832 1-345 .62832 32 125664 188496 20.10624 3 A 2)60.31872 A .... . {Continued^ 3)30.15936 116 COTTON MANUFACTURE. A .... . 4)10.05312 B . . 2.51328)2.51328 A. 2 X 3 X 4 — —24 Teeth in tlie wheel on the front-roller. B. 2.51328 2.51328, Diameter of the puUey on the stood, in inches. Answer. rrom the particulars found in the preceding example, find the number of yards in one layer of yarn. Worked out hy Ccmcellation. 1-2 1 1 Y2-6-2-1 1-2.51328 9-3 1-3-24 32-4 1-3-36 1 3.1416-1.25 1.25 X 4 X 3 = 15 Answer. The same without Ca/riGellation. Dividend . . . T2 x 9 x 32 x 3.1416 = 15 Divisor .... 2 x 2.51328 x 24 x 36 Answer. MASOiST S MULE. 117 MASON S MULE. An npriglit sliaft in a mule-room makes 180 revolutions per minnte, and has on a wheel that takes into a wheel with 60 teeth, on a lying-shaft. On the lying-shaft there is a pulley that drives a pulley 12 inches in diameter, on the twist-shaft. How many teeth should there be in the wheel on the upright shaft, and what should be the diame- ter of the pulley on the lying-shaft, to drive the mule SI' stretches per minute, the twist-shaft making 75 revolu- tions per stretch, and the time occupied in drawing out and twisting being three-quarters of the time necessary to perform the whole stretch ? IT.B. — The twist-shaft makes from one to three revolu- tions, according to the size of the cop, while taking in the carriage, but there is a loss of about that amount while falling from the maximum to the minimum speed neces- sary for backing off. Revolutions per minute of the upright shaft 180 Time necessary for drawing out and twisting 3 Y5 Revolutions per stretch of the twist-shaft. 4: Time necessary to per- form the whole stretch. 60 Teeth in the wheel on the lying-shaft. 113 COTTON MANDFACTrKK 12, Diameter of tlie pulley on the twist-shaft, in inches. 3,5 Stretches per minute. Worked out. 1-3480 75-25 1-3 4 604 124 3.5 25 4 100 4 400 3.5 2000 A . . . 1200 . 7)1400.0 A 10)200 B. . . . . 20)20 1 mason's aroLE. 119 A. 10 X 7 = 70 Teetli in the wheel on the upright shaft. B. 20 20, Diameter of the pulley on the lying- shaft, in inches. Answer. From the particulars found in the preceding example, find how many stretches per minute the mule will make. Worked out hy Cancellation. 1-545-75 1-60 1442 14 180-34 7047.5-3.5 20-54 3-1 3.5 Answer. The sarne without CoMcellation. Dividend . . . . 180 x 70 x 20 x 3 = 3.5 Divisor 75 x 60 x 12 x 4 Answer. The cam that permits the belt to pass from the fast to the loose pulley makes one revolution per stretch. On the same axis with the cam there is a wheel that takes into a wheel with 36 teeth on the worm-wheel-shaft. On 120 COTTON MANITFAOTUKE. tlie worm-wlieel-sliaft there is also a wheel that takes into a worm on the twist-shaft. How many teeth should there be in the wheel on the cam-shaft, and the wheel that takes into the worm, to permit the twist-shaft to make Y5 revo- lutions per stretch ? Worked out. 75 Revolutions per stretch of the twist-shaft. 36 Teeth in the driving wheel on the worm- wheel-shaft. B 75 36 450 225 5)2700 A 5)540 A 3)108 A 3)36 B 3)12 B 4)4 1 mason's mule. 121 A. 5x3x3 = 45 Teeth in the wheel that takes into the worm. B. 5x3x4 = 60 Teeth in the wheel on the cam- shaft. Answer. From the particulars found in the preceding example, find how many revolutions the twist-shaft makes per stretch. Worked out hy Cancellation. 4545 1-3-36 60-5 15 X 5 = 75 Answer. The same without Cancellation. Dividend . . . . . . . . 45 x 60 75 Divisor 36 Answer. The twist-shaft has on a wheel with 21 teeth that, by means of an intermediate, takes into a wheel on the front-roller. How many teeth are there in the wheel on the front-roller, if 68 revolutions of the twist-shaft turn out 59.816064 inches, the front-roller being one inch in diameter ? 6 122 COTTON MANUFACTUKE. Length turned out, in inches 59.816064 68 Revohitions of the twist-shaft. 21 Teeth in tlie wheel on the twist-shaft. 1, Diameter of the front- roller, in inches. 3.1416 Circumference. Worked out hy Cancellation. l-.284.r6-9.5249.04-59.816064 68-34-1Y4 21-75 1 3.14164 75 Answer. The same without Cancellation. Dividend 68 x 21 x 3.1416 . Divisor 59.816064 75 Answer. The wheel that takes into the worm has 45 teeth. On the same axis with this wheel there is a wheel with 36 teeth that takes into a wheel with 60 teeth, on the cam- shaft. The spindle-warl is one inch, and the twist-pulley MASON S MULE. 123 17 inclies in diameter, and the length of the stretch is 59.816064: inches. Kequired the twist per inch in the yarn. Teeth in the wheel on the same axis with the wheel that takes into the worm Diameter of the spindle warl, in inches . . Length of the stretch, 36 in inches 59.816064 45 Teeth in the wheel that takes into the worm. 60 Teeth in the wheel on the cam-shaft. IT, Diameter of the twist- pulley, in inches. Worked out iy Ccmcellation. 45-15-21.31 + 1-3-36 1 l-.'r037184-3.518592-59.816064 60-5-1 IM Answer. 21.31 + The saTYie without Ca/ncellation. Dividend . . . . 45 x 60 x 17 Divisor 36 x 59.816064 = 21.31 + Answer. 124 COTTON MANUFACTUEE. The Mason's Mule is so constructed as to take in and out the carriage by means of a spur-wheel and chain. The wheel has a certain number of spurs, and each spur takes into a link in the chain, and, taken together, they are, in effect, equal to a pulley and band 3 inches in effect- ive diameter. On the same axis with the spur-wheel (the back shaft), there is a wheel di'iven fi-om a wheel with 28 teeth, on an intermediate shaft. On the intermediate shaft there is also a wheel driven from a wheel with 30 teeth on the same axis with the front-roller. How many teeth are there in the wheel on the back shaft, and the driven wheel on the intermediate shaft, if the surface velocity of the front-roller and the traverse of the carriage are equal, the front-roller being one inch in diameter ? Worked out. Diameter of the front- roller, in inches . . 28 Teeth in the driving wheel, on the inter- mediate shaft. 30 Teeth in the wheel on the same axis with the front-roller. 3, Effective diameter of the spur-wheel and chain, in inches. mason's mule. 125 28 30 840 3 A 12)2520 A 6)210 B 35)35 1 A. 12 X 6 Y2 Teeth in the driven wheel, on the intermediate shaft. B. 35 = 35 Teeth in the wheel, on the back shaft. Answer. From the particulars found in the preceding example, find how many inches the carriage will be taken out while the rollers deliver 59.816064 inches. Worked out hy Cancellation. 59.816064 1-342-Y2 30-54 1-5-35 28-Y4 34 59.81 6064 Answer. 126 COTTON MANUFACTTJRE. Xlie same without Cancellation. Dividend . 59.816064 x 30 x 28 x3 _ ^^ ^^^^^^ Divisor . . 7-2 x 35 Answer. The wheel on the front-roller for taking ont the carriage has 30 teeth, and the rollers deliver 59.816064 inches per stretch. How many inches will the rollers deliver with a wheel with 32 teeth ? Worked out hy Oa/nceTlaUon. 59.81606444.954016 1-4-32 30-3.75 14.954016 X 3.75 = 56.07756 Answer. The sa/me without Cancellation. Dividend . . . 59.816064 x 30 _ ^^ ^^^^g Divisor .... 32 Answer. The front-roller delivers 56.07756, and the length of the stretch is 59.816064 inches. How many inches does the carriage gain per stretch ? mason's mule. 127 59.816064 56.077560 3.738504: Answer. From tlie particulars found in tlie preceding example, find the draught at the carriage. Worked out hy Cancellation. 1-66.07766 I 59.816064:-1.06 1.06 Answer. The spm'-wheel on the back shaft, and the chain by which the carriage is taken in and out are, in effect, equal to a pulley and band 3 inches in effective diameter. On the back shaft there is a wheel that takes into a wheel with 168 teeth, on an intermediate shaft. On the inter- mediate shaft there is a wheel that takes into the bottom sliding-rack. The relative velocity of the bottom to that of the top sliding-rack is as 5 to 4. On a second inter- mediate shaft there is a wheel with 21 teeth that takes into the top sliding-rack. On this shaft there is also a wheel that takes into a wheel with 24 teeth, on the same axis with the twist-pulley. How many teeth should there be in the whee] on the back shaft, the wheel that takes 128 COTTON MANUFACTUEE. into the bottom sliding-rack, and the wheel on the second intermediate shaft that takes into the wheel on the same axis with the twist-pulley ; and what should be the diame- ter of the twist-pulley and the spindle, to give the bare spindle a sm-face velocity equal to the velocity of the carriage while going in, the spindle-warl being one inch in diameter ? N.B. — There is nothing between the twist-pulley and the spindle-warl that needs to be taken into consideration in solving the above problem. 3, Effective diameter of the spur-wheel and chain, in inches. 168 Teeth in the wheel that takes into the wheel, on the back shaft. 21 Teeth in the wheel that takes into the top sliding-rack. 24: Teeth in the wheel on the same axis with the twist-pulley. 1, Diameter of the spin- dle-warl, in inches. 5, Relative velocity of the bottom sHding-rack. Relative velocity of the top sliding-rack . . mason's mule. 129 Worked out. 3 168 21 24-6 1 5 14 168 3 504 21 504 1008 10584 6 63504 5 E . . .5)317520.0 E . . .5)635040.0 D . . . 7)1270080 . . 7)181440 tntvnued.^ 130 COTTON MANUFACTURE. C . . . . . 12)25920 A 5)2160 D 2)432 C 8)216 B 2T)27 1 A. 7x6 = 35 Teetli in the wheel on the back shaft. B. 2Y 27 Teeth in the wheel that takes into the bottom shding-rack. C. 12 X 8 = 96 Teeth in the wheel on the second intermediate shaft, that takes into the wheel on the same axis with the twist-pulley. D. 7x2 == 14, Diameter of the twist-pulley in inches. E. .5 X .5 = .25, Diameter of the spindle, in inches. From the particulars found in the preceding example, find how much yarn will be wound on to the bare spindle whUe the spur-wheel takes in 59.816064 inches of chain. Worked out lyy Cancellation. 59.816064 1-342-3 .254 144468 35-74 {Continued.) MASON'fi MULE. 2T-9-3-1 1-5 4-1 1-3-21 1-3-24: 96-84 1 144 59.816064 inches. 131 Answer. Div. The same without Cancellation. 59.816064 X .25 x 35 x 27 x 4 x 96 x 14 Divisor, 3 X 168 X 5 X 21 X 24 = 59.816064 Answer. From the particulars found in the preceding example, find how many inches of chain will be taken in per stretch of 59.816064 inches. Worlced out hy Cancellation. 1-.25 1-5-35 1-3-9-2T 14 1-8-96 144 59.816064 34 168444 5-20-54 21-M 24-34 59-816064 Answer. 132 COTTON MANUFACTURE. The same without Cancellation. Dividend, 59.816064 x 3 x 168 x 5 x 21 x 24 _ ^^ 8igo64 Divisor, .25 X 35 X 27 X 4 X 96 X 14 Answer. From the particulars found in the preceding example, find the diameter of the twist-pulley. Worked out hy Cancellation. 1 l-7'35 16844 1-.25 3-1 21-3-1 1-4 5-1 1-3-9-27 1-8-96 24-342-3-1 14 inches. Answer. The same rDithoxvt Cancellation. Dividend . .168x3 Divisor . . . 35 x .25 X 21 X 5 X 24 -, . . , — 14 inches. x4x27x96 Answer. From the particulars found in the preceding example, find the diameter of the spindle. MASON S MULE. 133 Worked out lyy Ccmcellation. 34 21-74 14 54 1-3-9-2Y 1-8-96 24-34 1-5-35 168-14-1 144 1-.25 .25 = 1^ of an inch. The same wiiJiout Cancellation. Dividend . . 3 x 21 x 5 x 24 x 168 . Divisor . . . 4 x 27 x 96 x 35 x 14 Answer. .25 Answer. How many revolutions must the spindle make to wind the yam on to the bare spindle while the carriage is going in, the diameter of the spindle being a quarter of an inch, and the length of the stretch 59.816064 inches ? Worked out 'by Cancellation. 1-.25 1-3.1416 59.816064-19.04-76.16 76.16 Answer. 134 COTTON MANUFACTURE. The same without Cancellation. Dividend 59.816064 Divisor 3.1416 x .25 = 76.16 Answer. Find how many inches of chain the spur-wheel will take in, while the spindle makes 76.16 revolutions.^ Worked out hy Cancellation. 76.1649.04 144 1-8-96 24-34 21-74 1-4 54 1-3-9-27 1-5-35 168-144 34 3.1416 3.1416 X 19.04 = 59.816064 Answer. The same without Cancellation. Div., 76.16 X 24 X 21 X 5 X 168 X 3 X 3.1416 _ ^^ §16064 Divisor, 14x96x4x27x35 Answer. mason's mule. 135 The leugtK of the cop is regulated more or less by the eopping-rail and shaper, and not wholly by the length of traverse of the nut on the screw in the recess of the builder. It is found by observation that a well propor- tioned and well built cop, having on 630 stretches of l^o. 40 filling, will measure from extreme point to extrenie point, as much more than the traverse of said nut, as 19 is more than 14. On the same axis with the screw in the recess of the builder, there is a wheel that takes into a wheel with 2Y teeth. On the same axis with the latter wheel there is a spur-wheel that moves one spur per stretch. How many threads per inch are there in the screw ; how many teeth in the wheel on the same axis with the screw ; how many spm*s in the spur-wheel, and what is the length of the cop, if it contains 630 stretches, and the traverse of the nut on the screw in the recess of the builder, is to the length of the cop as 14 to 19 ? Proportionate length of traverse of the nut in the recess of the builder 14 630 Stretches on the cop. 27 Teeth in the wheel that takes into the wheel on the same axis with the screw. 