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No Member, whose annual contribution for the current year shall be unpaid, or who is in arrears for fines, shall be entitled to the privi- leges of the Library or Reading Room, Article 9. If any Member shall refuse or neglect to comply with the fore- going rules, it shall be the duty of the Actuary to report him to the Commit- tee on the Library. regulations : — '6 'J ^4 or Digitized by the Internet Archive in 2015 https://archive.org/details/mechanicalprinciOOIeon MECHANICAL PEINCIPIA; . CONTAINING ALL THE VARIOUS CALCULATIONS ON WATER AND STEAM POWER, AND ON THE DIFFERENT KINDS OF MACHINERY USED IN MANUFACTURING ; WITH TABLES SHOWINO THE COST OF MANUFACTURING DIFFEEENT STYLES OF COTTON GOODS. BY CHARLES ELBREDGE LEONARD. C NE W.YORK : LEAVITT, TROW & CO., 191 BROADWAY. 1848. IS/ /H8 Entered according to Act of Congress, in the year 1848, By LEAVITT, TROW & CO., in the Clerk's Office of the District Court of the United States for the Southern District of New-York. PREFACE. The present work pretends to no other merit than that of being a laborious collection of the most useful calcula- tions for the mechanic and manufacturer. All the various calculations on motive power have been condensed and arranged in as comprehensive a mode as pos- sible, which are such as to enable the mechanic to obtain the solution of any problem, simply by referring to the tables. Hence it will be seen, that those mechanics who possess very little mathematical knowledge, will be able to obtain the solution of the most intricate problems in mechanical science. To obtain the theoretical power of a water site or a steam engine becomes, as it were, a purely mechanical problem ; but unless the ratio of the theoretical and practical results are known, these solutions would be of very little practical use to the mechanic. So far as circumstances would permit, this ratio of the difference between theory and practice has been obtained, and the results carried out in the different tables. The table containing calculations on the steam engine shows the theoretical power, on account of the diversity of opinion in regard to the per cent loss of IV PREFACE. power due to escape-steam, friction of the engine, &c. It has been left optional with the mechanic, in making his calculations, what per cent to allow. From a great number of observations, we conclude that the effective power of a high-pressure engine, when the steam does not act expan- sively, is about 45 per cent less than that due to the pres- sure indicated by the gage on the boiler. Hence, to find the effective power of an engine, deduct 45 per cent of the pressure indicated by the gage. The tables showing the cost per yard of manufacturing different styles of goods from different prices of cotton, were predicated upon the yearly results of a large number of factories. There is no doubt that some of the recently erected factories, particularly those which are making printing goods, are able and do manufacture at less cost per yard, than the amounts represented in the tables. Some of those which are making printing goods containing 54 by 58, 60 by 64, and 64 by 68 threads per square inch, are able to manufacture probably for some three or four mills per yard less than represented in the tables ; but these are isolated cases, and should not therefore govern or influence in any manner the statements which profess to show the usual cost of manufacturing. The table which contains the calculated power of belts we believe is the first which has appeared of its kind. As the calculations are predicated upon practical results, we put them forward as correct data upon which all the various calculations on belting can be safely predicated. The elements from which these calculations were made are duly considered in the General Explanations of the different PREFACE. V tables. An experiment on the power of a belt is also given in one of the notes at the end of the work. The table showing the per cent loss of the power of a stream, when it is transmitted by the overshot or breast wheel, we believe will not differ essentially from the true and actu- al result. As every element which is involved in Note A is predicated upon mathematical truths, except the per cent loss of the power due to the velocity of the wheel, this ele- ment becomes as it were a distinct mathematical theorem, which, when considered in detail, gives a result nearly corresponding with that given in Note A. As this work was designed as a book of reference, it was concluded best not to give the mode of ascertaining the general results, but ta reserve that for another work which will be considered a Key to this, which will consist of two parts, the first giving the origin of all the rules in mechanical science in algebra, and also the origin of all the rules by which all the various calculations in this work were made ; the second part will give the same results, but in an arithmetical form. All must readily admit that it required no small amount of labor to perfect the present work, and that its design proposes a plan of arranging calculations, which cannot fail to be very useful to the mechanic and manufacturer. CONTENTS. WATER POWER. PAGK. Table showing: the number of cubic feet of water passing in streams per second. ... 12 Table showing the number of cubic feet of water passing over clams per second .... 13 Table showing the horse power of diiferent number of cubic feet of water when applied to overshot and breast wheels 14 Table showing the required area of the canal which conveys the water to flumes at the wheels. 18 Table showing the back water to wheels 19 Table showing the number of revolutions of the overshot and breast wheels running five feet per second 21 Table showing the number of revolutions of the pinion per minute which gears into the wheel 22 Table showing the number of cubic feet of water discharged per second under dif- ferent heads 23 Table showing the horse power of overshot and breast wheels 25 Table showing the per cent loss of power of the breast and overshot wheels 26 Table sht»wing the number of revolutions of the inward discharging turbine wheel per minute 27 Tables showing the horse power of the inward and outward discharging turbine wheels • 29 Table showing the number of revolutions per minute of the outward discharging turbine wheel 30 Note A, showing the mode of calculating the per cent loss of power, and the velocity and dimensions of the overshot and breast wheel 31 Note B, showing the allowance made in calculating the power of the turbine wheel 33 STEAM POWER. Table showing the horse power of the plain cylindrical boilers with one return flue. 37 Table showing the amount of anthracite coal consumed per day per horse power. . 39 Table showing the number of cords of southcn pine wood consumed per day per horse power 40 Table showing the number of cubic feet of water per hour that high pressure engines require per horse power 41 Table showing the mean pressure of steam upon piston when acting expansively. . . 44 Table showing the horse power of the condensing and non-condensing steam engines 47 Note A, showing the probable per cent loss of power by difl^erent engines 59 Note B, showing the mode of ascertaining the theoretical power from the eflfective. . 59 Note C, showing the mode of reducing the velocity of the pistons 60 viii CONTENTS. COTTON MANUFACTURING. PAGE. Table showing the cost of brick factories ; also, wheels, engines, gearing and belting 64 Table showing the dimensions of factories to contain different number of spindles with looms 64 Table showing the power required to drive different number and kind of spindles with looms 66 Tables showing the dimensions of overshot and breast water wheels, to drive differ- ent number and kind of spindles 67 Table showing the required area of all the openings in the outward discharging tur- bine wheel to drive different number of spindles with looms 73 Table showing the required area of all the openings in the inward discharging tur- bine wheel to drive different number of spindles with looms 74 Table showing the attendant machinery for different number of spindles, and also the cost of the machinery 76 Table containing the calculation of pnllies 78 Table showing the number of tons of anthracite coal consumed per year, to heat different sized factories 82 Table showing the dimensions of boilers to heat factories of different dimensions. ... 83 Table showing the number of operatives required to operate different number of spindles 84 Table showing the amount paid per week to operatives for different number of spindles 85 Table showing the amount paid, including all expenses except the cost of cotton, for different number of spindles 85 Table showing the cost per pound for manufacturing different numbers of yarn. ... 86 Table showing the cost per yard for manufacturing different styles of 4-4 goods. .. . 87 Table showing the cost per yard for manufacturing different styles of | goods 88 Table shuwing the cost per yard for manufacturing different styles of f goods 89 Table showing the usual number of revolutions of the front roller on different spin- • ning machines 90 Table showing the range of drafts and doublings which are adopted by manufac- turers 91 Table showing the number of hanks or skeins that frames will turn off per day 91 Table showing the twist per inch for filling and warp yarn 92 Table showing the twist per inch for