19, Proportionate length of the cop. 136 COTTON MANUFACTURE. Worked out. 630-9045 2Y 1-244 19 45 27 315 90 1215 19 10935 1215 A . . . . 3)23085 B . . 6)7695 C . . . 3)1282.5 C . . . 3)427.5 B. . . . 10)142.5 A . . . . 3)14.25 D . . 4.76)4.75 mason's mule. 137 A. 3x3 = 9 Threads per inch in the screw. B. 10 X 6 == 60 Teeth in the wheel on the same axis with the screw. C. 3x3 zi=:= 9 Spurs in the spur-wheel, D. 4.75 4.75, The length of the cop, in inches. Answer. From the particulars found in the preceding example, find the length of the cop, in inches. WorTced out lyy Cancellation. 1-9 63(0-9-l l-2-6(0 27-94.54 1-244 19-9.54.75 1-2-9 4.75 TJie same without CaMcellation. Dividend . . . . . 630 x 27 x 19 Answer. 4.75 Divisor 9 x 60 x 14 x 9 Answer. From the particulars found in the preceding example, find the number of stretches on a cop. 138 COTTON MANUFACTUKE. Worked out hy CanGellation. 4.754 9-3 1-3-27 6045 94 14.7549 14 15 X 14 X 3 630 Answer. The same without Ca/rhcellation. Dividend . . 4/r5 x 9 x 60 x 9 x 14 Divisor . . . = 630 27 x 19 Answer. From the particulars found in the preceding example, find the number of threads per inch in the screw. Worked out hy CanGellation. 1-4.75 63(0-7-1 l-3-6(0 27-9 1-9 1-244 19-4-24 Answer. MASON S MULE. 139 The sa/me witliout Ccmcellation. Dividend 630x27x19 9 Divisor 4.75x60x9x14 Answer. From tlie particulars found in the preceding example, find the number of teeth in the wlieel on the same axis with the screw. Worlced out ly Cancellation. 630-7040 1-9 27-3 1-9 1-244 194-2 14.Y5 10 x 3 X ^ >. 60 Answer. The sa/me without Cancellation. Dividend 630 x 27 x 19 Divisor = 60 9 X 9 X 14 X 4.75 Answer. The back-roller is seven-eighths of an inch in diameter. The front-roller wheel has 30, and the change-wheel 36 140 COTTON MAJSTDFACTURE. teeth. How many teeth should there be in the top-carrier and the back-roller wheel, and what should be the diame- ter of the front-roller to produce a draught of 9 ? Worked out. 7, Back-roller in eighths of an inch. 30 Teeth in the front-roller wheel. 36 Teeth in the change- wheel. 9, Draught. 36 30 1080 7 T560 9 A . . . . 4)68040 A . . . 2)17.010 B . . . . 5)8505 B . . . . 3)1701 (Continued.) mason's mule. 14:1 B . . . . Y)567 C. . . . 81)81 1 A. 4x2 == 8, Diameter of the fi'ont-roUer, in eighths of an inch. B. 5x3x7 = 105 Teeth in the top-carrier. C. 81 == 81 teeth in the back-roller wheel. Answer. From the particulars found in the preceding example, find the di'aught between the back and the front rollers. Worked out hy Ccmcellation. 1-7 1-2-30 1-9-36 844 105454 81-9 Answer. The sa/me without Cancellation. Dividend . . . . . . . 8x105x81 = 9 Divisor 7x30x36 Answer. 142 COTTON MANUFACTURE. THE FKANE.LIN MULE, A mule is driven from an upright shaft making 180 revolutions per minute, by a train of three pairs of pul- leys, and one pair of wheels. The driven wheel has 64 teeth, and the respective diameters of the driven pulleys are 20, 18, and 12 inches. How many teeth should there be in the driving wheel, and what should be the respective diameters of the driving pulleys, to drive the mule S^ stretches per minute, the twist-shaft making 72 revolutions per stretch, and the time occupied in drawing out and twisting being three-quarters of the time necessary to perform the whole stretch ? Revolutions of the up- right shaft per minute, 180 Time occupied in draw- ing out and twisting, 3 72 Revolutions of the twist- shaft per stretch. 3.25 Stretches per minute. 4 Time occupied in per- forming the whole stretch. 64 Teeth in the diiven wheel. 20, Diameter of the first driven pulley, in inch- es. 18, Diameter of the second driven pulley, in inch- es. THE FRANKLIN MULE. 143 12, Diameter of the third driven pulley (which is on the twist-shaft), in inches. Worked out. 148(0 1-3 72-24 3.25 4 64 2(0 184 12 {Continued.) 3.25 24 1300 650 78.00 4 312 64 1248 1872 144 COTTON MANUFACTURE. 19968 2 39936 12 T98Y2 39936 A . . . 12)479232 A . . . . 6)39936 D . . . 8)6656 C . . . . 2)832 . . 2)4:16 C . . B. . . . . 10)208 . 20.8)20.8 A. 12 X 6 72 Teeth, in the driving wheel. B. 20.8 == 20.8, Diameter of the first driving pulley, in inches. C. 10 X 2 ^= 20, Diameter of the second driving pul- ley, in inches. D. 8x2 : 16, Diameter of the third driving pulley, in inches. Answer. THE FBANKLIN MULE. 145 A mule is driven from an upright shaft making 180 revolutions per minute, by a train of three pairs of pul- leys and one pair of wheels ; the driving wheel has Y2, and the driven wheel 64 teeth. The respective diameters of the driving pulleys are 20.8, 20, and 16, and the driven pulleys 20, 18, and 12 inches. How many stretches per minute does the mule make, allowing the last driven pul- ley (which is on the twist-shaft), to make Y2 revolutions per stretch, and the time occupied in drawing out and twisting being three-quarters of the. time necessary to perform the whole stretch ? Revolutions of the twist- shp-ft per stretch , . Y2 Time occupied in per- forming the whole stretch 4 Teeth in the driven wheel 64 Diameter of the first driven pulley, in inch- es 20 Diameter of the second driven pulley, in inch- es 18 180 Revolutions of the up- right shaft per min- ute. 3, Time occupied in draw- ing out and twisting. Y2 Teeth in the driving wheel. 20.8, Diameter of the first driving pulley, in inches. 20, Diameter of the second driving pulley, in inches. 146 COTTON MAJSTUFACTUBE. Diameter of the third di'iven pulley (which is on the twi&t-shaft), in inches .... 12 16, Diameter of the third driving pulley, in inches. Worked out hy Cancellation. 1-Y2 18(0-1 14 34 1-8-64 72-1 ■ 1-2(0 20.8-2.6 148 20-10-1.25 1-342 16-4-1 2.6x1.25 3.25 Answer. T%e same without Cancellation. Dividend . 180 x 3 x Y2 x 20.8 x 20 x 16 . Divisor . . 72x4x64x20x18x12 3.25 Answer. The twist-pulley is 17 inches in diameter, makes 72 revolutions per stretch, and drives the pulley on the drum- shaft. On the drum-shaft there is a wheel with 50 teeth that takes into a wheel on the same axis with the di'um ; the drum is 10 inches in diameter, and drives the spindles. How many teeth should there be in the wheel on the same THE FKANKLIN MULE. 147 axis with the drum ; what should he the diameter of the pulley on the drmn-shaft, and the spindle-warl, and what should be the length of the stretch to put 20 turns of twist per inch into the jam ? Tm*ns of twist per inch in the yarn ... 20 72 Revolutions per stretch of the twist-pulley. 17, Diameter of the twist- pulley, in inches. 50 Teeth in the wheel on the di'um-shaft. 10, Diameter of the drum in inches. Worked out. 72-36 17 50 1-2(0 1(0 36 17 {ContMiued.) 148 COTTON MANUFACTURE. 252 36 612 50 A . . . . 10)30600 B. . . . 10)3060 B . . . . 2)306 B 3)153 C . . . . 51)51 D . . . . 1 A. 10 == 10, Diameter of the pulley on the di'um- shaft, in inches. B. 10 X 2 X 3 60, Length of the stretch, in inches. C. 51 ■ 51 Teeth in the wheel on the same axis with the drum. D. 1 == 1, Diameter of the spindle-warl, in inches. Answer. The twist-pulley makes 72 revolutions per stretch, is 17 inches in diameter, and di'ives the pulley on the drum- shaft which is 10 inches in diameter. On the drum-shaft there is a wheel with 50 teeth that takes into a wheel with 51 teeth, on the same axis with the drum. The THE FRANKLIN MULE. 149 drum is 10 inches in diameter and drives tlie spindles, the warls of which is one inch in diameter. How many turns of twist per inch is there in the yarn, the length of the stretch being 60 inches ? 72 Revolutions per stretch of the upright shaft. Diameter of the pulley 17, Diameter of the twist- on the drum-shaft, in pulley, in inches. inches 10 Teeth in the wheel on 50 Teeth in the wheel on the same axis with the di'um-shaft. the drum .... 51 Diameter of the spindle- 10, Diameter of the drum, warl, in inches . . 1 in inches. Length of the stretch, in inches .... 60 Worked out hy Ccmcellation. Y2424 1(0 147-51 1 1-6(0 5x4 = IM 5(0 1(0 20 Answer. 150 COTTON MANUFACTURE. = 20 The same without Ca/ncellation. Dividend. ..... 72x17x50x10 Divisor 10x51x60 Answer. The twist-sliaft makes 68 revolutions per stretch v^hile in connection with the rollers, and has on a wheel with 18 teeth that, by means of an intermediate, takes into a wheel on the roller-shaft. On the other end of the roller- shaft, there is a wheel with 40 teeth that takes into a wheel on the front-roller. How many teeth should there be in the driven wheel on the roller-shaft, and the wheel on the front-roller, to turn out 60.0831 inches per stretch, the front-roller being one inch in diameter ? 68 Revolutions per stretch of the twist-shaft while in connection with the rollers. 18 Teeth in the wheel on the twist shaft. 40 Teeth in the wheel on the roller-shaft that takes into the wheel on the front-roller. THE TBANKLIN MULE. 151 Length, turned out per stretch, in inches, 60,0831 1, Diameter of the froUer, in inches. 3.1416, Circumference. Worked out. 68-32 18-2 40 1-2.12649.125-60.0831 1 3.1416-1 32 2 64 40 A A A A B 4)2560 2)640 4)320 . 2)80 40)40 1 A. 4x2x4x2 the roller-shaft. 64 Teeth in the driven wheel on 152 COrrON ]\tANUFACTURE. B. 40 40 Teeth in the wheel on the front- roller. Answer. The twist-shaft makes 68 revolutions per stretch while in connection with the rollers, and has on a wheel with 18 teeth that takes into a wheel with 64 teeth, on the roUer- sliaft. On the other end of the roller-shaft there is a wheel with 40 teeth, that takes into a wheel with 40 teeth, on the front-roller. How many inches will be tm'ned out per stretch, the front-roller being one inch in diameter ? Teeth in the driven wheel on the roller- shaft ..,-... 64 Teeth in the wheel on the front-roller . . 40 68 Revolutions per stretch of the twist-shaft while in connection with the rollers. 18 Teeth in the wheel on the twist-shaft. 40 Teeth in the driving wheel on the roller- shaft. 1, Diameter of the front- roller, in inches. 3.1416 Circumference. THE FEANKLIN MULE. 153 Worked out hy Cancellation. 68-17 1-846-64 140 18-9 404 1 3.1416-.3927 17 X 9 X .3927 = 60.0831 . Answer. The same without CanGellation. Dividend . . . 68 xl8 x40x3.1416 _ ^^ ^gg^ Answer. Divisor "... 64x40 The front-roller is one inch in diameter, and has on a wheel that takes into a wheel with 40 teetli, on the roller- shaft. On the other end of the roller-shaft there is a wheel that takes into a wheel with 64 teeth, on the draw- ing-out shaft. On the other end of the drawing-out shaft there is a wheel that takes into a wheel with 40 teeth, on the scroll-shaft. How many teeth should there be in the wheel on the front-roller, the wheel on the roller-shaft that takes into the wheel on the drawing-out shaft, and the wheel that takes into the wheel on the scroll-shaft ; and what should be the diameter of the scroll to give it a surface velocity equal to that of the front-roller ? 7* 154 COTTON MANUFACTUKE. 40 Teeth in the wheel on the roller-shaft tliat takes into the wheel on the front-roller. 64 Teeth in the wheel on tlie drawing-out shaft that takes into the wheel on the roller" shaft. ^0 Teeth in the wheel on the scroll-shaft. 1, Diameter of the front- roller, in inches. Worked out. 64 40 2560 . . . 40 10)102400 A . . . . 10)10240 A .... . 2)1024 A .... . 2)512 {^Continued.) THE FKANKLESr MTJLE. 155 c . . . . 2)256 B . . . . 2)128 B . . . 2)64 B . . . 2)32 B ... 2)16 B . . . . . 2)8 D . . . . 2)4 D . . . . 2)2 1 A. 10 X 2 X 2 40 Teeth ] Ln the wheel on the front- roller. B. 2x2x2x2x2 32 I 'eeth in the wheel on the roller-shaft, that takes into the wheel on the drawing-out shaft. C. 10 X 2 : 20 Teeth in the wheel that takes into the wheel on the scroll-shaft. D. 2x2 =^ 4, Diameter of the scroll, in inches. Answer. The front-roller is one, and the scroll is 4 inches in diameter. The front-roller has on a wheel with 40 teeth that takes into a wheel with 40 teeth, on the roller-shaft. On the other end of the roller-shaft there is a wheel with 32 teeth that takes into a wheel with 64 teeth, on the 156 COTTON MANUFACTURK. di'awing-out shaft. On the otlier end of the drawing-out shaft there is a wheel with 20 teeth that takes into a wheel with 40 teeth, on the scroll-shaft. What is the surface velocity per stretch of the scroll, if that of the front-roller is 60.0831 ? !N^.B. — In practice it is necessary to add the diameter of the drawing-out band to that of the scroll. 60.0831, Surface velocity per stretch of the front- roller. Diameter of the front- 4,. Diameter of the scroll, roller, in inches . . 1 in inches. Teeth in the wheel on 40 Teeth in the wheel on the roller-shaft, that the front-roller. takes into the wheel on the front-roller . 40 Teeth in the wheel on the drawing-out shaft that takes into the wheel on the roller- shaft 64 Teeth in the wheel on the scroll-shaft . . 40 32 Teeth in the wheel on the roller-shaft, that takes into the wheel on the drawing-out shaft. 20 Teeth in the wheel on the drawing-out shaft, that takes into the wheel on the scroll- shaft. THE FEANKLm MULE. 157 Worked out hy Cancellation. 60.0831 1 44 140 404 1-2-64 324 14(0 2(04 60.0831 Answer. Dividend Divisor . The same witliout Cancellation. 60.0831 X 4 X 40 X 32 X 20 40 X 64 X 40 60.0831 Answer. The spindle is g^, the spindle-warl is one, and the drum is 10 inches in diameter. On the same axis with the drum there is a wheel with 51 teeth that takes into a wheel with 50 teeth, on the drum-shaft. On the drum- shaft there is also a wheel that takes into a wheel with 34 teeth, on the same axis with the winding-on drum. How many teeth should there be in the wheel on the drum-shaft that takes into the wheel on the same axis with the wind- ing-on drum ; and what should be the diameter of the winding-on drum, to give it a surface velocity equal to that of the bare spindle, when winding on the first stretch of yarn ? 158 COTTON MANTTFACTUKE. Diameter of the spindle- warl, in inclies . . 1 Teeth in the wheel on the same axis with the drum .... 51 .24, Diameter of the spindle, in inches. 10, Diameter of the drum, in inches. 50 Teeth in the wheel on the drum shaft that takes into the wheel on the same axis with the drum. 34 Teeth in the wheel on the same axis with the winding-on drum. Worked out. .24-.08 1 1-3-51 10 50 34-2 50 2 100 10 1000 .08 {^Continued.) THE FKAJiTKLIN MULE. 159 A . . . . 10)80.00 A 2)8 B 4)4 1 A. 10 X 2 20 Teeth in the wheel on the drum- shaft that takes into .the wheel on the same axis with the winding-on drum. B, 4 4, Diameter of the winding-on drum, in inches. Answer. The spindle is ^V ^^ ^^ i^ch in diameter, and has on a warl one inch in diameter, driven from a drum 10 inches in diameter. On the same axis with the drum there is a wheel with 51 teeth that takes into a wheel with 50 teeth, on the drum-shafb. On the drum-shaft there is a wheel with 20 teeth that takes into a wheel with 34 teeth, on the same axis with the winding-on drum. What is the sur- face velocity of the spindle when winding on the first stretch of yarn, if the winding-on drum throws off 60.0831 inches of chain, the winding-on drum being 4 inches in diameter ? 60.0831 Inches of chain thrown off when wind- ing on the first stretch of yarn. IGO COTTON MANUFACTURE. Diameter of the spindle, in inches 24 Teeth in the wheel on the same axis with the winding-on drmn 34 Teeth in the wheel on the drum-shaft that takes into the wheel on the same axis with the drmn .... 50 Diameter of the drum, in inches . . . . 10 4, Diameter of the wind- ing-on drum, in inches. 20 Teeth in the wheel on the drum-shaft that takes into the wheel on the same axis with the winding-on drum. 51 Teeth in the wheel on the same axis with the drum. 1, Diameter of the spindle- warl, in inches. Worked out hy Cancellation. 60.0831 1-.24 4-1 •2-8.5-34 2(04 ' 1-50 51-212.5-4.254 1(0 1 60.0831 Answer. T]ie same without Cancellation. Dividend . . 60.0831 x 4 x 20 x 51 Divisor. . . .24x34x50x10 60.0831 Answer. DKESSmG-MACHINE. IGl DEESSING-MACHINE. A dresser is driven from an upright shaft, making 180 revolutions per minute, by a train of three pairs of pul- leys and one pair of wheels ; the driving wheel has 96 teeth, and the driving pulleys are 20, 18, and 10 inches in diameter, respectively. How many teeth should there be in the driven wheel ; and what should be the diameter of the driven pulleys, respectively, to drive the first driven shaft of the dresser 100 revolutions per minute ? Revolutions of the first di'iven shaft of the dresser per minute . 100 180 Revolutions of the up- right shaft per min- ute. 96 Teeth in the driving wheel. 20, Diameter of the first driving pulley, in inches. 18, Diameter of the second dri^'ing pulley, in inches. 10, Diameter of the third driving pulley, inches. m 162 COTTON MANUFACTUKE. Worked out. 1(00 180 96 2(0 18 1(0 180 96 1080 1620 17280 2 34560 18 276480 34560 B . . . 10)622080 B . . . . 3)62208 {Continued.^ DKESSING-lVr A CHLNB. c . . 3)20736 A . . . . 4)6912 A . . . . 2)1Y28 A . . 2)864: A . . 4)432 c . . . 3)108 c . . . 3)36 D. . . . 12)12 1 163 A. 4x2x2x4 = 64 Teeth in the driven wheel. B. 10 X 3 = 30, Diameter of the first driven pulley, in inches. C. 3x3x3 2Y, Diameter of the second driven pulley, in inches. D. 12 12, Diameter of the third driven pulley, in inches. Answer. From the particulars found in the preceding example, find the revolutions per minute of the first driven shaft of the dresser. 164 COTTON MANUFAOTUKE. Worked out hy Cancellation. 18(0-6-2 1-2-8-64 96424 1-3(0 20-5 1-9-2Y 18-24 142 10 10x5x2 100 TTie same without Cancellation. Dividend . . . 180x96x20x18x10 Divisor .... Answer. = 100 64x30x27x12 Answer. The first driven shaft makes 100 revolutions per minute, and drives the centre beam by a train of 4 pairs of wheels and one pair of cones. The large end of the driving cone is 9 inches in diameter, and the driving wheels have 50, 20, 20, and 20 teeth respectively. What should be the diameter of the small end of the driven cone ; and how many teeth should there bein the driven wheels, respect- ively, to give the empty beam a surface velocity of 4 yards per minute, the beam being 5 inches in diameter ? 100 Revolutions per minute of the first driven shaft. DKESSING-MACHINE. 165 Inches in one yard . 36 Surface velocity per minute of tlie empty beam, in yards . . 4: 9, Diameter of the large end of the driving cone, in inches. 50 Teeth in the first driv- ing wheel. 20 Teeth in the second driving wheel. 20 Teeth in the tliird driv- ing wheel. 20 Teeth in the fourth driving wheel. 5, Diameter of the empty beam, in iuches. 3.1416, Circumference. Worlced out. 100 9-3 50 20 20 20'5 1-3-36 5 3.1416'.2618 14 166 co'rroN manufactuke. .2618 5 1.3090 5 6.5450 20 130.9000 20 2618.0000 50 130900.0000 3 392700.0000 100 E . 10)39270000.0000 E. . . 10)3927000 B 5)392700 B 5)78540 {Continued.) DKESSESTG-MACnmE. 167 B 2)15708 D 2)7854 C 5)3927 C 2)785.4 C 5)392.7 D 5)78.54 D . . . . 3)15.708 A 5.236)5.236 1 A. 5.236 5.236, Diameter of the small end of the driven cone, in inches. B. 5x5x2 == 50 Teeth in the first driven wheel. C. 5x2x5 == 50 Teeth in the second driven wheel. D. 5x3x2 = 30 Teeth in the third driven wheel. E. 10x10 = 100 Teeth in the beam-flange, or fourth driven wheel. Answer. From the particulars found in the preceding example, find the surface velocity of the empty beam per minute. 1G8 COTTON MANUFACTUKE. Worked out ly Ccmcellation. 100-1 1-2.618-5.236 9-1 1-50 50-1 1-5(0 2(0-1 1-3(0 2(0 1-100 20-5 1-4-36 5-1 3.1416-1.2-.4 5 X 2 X .4 = — 4 yards. The sa/ine without Cancelldtion. Div. ., 100 X 9 X 50 X 20 X 20 X 20 x 5 x 3.1416 Divisor, 5.236 X 50 X 50 x 30 X 100 x 36 Answer. = 4 yards. Answer. N.B. — The surface velocity of the empty beam, as shown in the preceding example, is as quick as will pro- bably ever be required for any kind of work ; in practice it is found necessary to vary the velocity according to cir- cumstances, such as facilities for drying, fineness of yarn, and the progressively increasing size of the beam, which is done by causing the belt to traverse on the cones. As some kinds of work requires more wind than others, DKESSma-MAOHINE. 169 and as local circiTmstances lias more or less to do with making it effective, it is impossible to lay down any rule that will answer in all cases with respect to quantity. It is estimated by some mechanicians that tlie circumference of a fan should have a velocity of 2600 yards per minute, to equal a storm of wind ; the way to find which or any other velocity that may be required, will be found in the following example : A fan, one yard in diameter, is driven from an upright shaft making 180 revolutions per minute, by a train of 3 pairs of pulleys and one pair of wheels. The driving pul- leys are 42, 39, and 20 inches in diameter, respectively, and the driving wheel has 96 teeth. What should be the diameter of the driven pulleys, respectively, and how many teeth should there be in the driven wheel, to give the circumference of the fan a velocity of 2600 yards per minute ? Velocity of the circum- ference of the fan per minute, in yards, 2600 180 Revolutions per minute of the upright shaft. 96 Teeth in the driving wheel. 42, Diameter of the first driving pulley, in inches. 170 OOrrON MANUFACTUKE. 39, Diameter of the second driving pulley, in inches. 20, Diameter of the third driving pulley, in inches. 1, Diameter of the fan, in yards. 3.1416, Circmnference. Wfyrked out. l-13-26(00 18(0-9 96 42 39-3 2(0 1 3.1416 96 9 864 42 1728 3456 {Continued •) DKESSING-MACHmE. 171 36288 3 108864 2 2in28 3.1416 1306368 217Y28 870912 217728 653184 A . . . . . 12)684014.2848 A 7)57001.1904 B 6)8143.0272 B 6)1357.1712 G 8)226.1952 C .... 4)28.2744 D . . . 7.0686)7.0686 1 172 COITON AIANUFACTURE. = 84 Teeth in the driven wheel; 36, Diameter of the first di'iven pulley, 32, Diameter of the second driven pulley, = Y.0686, Diameter of the third driven A. 12x7 = B. 6xQ = in inches. C. 8x1 = in inches. D. 7.0686 pulley, or pulley on the same axis with the fan, in inches. Answer. From the particulars found in the preceding example, find the velocity per minute of the circmnference of the fan. Worked out hy Cancellation. 1-7-84 1-6-36 14-32 l-2.^5-7.0686 180-8040 96-8 12-6-1 39-6.5 20-5 1 3.1116-1 Dividend, Divisor, 10 X 8 X 5 X 6.5 = 2600 yards. TTie smne without Ccmcellation. 180 X 96 X 42 X 39 X 20 X 3.1416_ 81x36x32x7.0686 Answer. 2600 yards. Answer. DRESSING-MACHINE, 173 In practice it is found, tliat on account of shrinkage in weaving a certain kind of cloth, that it takes 1,04 Y2 yards of warp to make one yard of cloth. The warp is mea- sured by the neck-roller, on the end of which there is a worm that takes into a wheel with 100 teeth, and every time the wheel makes a revolution it causes a mark to be made on the warp ; this mark indicates where to cut the cloth into lengths called cuts (hence the term cut-mark). "What should be the diameter of the neck-roller, to mark the warp into lengths requisite for weaving cuts of cloth 42 yards long ? Teeth in the wheel that takes into the worm. 100 Katio of circumference to diameter . . 3.14:16 42, Length of a cut of cloth, in yards. 36 Inches in one yard. 1.04Y2, Length of warp re- quired for one yard of cloth, in yards. Worked out hy Cancellation. 424.2-,42 36-12 1-10400 {Continued.) 1T4 COTTON MANUFACTUKE. 1-3-3.1416 l.(M724 12 X .42 5.04 inches. Answer. The same without Ca/ncellation. Dividend 42x36x1.0472 6.04 Divisor 100x3.1416 Answer. From tlie particulars found in the preceding example, find the number of yards in a cut of cloth. Worked out hy CcmcellaUon. 1-12-36 1-1.04Y2 5.04-.42 3.1416-3-1 100 100 X. 42 = 42 Answer. The same witJwut Ca/ncellation. Dividend 5.04x3.1416x100 :42 Divisor 36x1.0472 Answer. POWEK-LOOM. 175 POWEK-LOOM. A loom is driven from an upright sliaft making 180 revolutions per minute, by a train of two pairs of pulleys and one pair of wheels. The driving pulleys are 17^, and 8 inches in diameter, and the driving wheel has 96 teeth. What should be the diameter of the driven pulleys, respectively, and how many teeth should there be in the driven wheel, to drive the loom 140 picks per minute ? Picks per minute of the loom 140 180 Revolutions per minute of the upright shaft. 96 Teeth in the driving wheel. 17.5, Diameter of the first driving pulley. m inches. 8, Diameter of the second driving pulley, in inches. Worked out. 1-744(0 18(0-9 96 17.5-2.5 (^Continued.) 176 COTTON MANtlFAOTUEE, 96 9 864 8 6912 2.5 34560 13824 A 8)17280.0 A 8)2160 C 12)270 B 22.5)22.5 1 A. 8x8 64 Teetli in the driven wheel. B. 22.5 22.5, Diameter of the first driven pulley, in inches. C. 12 = 12, Diameter of the second driven pulley on the crank-shaft of the loom, in inches. Answer. From the particulars found in the preceding example, find how many picks per minute the loom will make. POWEE-LOOM. 177 Worked out hy Cancellation. 180-200 1-8-64: 1-.94.5-22.5 1-12 96-124 17.5-3.5-.7 84 200 X .7 MO Answer. Ths same without Cancellation. Dividend .... 180x96x17.5x8 . Divisor 64x22.5x12 140 Answer. The rateliet wheel of the take-up motion has 80 teeth, and takes up one tooth every two picks, and the emery- roller wheel has 90 teeth. How many teeth should there be in the wheel that takes into the emery-roller wheel ; and what should be the circumference of the emery-roller to produce cloth with 72 picks per inch ? 80 Teeth in the ratchet- wheel. 2, Takes up one tooth every two picks. 90 Teeth in the emery-roll- er wheel. 8* 178 COTTON MAJifTIFACTTIRB. Picks per ] nch in the cloth . . . . . . 72 Worked out. 80-10 2 _ 90-10 l'9-72 10 10 100 2 A . . . . . . . 8)200 A . • • • • • • 2)25 B . . . . . 12 .5)12.5 A. 8x2 16 Teeth in the wheel that takes into the emery-roller wheel. J3. 12.5 = 12.5, Circumference of the emery-roller, in inches. Answer. POWEK-LOOM. 179 From tlie particulars found in the preceding example, find the picks per inch in the cloth. Worked out hy Cancellation. 80-54 24 146 9048 1-.5-2.6-12.5 18x4. n Answer. The same without Cancellation. Dividend 80x2x90 = 72 Divisor ........ 12.5 x 16 Answer. From the particulars found in the preceding example, find the number of teeth in the ratchet wheel. Worlcsd out hy Cancellation. 140-90 1-2 16 12.54.25 72-84 16x4x1.25 80 Answer. 180 COTTON MAKUFACTUKE. Tlie sa/me without Cancellation. Dividend 16x12.5x72 80 Divisor ., 90x2 Answer. From the particulars found in the preceding example, find how many picks the loom makes while the ratchet- wheel moves one tooth. Worked out hy Cancellation. 140-90 1-5-80 164 12.5-2.5 72-8-.8 2.5 X. 8 Answer. TTie same without Cancellation. Dividend 16x12.5x72 2 Divisor 90x80 Answer. From the particulars found in the preceding example, find the number of teeth in the emery-roller wheel. POWEK-LOOM. 181 Worked out hy Cancellation. ' 16-.1 12.5-2.5 72-36 1-5-80 1-2 36x2.5 90 Answer. The same without Cancellation. Dividend 16x12.5x72 . Divisor 90 80x2 Answer. From the particulars found in the preceding example, find the number of teeth in the wheel that takes into the emery-roller wheel. Worked out hy Ca/ncellation. 90-18-1 1-.5-2.5-12.5 1-2-36-72 2-1 80-40-8-16 16 Answer. 182 COTTON MANUFACTUEE. The same without Ccmeellation. Dividend 90 x 2 x 80 16 Divisor 12.5x72 Answer. From the particulars found in the preceding example, find the circumference of the emery-roller. Worhed out hy Cancellation. 1-16 9040 24 80-54.25 14-8-Y2 10 X 1.25 = 12.5 inches. Answer. The sa/me without Cancellation. Dividend 90x2x80 12.5 Divisor 16x72 Answer. If the circumference of the emery-roller is 12|^ inches, what will be its diameter ? 12.5 ^ 3.1416 = 3.9788+ inches. Answer. If a change-wheel with 16 teeth puts in 72 picks per inch, how many picks per inch will a change-wheel with 18 teeth put in ? POWEK-LOOM. 183 Worked out hy Cancellation. 724 148 16 16x4 64 Answer. The same without Cancellation. Dividend Y2xl6 . Divisor 18 64 Answer. The taking-iip ratchet-wheel has 96 teeth, and on the same axis there is a wheel that takes into a wheel with 90 teeth, on the same axis with the emery-roller. How many- teeth are tliere in the wheel on the same axis with the ratchet-wheel ; and what is the circumference of the emery-roller, if the loom is putting in 100 picks per inch, and taking up one tooth every 2 picks ? Picks per inch in the cloth 100 96 Teeth in the ratchet- wheel. 90 Teeth in the wheel on the same axis with the emery-roller. 2 Picks put in while the ratchet-wheel takes up one tooth. 184 COTTON MANUTACTUKE. Worked out. 96 9(0 -.9 140(0 2' 96 .9 86.4 2 A . . . • • 6)172.8 A . . . • • 3)34.56 B . . 11. 52)11.52 A. 5x3 15 Teeth in the wheel on the same axis with the ratchet-wheel. B. 11.52 = 11.52, Circumference of the emery- roller, in inches. Answer. From the particulars found in the preceding example, find the picks per inch in the cloth. POWER-LOOM. 185 Worked out hy Cancellation. 2 96400 1-345 90-7.54.5-.5 1-.9641.52 100 X 2 X . 5 100 TJie same without Cancellation. Dividend 2x96x90 Answer. = 100 Divisor 15 X 11,52 Answer. The taking-iip ratchet-wheel containing 96 teeth takes up one tooth every 2 picks. On the same axis with the taking-up ratchet-wheel there is a wheel with 15 teeth that takes into a wheel on the same axis with the emery-roller containing 90 teeth. The diameter of the emery-roller is to that of the full beam as one to 3. The beam-flange containing 108 teeth takes into a wheel on a horizontal shaft. On the horizontal shaft there is also a wheel with 14 teeth that takes into a worm. On the same axis with the worm there is a wheel with 28 teeth that takes into a wheel on the same axis with the let-oif ratchet-wheel ; the latter wheel contains 120 teeth. How many teeth should there be in the wheel that takes into the beam-flange, and 186 COTTON MANUFACTURE, the wheel on the same axis with the let-off ratchet-wheel, if the latter wheel lets off one tooth per pick while weav- ing the first lap of a full beam, making no allowance for shrinkage in weaving ? Teeth in the taking-up ratchet-wheel ... 96 Teeth in the wheel on the same axis with the emery-roller . . 90 Relative diameter of the full beam .... 3 .5, The taking-up ratchet- wheel takes up one tooth every 2 picks, which is equal to one half tooth per pick. 15 Teeth in the wheel on the same axis with the taking-up ratchet wheel. 1, Relative diameter of the emery-roller. 108 Teeth in the beam- flange. 14 Teeth in the wheel that takes into the worm. 28 Teeth in the wheel that takes into the wheel on the same axis with the let-off ratchet- wheel. 120 Teeth in the let-off ratchet-wheel. POWEK-LOOM. 187 Worked out. 1-8-96 .5 1-9(0 15-5 1-3 1 108-9-1 14 28 12(0-1.5 28 1.5 140 28 42.0 14 1680 420 588.0 5 ( 3940.0 .5 {.Continued^ 188 COTTON MANUFACTURE. A .... . 10)14Y0.00 B 7)147 B 7)21 A 3)3 A. 10x3 30 Teeth in tlie wheel that takes into the beam-flange. B. 7x7 49 Teeth in the wheel on the same axis with the let-off ratchet-wheel. Answer. From the particulars found in the preceding example, find how many teeth the let-off ratchet-wheel will move while the loom makes one pick. Worked out by Cam^ceTlation. 1-2-8-96 1-9(0 1-3 1-345-30 1-749 2x.5 12(0-4-1 .5 15-5-1 108-9-1 14-2-1 28-4-2 Answer. WEIGHmG YAUN, SLIVEE, ETC. 189 The same without Ca/nceUation. Dividend . . 120 x. 5 x 15 x 108 x 14x28 Divisor. . . 96x90x3x30x49 WEIGHISTG TAEF, SLIVER, ETC. = 1. Answer. Correct instruments for weighing the sliver, roving, and yarn, in the various branches of carding and spinning, are of snch vast import- ance in the manufactm^e of cotton that the author has taken the hberty to mention a very excellent kind of scales, made by J. R. Brown & Sharpe, Providence, E.. I. They are intended for very delicate weighing, the tenth of a grain being easily estimated by them. Their general construction is so simple that the cut will show it without a description. The length of the beam is about eight inches, and the long arm, which has a small weight sliding upon it, is divided into a hundred parts ; these divisions indicate grains, and are numbered so as to be easily read. On the end of the long arm ^f the beam is a small pan, or hook, on which other weights are placed when more than 100 grains are required to be weighed. The extra weights are numbered 100, 200, 400, and 800, so that any number, from one to 1600 grains, can be weighed by them. As will be seen, the following tables are all made with 190 COTTON MANUFACTURE. a view to using some such scales as the above, but will answer equally well for any scales by which the weight in grains can be ascertained. The following table for weighing with troy weight, and reckoning by avoirdupois weight, will be found useful to those who use ounces, pennyweights, and grains, with the " beam and pans " scales : 24 grains equal one pennyweight. 18 pennyweights 5|- grains, troy, equal one ounce avoirdupois. 16 ounces equal one pound. The home-made weights too commonly used, made from bits of tin, wire, lead, or other small pieces of metal, can- not, as a general thing, be depended upon as being very correct, not because they cannot be made a definite weight, but rather because few have the means of making them so. Suppose that for want of sufficiently delicate tools in adjusting a weight of 175 grains, we should happen to make it 1T6 grains ; the difference would be but one grain, yet the consequence would be considerable. 1Y5 grains weight of l^o. 40 cotton yarn, is 840 yards in length, and 1Y6 grains weight of the same is 844.8 yards in length, a difference of 4.8 yards per hank, or 192 yards per pound. Yery true, yarn can be made as regular in size by using such weights ; but as to the accuracy of the size, it cannot be called better than a mere guess. PART II. CAJBDING. YARN, ROVING, AND SLIVEE TABLES. 54 inches == 1 thread. 4320 inches = 80 = 1 lea. 30240 inches = 560 = 7 = 1 hank, or 840 yards. Counts of yarn and hank-roving signify the number of hanks in one pound. Whatever number of yards are weighed, multiply them by the number of grains in one pound avoirdupois, for a dividend, and their weight in grains by the number of yards in one hank for a divisor, and the quotient will be the number. One hank contains 840 yards, and one pound avoirdu- pois contains 14 ozs. 11 dwts. 16 grains, troy, or YOOO grains. Hence, the yards in one hank are to the grains in one pound as 840 is to 7000, or 12 to 100. IST.B. — See tables on page 281. Mvample. If 50400 yards weigh one pound, what is the number ? 192 COTTON MANUFACTUKE. Worked out hy Cancellation. 1-7(000 1-12 5040(0-720-60 1(00 60 Answer. TTie same without Cancellation. Dividend 50100 x 100 _^^ Divisor 7000x12 Answer. How many yards are there in one pound of No. 60 yam? WorJced out hy Cancellation. 70(00 1(00 60 12 70x60x12.^=50400 Answer. The same without Cancellation. Dividend 7000x60x12 50400 Divisor 100 Answer. CAKDING. 193 K.B. — The same result will be found by multiplying the nmnber of yards in one hank by the number. Exarrvple. 840x60 = 50400. Answer. What is the weight of 50400 yards of ISTo. 60 ? WorTced out hy CanceUation. 50400-8400-700 1-6(0 142 10(0 TOO X 10 TOOO grains, or one pound avoirdupois. Answer, The same without Cancellation. Dividend 50400x100 TOOO • Divisor ....... 60x12 Answer. N.B. — It is by the above rule that all the compendious tables are made, Mcamples explam,atory of the sli/ver, roving, a/nd yarn tahles. What is the weight of 6 yards of Ko. .025 sliver ? 9 194 ITo. of the sliver COTTON MANUFACTURE. .025 ^ of 840 12 6, Length of sliver, in yards. 100 -Jg- of YOOO. Worked out l)y Cancellation. 1-.025 1-2-12 64 100-50-2000 2000 grains. The same without Cancellation Dividend 6x100 Answer. Divisor 025 x 12 = 2000 grains. Answer. If 6 yards of sliver weighs 2000 grains, what is the number ? Worked out hy Cancellation. 1-2000 1-242 64 100-50-.025 .025 Answer. The same without Cancellation. Dividend 6x100 .= .025 Divisor 2000 x 12 Answer. CARDING. 195 How many yards of 'No. ,025 sliver will it take to weigh 2000 grains ? Worked out hy GanceUation. 20(00 1(00 .025 12 20 X 12 X .025 = 6 Answer. The sa/me without Gam,ceUation. Dividend 2000 x. 025x12 = 6 Divisor 100 Answer. What is the weight of 12 yards of a four-hank roving % Worked out hy GanGellation. 1-4: 142 12-1 100-25 25 grains. Answer. The same without GanceUation. Dividend 1^x100= 25 grains. Divisor 4x12 Answer. 196 COTTON MANUFACTURE. I 12 yards of roving weigh 25 grains, what is the number ? Worked out hy Cancellation. 1-25 142 12-1 1004 4 Answer. The same without Cancellation. Dividend 12x100 , Divisor 25 x 12 Answer. How many yards of a four-hank roving will it take to weigh 25 grains ? Worked out hy Ca/ncellation. 254 14400 44 12 12 Answer. The sa/me without Cancellation. Dividend 25x4x12 12 Divisor 100 Answer. CAKDING. 19Y What is the weight of 840 yards or one hank of ISTo. 40 yarn ? Worked out l>y Cancellation. 14(0 142 84(0-7 100-25 25 X Y 175 grains. Answer. The sa/me without Ga/ncellation. Dividend 840x100 ^^^ = 175 grains. Divisor 40x12 Answer. If 840 yards of yarn weigh 175 grains, what is the number ? Worked out lyy Cam^cellal/ion. 1-7-175 1-12 840-70-10 100-4 10 X 4 = 40 Answer. The sa/me without Ca/ncellation. Dividend 840 x 100 = 40 Divisor 175 x 12 Answer. 198 COTTON MANUFACTURE. How many yards of N"©. 40 will it take to weigh 175 grains ? W(yrked out hy Ocmcellation. 175 4(0-.4 140(0 12 175xl2x.4 840 Answer. The scmie witJwut CoMcellation. Dividend 175 x 40x12 Divisor = 840 100 Answer. If 30 ounces of cotton is spread 48 inches in length, what proportion of a hank is it ? Weight of a spread, in ounces 30 Inches in one yard . . 36 Yards in one hank . . .840 16 Ounces in one pound. 48, Length of a spread, in inches. Worked out hy Cancellation. 30 9-36 70-840 16 4844 16 -T- 70 X 30 X 9 = 0.00084656^^ Answer. CAKDING. 199 The samie without Ga/rwellation Dividend . . . 16x48 Divisor . . . 30x36x840 0.00084666^^ Answer. If 30 ounces of cotton is spread on 48 inches of lattice, and the doublings are 3 at the finisher-lapper, 80 at the breaker-card railway, 8 at the finisher-card railway, 2 at the first head of drawing, 4 at the second head of draw- ing, 2 at the third head of drawing, and 2 at the fine fly- frame, what should be the draught at the mule, the fine fly-frame, the coarse fly-franie, the third head of drawing, the second head of drawing, the first head of drawing, the railway head, the finisher-cards, the breaker-cards, the finisher-lapper, and the breaker-lapper, to produce IS^o. 40, making an allowance of 14 per cent, for loss in working ? Ounces in one pound . 16 Length of a spread, in inches 48 Cent 100 30, Weight of a spread, in ounces. 36 Inches in one yard. 840 Yards in one hank. 40 l!^o. produced. 86, Cent less 14. 3, Doubling at the finisher- lapper. 200 COTTON MANtTFACTUEE. 80, Doubling at the break- er-card railway. 8, Doubling at the finish- er-card railway. 2, Doubling at the fii'st head of drawing. 4, Doubling at the second head of drawing. 2, Doubling at the third head of drawing. 2, Doubling at the fine fly-jframe. 1(00 Worked out. 1-2-16 3(0 1448 36 84(0-7 40 86 3 80 84 24 4-1 2 2 {Continued^ CAKDING. 201 36 3 108 7 756 40 30240 86 181440 241920 2600640 3 7801920 80 624153600 2 1248307200 2 G- . . . . 2)2496614400 (Continued.) 9* 202 C COTTON MA D . . . JSiM FAC TIJ] BE. 2)1248307200 D . . . 2)624153600 E . . . . E . . . 2)312076800 2)156038400 F . . . 2)78019200 F . . . H . 2)39009600 2)19504800 H . 2)9752400 H 2)4876200 H . 2)2438100 2)1219050 1 I .• . 2)609525 . 2)304762.5 1 . 2)152381.25 1 . 2)76190.625 I {Continued.') 5)38095.3125 CAKDING. 203 C 8)Y619.0625 A 3)2539.6875 A 3)846.5625 J . . . 3)282.1875 H . . . . . 6)94.0625 B 7)18.8125 K . 2.6875)2.6875 1 A. 3x3 = 9, Drauglit at the mule. B. 7 = 7, Draught at the fine fly-frame. C. 3x2 = 6, Draught at the coarse fly-frame. D. 2x2 == 4, Draught at the third head of drawing. E. 2x2 ==: 4, Draught at the second head of drawing. r. 2x2 = 4, Draught at the first head of drawing. G. 2 = 2, Draught at the railway head. H. 5x2x2x2x2 80, Draught at the finisher- cards. I. 5x2x2x2x2 80, Draught at the breaker- cards. J. 3 = 3, Draught at the finisher-la]3per. K 2.6875 2.6875, Draught at the breaker-lapper. Answer. 204 COTTON MANUFACTUKE. From the particulars found in the preceding example, find the number produced. Worked out hy Cancellation. 1-3(0 16-2-1 1-9-36 484-1 l-7-84(0 1-2.687540.7543-86 1(00 2.6875-1 1-3 3-1 80-1 1-80 80-40 1-8 2-1 1-2 4-1 14 4-1 1-2 4-1 6-24 1-2 7-1 94 40 Answer. The same without Cancellation. Dividend, 16 x 48 x 100 x 2.6875 x3x80x80x2x4 X4x4x6x7x9 . Divisor, 30 x 36 x 840 x 86 x 3 x 80 x 8 x 2 x 4 x 2 x2 Answer. 40 CAEDING. 205 From the particulars found in the preceding example, find the weight of a spread. Worked out hy CcmcellaUon. 16-2-1 Ounces in one pound. 1-9-36 4844 l-7-84(0 1-2.6875-10.Y543-86 10(0-5 2.68754 1-3 34 804 1-80 80-24 1-8 24 1-2 4-1 14 4-1 1-2 4-1 6 1-2 7-1 94 140 6x5 30 ounces. Answer. The same without Ccmcellation. Dividend, 16 x 48 x 100 x 2.6875 x3x80x80x2x4 X4x4x6x7x9 Divisor, :30 36x840x86x3x80x8x2x4x2x2 x 40 Answer. 20G COTTON MANUFACTURE. From the particulars found in the preceding example, find the length of a spread. Worked out hy Cancellation. 364 Inches in one yard. 1-246 3(04 84(042 1(00 86-21.5-5.375-2.68Y64 1-2.68Y5 1-3 34 1-80 1-2-80 80-] 1-2 84 14 24 14 44 14 24 1-3-6 1-Y 24 1-9 404 12 X 4 48 inches. Answer. The same without Cancellation. Dividend, 36 x 30 x 840 x 86 x 3 x 80 x 8 x 2 x 4 x 2 Divisor, x2x40 16 X 100 X 2.68Y5 x3x80x80x2x4 x4x4x6x7x9 Answer. -=48 CAJBDING. 20Y From the particulars found in the preceding example, find the decimal of a hank of a spread. Worked out hy Ccmcellation. 4(0 9 7 24 3-6 14 24 1-4: 44 14 24 1-2 84 540-80 804 1-80 1-3 34 1-2.68T5 540(0 86-21.5-5.375-2.68754 4-^9x7x3x5x5 = 0.00084656^ Answer. The sarnie without Ca/ncellation. Div. 40x2x2x4x2x8x80x3x68 . Divis. 9x7x6x4x4x4x2x80x80 x 3 X 2.6875 x 100 0.00084656^ Answer. 208 COTTON MANUFACTHEE. From the particulars found in the preceding example, find what the number would be if there was no loss in working. Worked out hy Ccmcellation. 1-5-30 16-2-1 14-36 484-2 l-7-84(0 2.6875-.53T5 1-3 34 « 804 1-80 8(0 1-8 2-1 1-2 4-1 14 4-1 1-2 4 64 1-2 7-1 9-1 .53T5 X 2 X 8 X 4 34.4 Answer. Div. Divis. The same without Ccmcellation. 16 X 48 X 2.6875 x3x80x80x2x4x4x4 x6x7x9 34.4 30x36x840x3x80x8x2x4x2x2 Answer. CAEDING. 209 K.B. — The particulars found in the fourteen following examples, are taken from the above. From the particulars found in the preceding example, find the decimal of a hank, produced at the breaker-lap- per, commencing at the length and weight spread on the lattice, making no allowance for loss in working. Worked out hy CcmcellaUon. 30 9-36 TO-840 16 484-1 2.68Y5 2.6875 X 16 -^ 70 X 9 X 30 = 0.00227 3^ Answer. The sa/me without Ccmcellation. Dividend. . . 16 x 48x2.6875 ^ ^ q^^^;^ ^^ Divisor ... 30x36x840 ' ^^ Answer. Find the decimal of a hank produced at the breaker- lapper, commencing at the number produced, making no allowance for loss in working. 210 COITON MANUFACTURE. I) IV. Worked out hy Cancellation. 34.48.6-.86 9 7 24 6 1-24 2-1 14 41 14 2-1 1-2 8-1 140-80 804 1-80 1-3 3-1 .86 -^9x7x6^ 0.009,^,7 ,Vg- Answer. The sa/me without Ga/ncellation 34.4 X2x2x4x2x8x80x3 Divisor, 9x7x6x4x4x4x2x80x80x3 = 0.00227^^ Answer. Find the decimal of a hank produced at the breaker- cards, commencing at the length and weight spread on the lattice, making no allowance for loss in working. Worked out hy CoMoellation. 1-5-30 9-36 16-44 48-8 {Conti/nued^ CAEDING. 211 21-84(0 1-3 2.68Y5-.63T5 34 8(0 .5375 x8x8-T-21x9 = 0.182 -jf The sa/me without CcmcellaUon. Dividend, 16 x48 x2.68Y5 x3 x80 Divisor, 30 x 36 x 840 x 3 Answer. 0.182^ Answer. Find the decimal of a hank produced at the breaker- cards, commencing at the number produced, making no allowance for loss in working. Worked out hy CcmcellaUon. 34.4 9 7 24 3-6 1-4 24 1-4 44 1-2-4 24 1-2 8-24 1-80 804 34.4 -^9x7x3 = 0.182 ^f^ Answer. 212 COTTON MANUFACTUBE. The same without Ca/ncellation. Dividend, . . 34.4:x2x2x4x2x8x80 _ Divisor . . . 9x7x6x4x4x4x2x80 0.182 -rf, Answer. Find the decimal of a hank produced at the railway- head, commencing at the length and weight spread on the lattice, making no allowance for loss in working. Worked out J)y CancellaUon. 3-6-30 16 9-36 484-1 7-84(0 - 2.6876-.5375 1-3 34 80-1 1-80 8(04 1-8 24 .5375 X 16 ^3x9x7 = 0.0455 -A TST Answer. The sa/me without Cancellation. Dividend, 16 x 48 x 2.6875 x 3 x 80 x 80 x 2 _ ^ ^^gg - Divisor, 30x36x840x3x80x8 ~ Answer. CAHDING. 213 Find the decimal of a liank produced at the railway- head, commencing at the number produced, making no allowance for loss in working. Worked out hy Cancellation. 34.4-8.6 9 Y 2-1 3-6 •2-4 24 1-4 44 1-4 24 8.6 -^ 9 X Y X 3 = 0.0455 ^ The same without Cancellation. Dividend . . 34.4 x2x2x4x2 Divisor . . Answer. 9xYx6x4x4x4 = 0.0455 y|. Answer. Find the decnnal of a hank produced at the first head of drawing, commencing at the length and weight spread on the lattice, making no allowance for loss in working. WorTced out hy Co/ticellation. 16 48-44 3-6-30 9-36 7-84(0 {Continued.) 214 COrrON MAJSfUFACTUEE. 2.6875-.53T5 1-3 34 8(0-1 1-80 804 1-8 24 1-2 4-2 .53Y5 xl6x2^9x7x3 = O-OOl^^ Answer. The sarnie without Cancellation. Div. 16 X 48 X 2.6875 x3x80x80x2x4 Divisor, 30 x 36 x 840 x 3 x 80 x 8 x 2 =: 0.091 -rfj Answer. Find the decimal of a hank produced at the first head of drawing, commencing at the number produced, making no allowance for loss in working;. Worked out hi ( CoAicellation. 34.4-8.6 9 Y 2 3-6 1-4 2-1 1-4 4-1 8.6x2^9x7x3 = 0.09ia T87 Answer. CARDING. 215 The same without Cancellation. Dividend .... 34.4x2x2x4 , Divisor . . . . 9xTx6x4x4 0.091t| TST Answer. Find the decimal of a liank produced at tlie third head of drawing, commencing at the length and weight spread on the lattice, making no allowance for loss in working. Worked out hy GomxieUajtion. 3'6-30 16 9-36 48-4 T-84(0 2.68Y5-.53Y5 1-3 3-1 8(0-1 1-80 804 1-8 24 1-2 44 1-4 44 1-2 4-24 .53Y5 xl6x4-T-9xYx3 = 0.182^ Answer. The same without Cancellation. Dividend, 16 x 48 x 2.6875 x3x80x80x2x4 x4x4 Divisor, 30 x 36 x 840 x 3 x 80 x 8 x 2 x 4 x 2 = 0.182^ Answer. 216 COTTON MANUFACTURE. Find tlie decimal of a hank produced at the third head of drawing, commencing at the number produced, making no allowance for loss in working. Worked out hy CcmcellaUon. 34.4 9 Y 3-6 2-1 34.4 -=- 9 X 7 X 3 r= 0.182t|^ Answer. The same without Cancellation. Dividend 34.4x2 9x7x6 = 0.182^ Answer. Find the hank-roving produced at the coarse fly-frame, commencing at the length and weight spread on the lat- tice, making no allowance for loss in working. Worhed out hy Ga/ncellation. 1-5-30 16 9-36 48-4 7-84(0 2.6875-.5375 {Conti nued.) CAKDING. 217 1-3 1-80 1-8 1-2 14 1-2 34 8(04 804 2 44 44 4-24 64 Answer. .5375 xl6x4x2-^9x7 = 1.092^ The same without Cancellation. Div. 16 X 48 X 2.6875 x3x80x80x2x4 x4x4x6 . Divisor, 30x36x840x3x80x8x2x4x2 1.092^ Answer. Find the hank-roving produced at the coarse fly-frame, commencing at the number produced, making no allow- ance for loss in working. 34.4 34.4 X 2 H- 9 X 7 = 1.092^ 10 Answer. 218 COITON MANUFACTUKE. Find the hank-roving produced at the fine fly-frame, commencing at the length and weight spread on the lat- tice, making no allowance for loss in working. Worked out hy Ocmcellation. 1-5-30 16 9-36 484 142-84(0 2.68Y5-.5375 1-3 34 8(04 1-80 804 1-8 24 1-2 44 14 44 1-2 4-24 64 1-2 74 .53Y5x4xl6-^9 = 3.8| Answer. The samfie without Cancellation. Div. 16 X 48 X 2.6875 x3x80x80x2x4x4x4 x6x7 3.84 Divisor, 30x36x840x3x80x8x2x4x2x2 Answer. CAKDING, 219 Find the hank-roving produced at the fine fly-frame, commencing at the number produced, making no allow- ance for loss in working. 344 34.4 ^ 9 = 3.8| Answer. From the length and weight spread on the lattice, the doubling, and the particulars given, to find the draught at each and every machine from the lapper to the mule. Find the nimaber produced, making an allowance of 14 per cent, for loss in working. Worked out hy Cancellation. 1-3(0 16-24 1-9-36 48-4-1 l-7-84(0 •2.68Y5-10.Y543-86 1(00 Single. Breaker-Lapper. 14 6.98Y5-2.68754 1-9 30-3-1 14545 100-1 1-2-32 T2-8-2-1 1-32 32-1 1400 154 {Conti nued.) 220 COrrON MAJSrUFACTUKE. 1-2.6-26 164 Doublings . . . 1-3 Finislier-Lapper 14 7-1 , 1-9 3(0-1 1-2-642 Y8-3-1 1-2-32 8(0-4-2-1 1-2-32 36-4-1 1(00 164 1-26 16-1 Single. Breaker Cards. 14.54.5 1(0 1(0 33-1 143 6(0-3-1 1-33 5(0-1 1-20 80-40 1-24 15-1(0 1-840 9143-1 1-7(0 16-2-1 1(00 20-1 Doubling . . . . 1-80 Finisher Cards. 1-1.5-4.5 1(0 1(0 334 143 6(0-3-1 1-33 5(04 1-20 80-1 1-24 {Conti 154(0 ',nued.) CARDING. 221 Doubling Doubling Doubling Doubling 1-840 1-7(0 1(00 . . 1-8 1 1-80 1-4-100 1-4-18 1-3 1-.5-1.5-51 . . 1-2 1 1-6(0 1-3-36 1-27 . . 1-4 1 1-6(0 1-3-36 1-27 . . 1-2' 1 1-6(0 1-3-36 1-27 Single. 91-13-1 16-2-1 20-1 Railway Head. 3-1 34-1 80-1 75-3-1 4.5-1 16-4-8-2-1 First head of drawing. 3-1 27-1 4(0-1 72-6-2-1 Second head of drawing. 3-1 27-1 4(0-1 72-6-1 Third head of drawing. 3-1 27-1 4(0-1 72-6-1 Coarse Fly-Frame. (Continued.) 222 COTTON MANUFACTUKE. 1-8 1(0 1-32 9648-6-1 1-24(0 64-2-1 Doubling 1-2 Fine riy-Fraine. 1-8 1(0 14-32 56-7-1 1-3(0 96-24-84 Single. Mule. 1-r 8-4-1 1-2-30 105-154 1-9-36 81-94 40 LOSS IN WORKING. Answer. The number sbown bj tbe draughts and doublings, and the number produced, are proportional to the weight of spread in an inverse ratio. Example. The number shown by the draughts and doublings is 34.4, but the number actually produced is 40. Required the loss in working, the weight of a spread being 30 ounces. LOSS EST WOEKESTG. 223 14(0 3(0 34.4-8.6 8.6 X 3 == 25.8 ounces utilized. 30 ounces weight of a spread. 25.8 weight utilized. 4.2 ^=: 4 ounces and 87^ grains loss in working from 30 ounces. Ans"y Cancellation. 40 14 Y.54.25 1-6(0 4(0-1 40 x 1.25 50 Answer. 246 COTTON MANUFACTURE. The same without Ca/iicellation. Dividend 40xY.5x40 , Divisor 50 4x60 Answer. A set of cops weighs 11 lbs., and has on 630 stretches. Length of stretch, 60 inches ; number of cops in the set, 352. Keqtdred the average number. Worked out ly Cancellation. '352-32-8 1-3-36 60-5 l-21-84(0 141 63(0-21-1 8x5 = 40 Answer. The same without Ca/ncellation. Dividend 352x60x630 40 Divisor 36x840x11 Answer. From the particulars found in the preceding example, find the number of stretches in the set. WorTced out hy Cancellation. 11-1 40-5 (^Continued.) sPEsnsriNG. 247 14-32-352 1-6(0 84(0-21 36-6 21 X 6 X 5 630 The same without Cancellation. Dividend .... 11 x 40 x 840 x 36 Divisor Answer. = 630 352 X 60 Answer. From the particulars found in the preceding example, find the length of the stretch. Worked out hy Cancellation. 11-1 1-4-32-352 1-21-63(0 40-5 84(0-21-1 36-12 12 X 5 60 inches. The sa^ne without CamjCellation. Dividend . . . 11 x 40 x 840 x 36 Divisor . . . 352x630 Answer. 60 inches. Answer. From the particulars found in the preceding example, find the number of cops in the set. 248 COIiTON MAITUFACTTIKE. Woi'lced out hy GancellaUon. 11 4(0 l-r-21-63(0 84(0-284 1-6(0 36-6-2 11x4x4x2^=352 Answer. TJie same without Cancellation. Dividend .... 11x40x840x36 . Divisor 352 630 X 60 Answer. From tlie particulars found in tlie preceding example, find the weight of the set. Worlced out hy Cancellation. 352-88-22-11 1-21-84(0 63(0-21-1 1-4(0 1-2-6-36 6(0-1 11 lbs. Answer. SPINNING. 24:9 The sa/me without Cancellation. Dividend 352x630x60 = 11 Divisor 840x40x36 Answer. The power furnislied for driving mules is sufficient to drive tliem 3 stretches per minute, and they utilize -^ of the same. Required the product per spindle per day of 12 hours, the length of the stretch being 60 inches. Inches in one yard Power furnished . Yards in one hank 36 15 840 60, Length of stretch, in inches. 3 Stretches per minute. 60 Minutes in one hour. 12 Hours per day. 14, Power utilized. Worked out hy Oam^Gellation. 1-3-36 60-5-] 34 6(0-2 124 1-345 14-2 l-Y-84(0 2x2 4 hanks. Answer. 250 COTTON MANUFACTURE. Tlie same without Cancellation. Dividend . . 60 x 3 x CO x 12 x 14 _ ^ ^^^^^^^ Divisor ... 36x15x840 Answer, A pair of mnles, each containing 352 spindles, produce 4 hanks per spindle per day. How^ many hanks will that be per week, and what will the spinners' wages amount to, at 4|- cents per 100 hanks ? 352 Spindles in each mule. 2, ISumber of mules. 4, Product per spindle per day, in hanks. 6 Days per week. 4.5 Cents per 100 hanks. 352 X 2 X 4 X 6 ■ 16896 hanks per week. 16896x4.5 -r- 100 = $7.60^ Answet*. To find the requisite number of turns of twist per inch for warp and filling. Rule. For warp, multiply the square root of the number by 8f , and for filling, by 3|-, and the product will be the number of tm-ns of twist per inch required. SPINNING. 251 Examjples. How many turns of twist per incli will be required for ]Sro. 40 warp ? 6)40(6.324-1- 36 123)400 369 1262)3100 2524 12644)57600 50576 7024 6.324 3.75 31620 44268 18972 23.71500 Answer. 252 COTTON MAJSrUFAOTUEE. How many turns of twist per inch will be required for No. 40 filling ? 6)40(6.324+ 36 123)400 369 1262)3100 2524 12644)57600 505Y6 Y024 6.324 X 3.25 = 20.553 Answer. Another way to find the requisite turns of twist per inch of yarn : — Admitting that 25 turns of twist per inch of yarn is sufficient for JSTo. 50 warp, and the same for No. 60 filling, and that the twist in different numbers of yarn is as the square of the twist to the number of the yarn, we get the following Rule. As No. 50 is to the square of 25, so is the giv^en No. to the square of the twist per inch required. SPINNING. 253 JExample. How many turns of twist per incli is required for ISTo. 40 warp ? 1-5(0 25 X 25 r= 625425 4(0 125 4 2)5^00(22.36+ Answer. 4 42)100 84 443)1600 1329 4466)27100 26796 304 How many turns of twist per incli is required for Ko. 40 filling? 254 COTTOX MANUFACTUKE. 1-6(0 25 X 25 = 625 4(0-.6666 + 625 33330 13332 39996 2)4^16;62^50(20.41+ Answer. 4 404)1662 1616 4081)4650 4081 569 N.B. — There are many other rules in use for finding the requisite twist per inch of yarn, each of which has its advantages, but the above are generally considered the simplest and best. The pracHcal rule is, to try the yam by breaking it. If the fibres draw out of warp instead of breaking off short, it has not twist enough ; for filling, that need not be minded, if it works well in the mule and the loom. f^. m '^' ^ ^1 M A NTJFACTUBING. 255 MAKTJFACTUEIIsrG. How many hanks of yarn will be required to make a warp of 14 cuts, each 42 yards long, 30 inches wide at the reed, and 64 threads to the inch, allowing Jg- for shrinkage in weaving ? Worked out hy Cancellation. l-2'84(0 42-1 3(0 64 14-Y 64xYx3+iig 1418.66+ Answer. Dividend Divisor . The same without Cancellation . 42 X 30 X 64 X 14 840 + iV = 1418.66 + Answer. ■ How many hanks of filling will be required to fill a warp of 14 cuts, each 42 yards long, 30 inches wide at the reed, and 64 picks to the inch, allowing -^ for waste? Worked out hy Cancellation. l-2-84(0 424 3(0 64 14-7 64x'7x3+JL "BIT 1366.4 Answer. 256 COTTON MANUFACTUEE. The same without Ccmcellation. Dividend . . . . 42 x 30 x 64 x 14 , . ., o^/; a + eV = 1366.4 Divisor .... 840 Answer. In 1418.666 hanks of l!^o. 36, hovr many pounds ? Wo7'ked out hy Cancellation. 1-4-32 I 1418.6664YT.333-44.333 44.333 Answer. In 1366.4 hanks of I^o. 30, how many pounds ? Worked out hy Cancellation. 1-3-36 I 1366.4413.866-3Y.955 37.955 Answer. If 44.33 + pounds of yarn be sufficient for a warp of 14 cuts, each 42 yards long, including shrinkage in weaving, and 37.955 pounds of filling be sufficient to fill the same including waste, what will be the total weight of warp and filling necessary to make the 14 cuts ? MANUFACTUSmG. 25Y M.333 3Y.955 82.288 pounds. Answer. If 82.288 pounds of warp and filling liave been used in making 14 cuts of cloth, each 42 yards long, how many yards per pound is utilized ? Worked out hy GoMceUaUon. 42-.5104 14 1-82.288 14 X .5104 = 7.1456 The sa/me without (Ja/nceUaUon. Dividend 42x14 Answer. = 7.1466 Divisor 82.288 Answer. Another way to find the number of yards per pound utilized from the same particulars : — 258 COTTON MANUFACTU-RE. 64+,5V Picks =: 65.666 G4 + _i^ Reed = 67.555 133.221 Width of the reed, in inches .... 30 Warp and filling in- cluded 2 36 No. of filling. 32 No. of warp. 68 840 Yards in one hank. Worked out by CcmGellation. 67.555 1433.221 1-3(0 1-2 36 32 68-.51 + 84(0-28-14: 14 X. 51 + = 7.14+ Answer. Find the number of yards of cloth per pound from the following particulars : — Count of reed 72 Width of reed 42 inches. MANUFACTURING. 259 Picks per inch 100 Counts of filling 40 Counts of warp 32 Shrinkage of warp in weaving -j^^- Worhed out hy Cancellation. Ko. of filling . . 14(0 142 42-3.5, Width of reed. 100*25 Picks per inch. 10(0 25 X 10 X 3.5 = 875 grains weight of filling in one yard of cloth. Ko. of warp 14-32 1-12 42-5.25, Width of reed. 72-6, Count of reed. 100-25 25 x6x5. 25 +-ji(j- = 866.25 grains weight of warp in one yard of cloth. 866.25 875.00 174.25)7000.00(4+ yards. 6965.00 35.00 Answer. 260 COTTON MANUFACTUEE. Another way to find the number of yards of cloth per pound from the same particulars : Worked out hy Cancellation. '^2+1^ 100 - z79.2 1-179.2 142 1-2 40 32 72-.4+ 840-2040 10 X. 4+ 4+ Answer. If it requires 866.25 grains of warp to make one yard of cloth, as seen in a preceding example, how many pounds will be required to make a warp of 10 cuts, each 40 yards long ? Worhed out hy Ca/ncellation. 1(0 i-T-ro(oo 4(0-.4 866.25-123.75 123.75 X .4 49.5 Answer. The same without Cancellation. Dividend .... 10 x 40 x 866.25 , Divisor 7000 49.5 Answer. MANUFACTUKtNG. 261 If it requires 8Y5 grains of filling to make one yard of cloth, how many pounds will it require to make 10 cuts, each 40 yards long ? Worked out hy CancellaUon. 1(0 i-r-7o(oo 4(0-.4 8Y5425 125 X .4 == 50 Answer. The same without Cancellation. Dividend 10x40x875 = 50 Divisor 7000 Answer. If it requires 49|- pounds of warp, and 50 pounds of filling, to make 10 cuts of cloth, each 40 yards long, what is the total weight of warp and filling required ? 49.5 50.0 99.5 pounds. Answer. How many hanks of yarn will be required to make a warp of 10 cuts, each 40 yards long, to be woven in a 72 262 COTTON MA.NUFACTUEE. reed, 42 inches wide, making an allowance of -^ for shrinkage in weaving. Worked out hy Cancellation. 1(0 40 42-6 Y2-6 l-Y-84(0 40 X 6 X 6 + Jj- = 1584 Answer. The same without Cancellation. Dividend . . . 10 x 40 x 42 x 72 j_ ^ ^^g^ Divisor 840 Answer. If 1584 hanks of yarn weigh 49|- pounds, what is the number ? Worked out hy Cancellation. 1584-32 1-49.5 1-7(000 1-12 84(0-12-1 1(00 32 Answer. MANUFACTURING. 263 The sarnie without Ccmcellation. Dividend 1584x840x100 32 Divisor 49.5x7000x12 Answer. In 10 cuts of clotli, each 40 yards long, woven in a reed 42 inches wide, 100 picks to the inch, how many hanks of filling? Worked out hy CanceUat/lon. 1(0 4040 42-2 l-21-84(0 100 100 x 10 x 2 = 2000 Answer. The sa/me without Ccmcellation. Dividend .... 10x40x42xl00 _ ^^^^ Divisor 840 Answer. If 2000 hanks of filling weigh 50 pounds, what is the number ? 264: COTTON MANUFACTURE. Worked out hy Cancellation. 1-50 1-7(000 142 2(000 84042040 100-2 10x2x2=40 Answer. The same witJiout Ca/ncellation. Dividend 2000x840x100 40 Divisor 50x7000x12 Answer. Find tlie number of yards per pound of clotli from the following particulars : Counts under tlie glass, QQ threads of warp and 80 of filling per inch. "Width of reed .... 33 inches. Counts of warp .... 33 Counts of filling .... 40 Shrinkage in weaving of warp and filling, ■^. MANUFACTURING. 265 Worked out hy Cancellation. 324, Width of reed. 66-5.5 Threads of warp per inch. Counts of warp 1-33 1-12 100 100 X 5.5 +^ 584.3Y5 grains weight of warp in one yard of cloth. Counts of filling 140 1442 3341, Width of reed. 80-2 Picks per inch. 100-25 25 X 11 x2+-jig- = 584.375 grains weight of filling in one yard of cloth. 584.3Y5 584.3Y5 1168.75(0)7000.00(0(5.9 + 5843.75 Answer. 1156.250 1051.875 104.375 266 COTTON MANUFACTURE. Another way to find the number of yards of cloth per pound from the same particulars : Reed Picks Worked out hy CcmGellation. 80 1-2-146 1-33 1-2 33 Warp. 40 Filling. 73-1 840420-210-6.36 6.36 less iV 6.9 + AnSwer. How many pounds of I^o. 50 yarn will it take to make a beam of 10 cuts, according to the following particulars : Length of cuts . . . . 60 yards. Count of reed .... 92 Width of reed .... 42 inches Shrinkage in weaving . . -^ Worked out hy Ccmcellation. 1(0 6(04.2 42-3.5-.5 {Conti nued.) TVrANUFACTUBING. 267 1-5(0 l-Y-84(0 92 92xl.2x.5+JL 60.T2 Answer. The same without Cancellation. Dividend . . . 10x60x42x92 Divisor .... 50x840 +J^=60.72 Answer. How many pounds of 1S.Q. 60 filling will it take to fill 10 cuts, according to the following particulars ? Length of cuts . Width of reed . Picks per inch . 60 yards. 42 inches. 108 Worked out hy Gam^cellat/ion. 1(0 604 42-6 l-12-84(0 1-60 108-9 9x6 54 Answer. 26S COTTON MANUFACTTJKE. The same without Cwncellation. Dividend 10x60x42x108 Divisor = 54 840 X 60 Answer. If there are 60. Y2 pounds of warp and 54 pounds of filling in 10 cuts of cloth, each 60 yards long, how many yards of cloth are there to the pound ? Worked out hy Cancellation. 60.72 54 141.472-114.Y2 104 60-5.2 + 5.2 + Answer. rind the number of yards per pound of cloth from the following particulars : Count of reed . . . 92 "Width of reed . . 42 inches. Picks per inch . . . 108 Counts of warp . . . . 50 Counts of filling . . 60 Shrinkage of warp in weaving, ^. MASrUFACTUKING. 269 Worked out hy OmiGellation. 42-3.5 1-50 142 92 100-2 92 X 3.5 X 2+ J^ = 708.4 grains weight of warp in one yard of cloth. 1-6(0 1-12 42-Y 108-9 10(0 10 X 9 X Y 630 grains weight of filling in one yard of cloth. 708.4 630.0 1338.4)7000.0(5.2+ 6692.0 Answer. 308.00 267.68 40.32 Another way to find the number of yards of cloth per pound from the same particulars : 270 COTTON MAJSrUEACTURE. Wo7'Tced out l)y Cancellation. Eeed92+-jV 101.2 50 Warp. Picks . . . 108 60 Filling. 1-209.2 110-.52 + "Width of reed , . . 142 Warp and filling . . 1-2 840-2040 10X.52+ 5.2 + Answer. Another way to find the number of yards of cloth per pound : Rule. Cut from the cloth a piece two inches square. The weight of this multiplied by half the width of the cloth, gives a product which, divided into 389, equals the num- ber of yards per pound. Example. . In the above example the cloth is 42 inches wide, con- sequently, one yard contains 42 x 36. =1512 square inches, and weighs Y08.4 + 630. =1338.4 grains. A piece of cloth 2 inches square contains 2 x 2=4 square inches. Hence, 1338.4x4^1512=3^3^ grains weight of the 4 square inches. manhfactueing. 271 If 4 square inches of cloth weigh S^^ grains, how many yards are there to the pound ? TSJ" "R Q 1 2- 2 — 669:2 Worked out hy Cancellation. 669.2 1-7-21 189-63-9 389 389x9-^669.2 The sarnie without Cancellation Dividend 189 x 389 Divisor 669.2x21 5.2 yards. Answer. ation. = 5.2 yards. Answer. A piece of lawn is 36 inches wide, and counts, under the glass, 80 X 80. The filling is ISTo. 80, and the warp ISTo. 75 ; how many yards are there to the pound, admitting the warp and filling to shrink -^ in weaving ? Worked o%tt hy Cancellation. 36-34 1-3-75 142 80 1004 80 X 4+^ 336 grains weight of warp in one yard of cloth. 272 COTTON MANUFACTURE. 1-80 142 36-3 80-1 100 100 X 3+^ 315 grains weight of fiUing in one yard of cloth. 336 315 651)7000(10.7+ 651 Answer. 4900 4557 343 Another way to find the number of yards of cloth per pound from the same particulars : Worked out hy Cancellation. Eeed Picks 80+^: 80 + ?T 84 84 1-2.4468 Width of cloth . . 1-3-36 Warp and filling . . 1-2 80 Warp. 75 Filling. 155-77.5-32.240.7+ 840-70-1 10.7 Answer. MA^SrUFACTIIRING. 273 Suppose a loom to work successively at the rate of 140 picks per minute, how long would it be weaving a cut of 42 yards with 100 picks per inch ? Worked out hy Cancellation. 42-3-1 36-18 144(0 1(00 l-2-6(0 18 h( Durs. The same without Ca/rhcellation. Dividend .... 42 x 36 x 100 Divisor 140x60 Answer. = 18 hom's. Answer. If the power furnished for driving a loom be sufficient to drive it 140 picks per minute, and the actual product is 34,125 yards, containing 100 picks per inch, in 18 hours, how much per cent, of the power does it utilize ? Worked out hy Cancellation. 100-50 34.125-4.875-1.625 36-2-1 1-M4(0 1(00 1-18 l-3-6(0 50x1,6^5 81.25 per cent. Answer. 274 COTTON MANUFACTURE. The same without Camcellation. Dividend . . . 100x34.125 x 36 xlOO _ g^ 25 Divisor ... 140x18x60 Answer. Suppose a loom to work successively at the rate of 128 picks per minute, how long will it be weaving a cut 46 yards long, containing 80 picks per inch ? Worked out iy Ca/ncellation. 46-5.Y5 1-846-128 1-5-60 36-3 80-10-2-1 5.T5 X 3 17.25 17 hours 15 minutes. Answer. The same without Ganficellation Dividend 46 x 36 x 80 = 17.25 Divisor 128x60 Answer. If the power furnished for driving a loom is sufficient to drive it 128 picks per minute, and the actual product is 28f yards, containing 80 picks per inch, in 12 hours, how much per cent, of said power does it utilize ? WAMUJ^'ACTURING. 27 Worked out hy Cancellation. 100-25-6.25-3425 28.75 36-34 1446428 8(04 142 l-2-6(0 28.75 X 3425 89.84375 per cent. The same without Cancellation Dividend . . 100 x 28.75 x 36 x 80 Divisor. . . 128x12x60 Answer. = 89.84375 Answer. Admitting the power furnished for driving looms to be sufficient to drive them 120 picks per minute, and that they utilize 90 per cent, of the same, the cloth to be made into cuts each 45 yards long, containing 80 picks per inch, what will be the monthly wages of a five loom weaver at 36 cents per cut, allowing 12 hours to the day, and 24 working days to the month ? Worked out hy Cancellation. 364 1-8(0 12(0 {Continued^ 276 COTTON MANXJFACTUKE. 1(00 1-545 1-36 6(0 12 24-3 5-1 9(0-1 12x12x6x3 $25.92 Answer. Dividend Divisor . The sa/me without Cancellation. . . 36 X 120 X 60 X 12 X 24 X 5 X 90 80x100x45x36 X $25.92 Answer. Admitting the power furnished for driving looms to be sufficient to drive them 118 picks per minute, and that they utilize 75 per cent, of the same, the cloth to be made into cuts, each 60 yards long, containing 108 picks per inch, how much per cut should be paid to a three-loom weaver to make $36 per month, allowing 12 hours to the day, and 24 working days to the month ? Worked out hy Cam,Gellation. 36-3-1 1-59418 108-9-3 1-60 {Contimied.) MANUFACTUBING. 277 142 1-2-24 1-3 1-3-75 1004-2 604 3648-^ 3x2x-^. 'TW The scmie without Cancellation. Dividend . . . 36x108x100x60x36 Divisor. . . . 118x60x12x24x3x75 Answer. = $1.83^ T? Answer. From the particulars found in the preceding example, find the weaver's monthly wages. Worked out Iry Cancellation. 1-59 1084 . . . (V^of$l.) 1408 118-2 604 12-1 24-6 34 14400 75-3 1-60 1-3-36 6x2x3 $36. Answer, 278 COTTON MANUFACTURE. Tlie same without Ca/acellat/lon. Dividend . . . 108x118x60x12x24x3x75 = $36. Divisor . . . 59x108x100x60x36 Answer. Admitting the labor and skill required to weave 14 twill cuts per loom, on five looms per month, to be equal to that required to weave 16 cambric cuts per loom on 4 looms in the same time, and the price paid for the cam- bric 39 cents, and the twill 28 cents per cut, how much per cut should be advanced on the twills to make the monthly wages of the weavers equal, if the cambric is advanced to 42 cents per cut % Worked out hy Cancellation. 42-6 1-5 1-744 4-.8 16-8 8 X 6 X .8 — 28 10.4 cents. Answer. The same without Cancellation. Dividend. . . i2x4><16_ 28 ^10.4 cents. Divisor. ... 5x14 Answer. MAJSrUFACTUKING. 279 From the particulars found in the preceding example, find the monthly wages of the twill and cambric weavers at the advanced price. Twill 38.4 X 14 X 5 :=: $26.88 Cambric 42x16x4 =$26.88 Answer. Admitting the labor and skill required to weave 16 cambric cuts per loom on 4 looms per month, to be equal to that required to weave 14 twill cuts per loom on 5 looms in the same time, and the price paid for the twill is 38.4 cents per cut, how much per cut should be paid for the cambric to make the monthly wages of the weavers equal ? Worked out hy Oancellat/ion. 38.4-4.8-1.2 1-4 5 1-8-16 14-7 Tx5xl.2 = — 42 cents. Answer. The sa/me without Cancellation. Dividend 38.4x5x14 .^ = 42 cents. Divisor 4x16 Answer. 280 corroN manufacture. If one weaver weaves 16 cambric cuts per loom per month on 4 looms, and another weaves 14 twill cuts per loom on 5 looms in the same time, and an advance of 6 cents per cut is made on the twill, how many cents per cut should the cambric be advanced to make the monthly advance of the weavers' wages equal? Worked out h[ 146 1-2-4 1/ Cmicellation. 6-3 14-T-.43Y5 5 5 X 3 X .43Y5 z= — 6-^ cents. Answer. The sa/me without Cancellation. Dividend ...... 6x14x5 ^ g_,^ ^^^^^^ Divisor 16x4 Answer. From the particulars found in the preceding example, find the monthly advance in the weavers' wages. Cambric 6^^x16x4 $4.20 TwiU 6x14x6 =$4.20 Answer. CAEDESTG. 281 SLIYEK TABLE, Showing the size of sliver from "No. .01 to .09, by the weight of 6 yards, in grains. Number. Grains. Number. Grains. Number. Grains. .01 5000 .037 1351 .064 781 .011 4545 .038 1316 .065 769 .012 4167 .039 1282 .066 758 .013 3846 .04 1250 .067 746 .014 3571 .041 1220 .068 735 .015 3333 .042 1191 .069 725 .016 3125 .043 1163 .07 714 .017 2941 .044 1136 .071 704 .018 2778 .045 1111 .072 694 .019 2632 .046 1087 .073 685 .02 2500 .047 1064 .074 676 .021 2381 .048 1042 .075 667 .022 2273 .049 1020 .076 658 .023 2174 .05 1000 .077 649 .024 2083 .051 980 .078 641 .025 2000 .052 962 .079 633 .026 1923 .053 943 .08 625 .027 1852 .054 926 .081 617 .028 1786 .055 909 .082 610 .029 1724 .056 893 .083 602 .03 1667 .057 877 .084 595 .031 1613 .058 862 .085 588 .032 1563 .059 847 .086 581 .033 1515 .06 833 .087 575 .034 1471 .061 820 .088 568 .035 1429 .0^2 806 .089 562 .036 1389 .063 794 .09 556 282 COTTON MANUFACTUKE. SLIVER TABLE, Showing the size of sliver from 'No. .091 to No. .236, by the weight of 6 yards, in grains. Number. Grains. Number. Grains. Number. Grains. .091 549 .134 373 .186 269 .092 543 .136 368 .188 266 .093 538 .138 362 .19 263 .094 532 .14 357 .192 260 .095 526 .142 352 .194 258 .096 521 .144 347 .196 255 .097 515 .146 342 .198 253 .098 510 .148 338 .2 250 .099 505 .15 333 .202 248 .1 500 .152 329 .204 245 .102 490 .154 325 .206 243 .104 481 .156 321 .208 240 .106 472 .158 316 .21 238 .108 463 .16 313 .212 236 .11 455 .162 309 .214 234 .112 446 .164 305 .216 231 .114 439 .166 301 .218 229 .116 431 .168 298 .22 227 .118 424 .17 294 .222 225 .12 417 .172 291 .224 223 .122 410 .174 287 .226 221 .124 403 .176 284 .228 219 .126 397 .178 281 .23 217 .128 391 .18 278 .232 216 .13 385 .182 275 .234 214 .132 379 .184 272 .236 212 CARDING. 283 SLIVEK TABLE, Showing the size of sliver from 'No. .238 to No. 1, by the weight of 6 yards, in grains. Number. Qratns. Number. Grains. Number. Grains. .238 210 .292 171 .53 94 .24 208 .294 170 .54 93 .242 207 .296 169 .55 91 .244 205 .298 168 .56 89 .246 203 .3 167 .57 88 .248 202 .31 161 .58 86 .25 200 .32 156 .59 85 .252 198 .33 152 .6 83 .254 197 .34 147 .62 81 .256 195 .35 143 .64 78 .258 194 .36 139 .66 76 .26 192 .37 135 .68 74 .262 191 .38 132 .7 71 .264 189 .89 128 .72 69 .266 188 .4 125 .74 68 .268 187 .41 122 .76 66 .27 185 .42 119 .78 64 .272 184 .43 116 .8 63 .274 182 .44 114 .82 61 .276 181 .45 111 .84 60 .278 180 .46 109 .86 58 .28 179 .47 106 .88 57 .282 177 .48 104 .9 56 .284 176 .49 102 .92 54 .286 175 .5 100 .94 53 .288 174 .51 98 .96 52 .29 172 .52 96 ■.98 1. 51 50 284 COTTON MANUFACTURE. KOVESTG TABLE Showing the size of roving from No. .05 to No. 8, by the weight of 12 yards, in grains. Number Grains. Number. Grains. Number. Grains. Number. Grains. .05 2000 .108 926 .185 541 .8 125 .052 1923 .11 909 .19 526 .85 118 .054 1852 .112 893 .195 513 .9 111 .056 1786 .114 877 .2 500 .95 105 .058 1724 .116 862 .205 488 1. 100 .06 1667 .118 847 .21 476 1.05 95 .062 1613 .12 833 .215 465 1.2 83 .064 1563 .122 820 .22 455 1.25 80 .066 1515 .124 806 .225 444 1.3 77 .068 1471 .126 794 .23 435 1.35 74 .07 1429 .128 781 .235 426 1.4 71 .072 1389 .13 769 .24 417 1.5 67 .074 1350 .132 758 .245 408 1.65 61 .076 1316 .134 746 .25 400 1.8 55 .078 1282 .136 735 .275 364 2. 50 .08 1250 .138 725 .3 333 2.25 44 .082 1220 .14 714 .325 308 2.75 36 .084 1190 .143 699 .35 286 3. 33 .086 1163 .146 685 .375 267 3.5 29 .088 1136 .149 671 .4 250 4. 25 .09 1111 .152 658 .425 235 4.5 22 .092 1087 .155 645 .45 222 5. 20 .094 1064 .158 633 .475 211 5.5 18 .096 1042 .161 621 .5 200 6. 17 .098 1020 .165 606 .55 182 6.5 15 1 1000 .169 592 .6 167 7. 14 .102 980 .173 578 .65 154 7.5 13 .104 962 .177 565 .7 143 8. 13 .106 943 .181 552 .75 133 SPESTNING. 285 YAEN TABLE, Showing the size of yarn from Ko. 1 to ISTo. 120, by the weight of one hank in grains. No. Grains. No. Grains. No. Grains. No. Grains. No. Grains. 1 7000 25 280 49 143 73 96 97 72 2 3500 26 269 50 140 74 95 98 71 3 2333 27 259 51 137 75 93 99 71 4 1750 28 250 52 135 76 92 100 70 5 1400 29 241 53 132 77 91 101 69 6 1167 30 233 54 130 78 90 102 69 7 1000 31 226 55 127 79 89 103 68 8 875 32 219 56 125 80 88 104 67 9 778 33 212 57 123 81 86 105 67 10 700 34 206 58 121 82 85 106 66 11 636 35 200 59 119 83 84 107 65 12 583 36 194 60 117 84 83 108 65 13 538 37 189 61 115 85 82 109 64 11 500 38 184 62 113 86 81 110 64 15 467 39 179 63 111 87 80 111 63 16 438 40 175 64 109 88 80 112 63 17 412 41 171 65 108 89 79 113 62 18 389 42 167 66 106 90 78 114 61 19 368 43 163 67 104 91 77 115 61 20 350 44 159 68 103 92 76 116 60 21 333 45 156 69 101 93 75 117 60 22 818 46 152 70 100 94 74 116 59 23 304 47 149 71 99 95 74 119 59 21 292 48 146 72 97 96 73 120 58 286 corroN manufacture. EXPLANATION OF THE KEED TABLE. 1. Manchester, Stockport, and the United States count by the number of ends in one inch. 2. Bolton counts by the number of beers on 24^ inches, 20 dents to a beer. 3. Blackbiu'n counts by the number of beers on 45 inches, 20 dents to a beer. 4. 6-4thB, Preston, counts by the number of beers on 58 inches, 20 dents to a beer. 5. 9-8ths, Preston, counts by the number of beers on 44 inches, 20 dents to a beer, 6. 4-4ths, Preston, counts by the number of beers on 39 inches, 20 dents to a beer. 7. 7-8ths, Preston, counts by the number of beers on 34 inches, 20 dents to a beer. 8. l!^ankeen counts by the number of beers on 20 inches, 19 dents to a beer, 9. Scotch and Carlisle count by the number of dents on 37 inches. Goods shrink about -^ in bleaching or finishing. The following table shows at a glance the number of dents in an inch, and the corresponding count of reed. EXPLANATION OF THE REED TABLE. 287 The first column contains the number of dents in one inch, opposite to which are the counts of the reeds accord- ing to the system of counting. 288 COTTON MANTJFACTUEE. li go Ot-'*T-tG0»O(M(3i'X>C0Ot-'+li-(Q0i0J CO CO -* 'rf^ O lO CO CO t-; b^ CO GO tA cm" Co' '*" lO CO t-^ GO* OJ O i-H C^ CO -* IQ CO* t-^ (yi1 lO t-^ (M lO t-- oi^oiT-H*^cdGO*ocoid-fc-^aJa^-^*coGdTH ^';tf'*^OiOlOCOCOCOCOCDt-t-4>»t^OO |2 t- 'tH T-J GO lO Ol O:' CO CO ^ "* '^, "^ *^ <^ ^ O* t-^ Ci O* S^ ^* O* t-^ ci rH CM* -** CO* t^ Oi r-5 COCOCOCO^-*'*'*^-^iOlOlO»OlOiOCO SS , II C3iOiOOQqt-;t-;COt-K:>lO^':}HCOCOCM0 t- OT lO t- OT lO t- OT lo ^^- KEED TABLE. 289 Ci':CCOO^,~-^THGOlOCOO^-'5i^THOO^OO^Oi':OCOO CO O -+ O) T-l O Oi -^-J O O CO 1-^ T-H O CO Ol CO O Ot) -t- O -* CO G<1 CO -* -H -H lO O iO O ■:© tr- t- t- QO -X) CO Cfi O o5 O' O r-H rH T-H C>T 1— ItHt— (t— IT— IrHTHr-ti— It— IrHrHi— ti-HT-I^T-ii-lG C55 o t— i r— ■ 00 c; i-H oi co' -^' id iiD i>^ .6 ci o th oi oo --t^ o* '-^ t- co o th ot co' CO-NH^-:H'*-^^':H-+l^^iOKt.OOiOiOiO>OiO<:OCD<:OCO lO lO »0 lO G^0(>i^<:da^i-lcooaooG^-^t^CDrHco'<:oo6oG^*io GOG000050iOi050SOOOOi-HT— ItHtHt— ICMO^OICMOOOOCO Cti O OO .t- ^1— ICZii-OCMOlOCO t^'rHr-IOOiOO^OiOCO (>i -^ O 00 oi 1-^ CO "^ i:© GO oi rH CO O CO go" O tH" CO id 1:0' 00 o O^ ^Ci(MidQ6i-5-+i Ot— (tHt— lTH(^"^^cd'*'ld<:OG6a^cdTHco^ldcdJ~~^aio1-HC^ ■*-+!-*. '^•^iOlOiOiOiOiOiOiOCOCOCOCOCOCOCOi^t-t^ '*COQOC;'(M-dH<:OOOOCM^i:CCOOG FLj^-^' YARS AND MACHINEKY AGENCY. THOMAS PRAY, Jr., No. 4 MRKET SQUAHE, Bank of Commerce Building, I^-ZFLOATIIDEIlSrOB, FL. I. COTTON YARNS OF EVERY CONCEIVABLE KIND AND COLOR, BLEACHED, GLAZED, AND GRAY. YAI^NS, TWINES, &c., TO ORDEI^ ONLY. TARNS in Cop, Skein and Beam, single, 2, 3, 4, 6, and more ply. FOREIGN THREAD TARNS, Cop and Skein, from 30 to 250. DRESSED WARPS, of aU varieties. SEINE TWINE. THE SPOOL THREAD TRADE A SPECIALTY. NEW AND SECOND HAND STEAM BOILERS, STEAM ENGINES, (STATIONARY AND PORTABLE AND STEAM FIRE,) STEAM FITTINGS, WATER WHEELS, MACHINE TOOLS, COTTON MACHINERY, (AMERICAN AND ENGLISH,) COTTON MANUFACTURERS' SUPPLIES, WOOLEN MACHINERY, ENGLISH SEINE KNITTING MACHINES, ETC., ETC. !Reed <^ Harness Manufacturers, (Established 1834.) Rooms over 58, 59 & 60 SOUTH WATER ST., PI^OVIDENCE, I^. I. Also, Corner Pocasset and 2d Sts., Fall River, Mass. MANUFACTURERS' SUPPLIES CONSTANTLY ON HAND. H. A. BRIGGS & CO., MANUFACTURERS OF YARNS, BANDINaS, BATTS, LACE AND PIGER STRING LEATHEI Dealers in Cotton Waste, Paper Stock, and Manufacturers' Supplies. OPPOSITE RAILROAD DEPOT, PAWTUCKET, B. I. H. A. BRIGGS. RUSSELL BRIGGS. H. A. BRIGGS, JUN. 47 Exchange Place, Opposite the Depot, I=>J=l.O^;7"IXDE:iSrOE!, 3FL. I. MANUFACTUBEBS OF Improved POINTED BELT HOOKS, HARNESS EYES, RING TRAVELERS, SPINNING RINGS, HARNESS HOOKS, STRAP HOOKS, JACK HOOKS, GUIDE WIRES, COTTON YARNS, COTTON BANDING, COTTON ROPE, COTTON LINES, AND COTTON TWiNES OF EVERY DESCRIPTION. Dealers and Agents for furnishing Manufacturers' Supplies. 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GUIDE WIRES, HARNESS-TWINE, HARNESS-EYES, HAMMERS, JACK HOOKS, JACKET CLOTH, KNIVES, LACE LEATHER, LAP SCALES, LATHES, LEVERS, LOOM STRAP HOOKS, NAPPERS, NUTS, OIL, PAILS, PAPER, PAPER COP TUBES, PICKER LEATHER, PICK GLASSES, PLIERS, PUNCHES, REED HOOKS, REELS, RING TRAVELERS, ROLLER LEATHER, ROVING GUIDES, RUBBER BELTING, RUBBER GASKETS, RUBBER PACKING, RULES, SAND PAPER, SCREWS, SCREW DRIVERS, SCALES, SPINNING RINGS, SPINDLES, SPOOLS. STIRRUPS, STRIPPERS, STEEL COMBS, STARCH, TACKS, TEMPLES, TWINES, VARNISH, WASHERS, WIRE HEDDLES, WRENCHES, YARN ASSORTERS, YARN SCALES, YARN REELS. Particular attention given to orders for Supplies, and furnished at the lowest cash prices. Reeds I^eset and I^epaired ii\ tl^e best manner. THREE USEFUL Little Volumes, I. The Art of Saw-Filing. The Art of Saw-Filing scientifically treated and explained on philosophical pnn- ciples, with fuU and explicit directions for putting in order all kinds of Saws, from a Jeweler's Saw to a Steam Saw-Mill. Illustrated with 44 "Wood Engravings. Bv H W. Holly. 1 vol. 18mo., clotli. 75 cents. II. The Carpenter's and Joiner's Hand-Book. A new and useful Book for Carpenters and Wood Workers. Illustrated by 37 Engravings on Wood. By H. W. Hollt, Architect, etc. 1 voL 18rao., cloth. 75 cents. "I believe every workman, by providing himself with one of these books, would be saved many times from much trouble and perplexity." — B. Burdtok, Architect. III. The Boston Machinist. Being a Complete School for the Apprentice as well as the advanced Machinist, showing how to make and use every tool in every branch of the business; with a treatise on Screw and Gear Cutting. By Walter Fitzgerald, Inventor and Mechanical Engineer. Illustrated with plates. 1 vol. 18mo., cloth. 75 cents. Published and for sale by JOHN WILEY & SON, 535 Broad-way, Nevr York. R U S K 1 N ' S WORKS UNIFORIIE IN size: AND STYLE. MODERN PAINTERS.— 5 vols., tinted paper, beveUed boards. Plates. Inbox $14 00 Ditto. ditto. half calf 21 00 Ditto. white paper, without plates . . . 9 00 Ditto. ditto. ditto. half calf . , . 17 50 bTONES OF YENICE.— 3 vols, on tinted paper, bevelled boards. In box 7 00 Ditto. ditto. half calf 12 00 MISCELLANEOUS WORKS— (including all the Volumes named below). 5 vols, on tinted paper, beveUed boards, in box 14 00 Ditto. ditto. half calf . , , . 20 00 SEVEN LAMPS OF ARCHITECTURE— 1 vol. 12mo., cloth 1 25 Ditto. ditto. 1 vol. 12mo., plates, cloth . . 1 75 LECTURES ON ARCHITECTURE AND PAINTING— 1 vol. 12mo., cloth 1 60 TWO PATHS— Being Lectures on Art. 1 vol. 12mo., cloth, plates 1 25 ELEMENTS OF DRAWING— 1 vol. 12mo., cloth . . 1 00 ELEMENTS OF PERSPECTIVE— 1 vol. 12mo., cloth . 1 00 POLITICAL ECONOMY OF ART— 1 vol. 12mo. . . 1 00 PRE-RAPHAELITISM— Construction of Sheepfolds— King of the Golden River. 1 vol. 12mo., cloth . . . I 00 SESAME AND LILIES— Two Lectures on Books and Women. 1 vol. 12mo., cloth 1 00 LECTURE BEFORE SOCIETY OF ARCHITECTS . RUSKIN'S COMPLETE WORKS— 13 vols., tinted paper, bevelled boards 35 00 Ditto. ditto. 13 vols, half calf . . , ,55 00 BEAUTIES OF RUSKIN ; OR, THE TRUE AND BEAU- TIFUL— Selected from the Works of John Ruskin, by Mrs. L. C. Tuthill. 1 vol. 12mo., tinted paper, bevelled boards, gilt top 2 50 Ditto. ditto. white paper, cloth . . . 2 00 Ditto. ditto. half calf 4 00 PRECIOUS THOUGHTS, MORAL AND RELIGIOUS- Selected from the Works of John Ruskin, by Mrs. L. 0. Tuthill. 1 vol. 12mo,, tinted paper, bevelled boards, gilt top 2 00 Ditto. ditto. half calf 4 00 Published and for Sale by JOHN WILEY & SON, 535 Broadway, N. Y. *^* Any of the above works will be prepaid by mail on receipt of the price. valuable Scientific Works JOHN WILEY, 535 BROADWAY. 3URGESS, N. G. THE PHOTOGRAPH ANI AMBROTYPE MANtJAL A Practical Treatise oi the art of taking Positive and Negative Photographs onPapei and Glass, &c. 1 vol. 18rao. Cloth. $1 00. FAIRBAIRN (WM.) C.E., E.R.S, ETC. ON THE APPLICATION OF CAST AND WROUGHT IRON TO BUILDING PURPOSES. 1 vol. 8vo. Numerous cuts. Cloth. $2 00. " No engineer can do without ihis book." — Scientifio American. n.AND BOOK OF YOUNG ARTISTS AND AMATEURS IN OIL PAINTING; Buing chiefly a condensed compilation from the celebrated Manual of Bouvier, and other distingiii.shed Continental Writers on the Art. Adapted for a Text-Book, as well as for Self-luslniction. Appended — a new Explanatory and Critical Vocabulary. By an American Artist. 12mo. Cloth. $2 00. HATFIELD (R. G). THE AMERICAN HOUSE CARPENTER. A Treatise upon Architecture, Cornices, and Mouldings, Framing, Doors, Windows, and Stairs, etc. New, thoroughly revised and improved edition, with about 150 additioiir.) pages and numerous additional plates. 1 vol. Svo. $3 50. "Every House Carpenter ought to possess one of these books." — Journal of Gommerce, LESLEY (J. P.). THE IRON MANUFACTURER'S GUIDE, To the Furnaces, Forges, and Kn. $36 00. IMl'OKTANT MILITARY WORKS. MA HAN'S FIELD FORTIFICATIONS. t TREATISE ON FIELD FORTIFICATIONS; containing instructions en the Methods of Laying out, Constructing, Defending, and Attacliing lutrencbments. With the General Outlines, also, of the Arrangement, the Attack and Defence of Permanent Fortifications. Third Edition, revised and enlarged. By D. H. Mahau, Prof. U. S. Military Academy, West Point. 1 vol. Full cloth, with plates, $8 50. MAHAN'S ADVANCED GUARD AND OUT-POSTS. 4N ELEMENTARY TREATISE ON ADVANCED GUARD, OUT-POST, AND DETACHMENT SERVICE OF TROOPS, and the Manner of Posting and Ilaudling them in the presence of an enemy. With an Historical Slvetch of tlie Rise and Progress of Tactics, &c., &c., intended as a Supplement to the System of Tactics adopted for the Military Service of Vnu United States, and especially for the use of Officers of Miliiia and Volunteers. By D. H. Mahan, Prof. U. S. Military Academy, West Point. 1 vol ISmo. Full Cloth, new edition, with plates, $1 25. REOOMMENDATIONS. Headquarters op the Army, Washington, Sept. 6, 1861. Dear Sib : I learn, with pleasure, that you propose issuing new editions of your works on ^^ Field FortiJicaUons" and" Oui-Fosts." The former I consider the best treatise on the subject in our language ; and the latter contains much, in a small compass, of high value to officers, volunteers, and others, in the present war. Yours very truly, WINFIELD SCOTT. Prof. D. H. Mahan, V. S. Ililifary Academy, West Point, J^. Y. The small volume of Prof Mahan, of the United States Military Aca- demjr, on Field Fortifications and some kindred subjects, contains most valuable information well digested and clearly set forth. It can be commended to the officers of volunteers, and all who desire such information, as containing, in moderate compass, a large amount of important mUitary knowledge. The little treatise on Out-Posts, &c., of the same author, also presents a subject of great interest, especially to Infantry and Cavalry Officers. Tours, G. TOTTEN, Br. Brig.-Gen. U. S. Ekg. Encmneer DeparTiMENT, Sept. 6, 1861. PUiiLISHED AND FOR SaLE BY JOHN WILEY, 5G Walker St., New York. Joiin Riiskm^s Works, (UNIFOKM HKKIES). PUBLISH'^^.D BY JOHN WILEY, 535 BROADWAY. t.— MODERN PAINTERS. VOL. I— GENERAL PRINCIPLES OF ART &.nd Truth as an Essential Element. $2 00. "A very extraonlinary and delightful book, full of truth and goodness, of T)Ower anc Deauty." — Marth British Revimo. VOL. II.— TRUE IDEAS OP BEAUTY. Price, %\ 00. " Mr. Euskin's work will send the painter more than ever to the study of nature ; will train men who have always been delighted spectators of nature, tc be also attentive observers. Our critics will loarn to admire, and mere admirers will learn how to criti- cise ; thus a public will be educated."— j6?acA;'icood's Magazine VOL. III.— STYLE, EINISH, LANDSCAPE, ETC. ; With cuts and eighteen illustrations, drawn by the author. $2 60. "This book may be taken up with equal pleasure whether the reader be acqnalnt«a m not with the previous volumes, and no special artistic culture is necessary In order tf snjoy its excellences or proflt by its suggestions." — Westminster Remienn VOL. IV.— MOUNTAIN BEAUTY. With numerous cuts. $2 00. 2.— THE SEVEN LAMPS OP ARCHITECTURE. I vol. With Fourteen Etchings, by the author. $1 75. "The politician, the moralist, the divine, will find in it ample store of instructive nutter, as well as the artist." — Exaininer. 3.— THE STONES OF VENICE. Illustrated by numen ns w'ood-cnts from Drawings bv the Hiunor. 3 vols. $7 00. "No one who has visited Venice can read this book without having a richer glow thrown over his rcmembrauces of that city, and for tho.se who have not, Mr. Kuskin paints it with a firmness of o\itline and vividness of colouring that will bring it before the imagination with the force of reality." — Literary gazette. 4.— PRE-RAPHAELITISM, AND NOTES ON THE CONSTRUCTION OF SHEEPFOLDS. In 1 vol. $1 00. " There is much to be collected from it which it is very important to remember." — Q-aardian. 5.— LECTURES ON ARCHITECTURE AND PAINTING. Delivered at Edinburgh in Nov. 1853. 1 vol. 12nio. With fifteen Illustrations on tinted paper, after Drawings by the author. $1 60k 6.— THE ELEMENTS OF DRAWING. In Three Letters to Beginners. 1 vol. Plates. $1 00. "We close this book, feeling confident that no student of Art should launch forth irithout this work as a compass in the binnacle." — AthenopMm. 7.— THE POLITICAL ECONOMY OF ART; to Gardening."— P^iZff. City Item. VII,. cl.\uss]':n. thic flax moveaient. Its Importance and Advantages ; with Directions for the Preparation ot Flai Cotton, »ud the Cultivation of Flax. By the Chevalier Claussen. 12mo. 12 cents. LIEBTG. PRINCIPLES OF AGRICULTURAL CHEmSTRT With special reference to the late researches nuide in Knglaiul. 1 vol. 12mo. Cloth. 60o **♦ Cnpies will he mailed to any ctddresx, amd jjrepaid. on the 7'eceipt of theprio* Ctu/iD and Societies iviU lie nupplied- with the v'orks/nr jir eirAwrs, at a discoutU. ^<'^^- ,•0^^ .V V •^ V^/".. '•> """ .0^ i7 o^- ^ V-- A .0^ • '00 ^. ^r^.* o:^" '^''-^^ .^^(P o'^ J- r,- \> -^ k\ K ^ J,- ■■ ■ ' « ♦ , «^r * .1. . « ^ .^^^ ^. * ^' i 'c- ^^ "% x^°^. =v^^ %. A %, * ■> N ' , V -I- a\ .^ -< N>^-^ ^^ ^, y \^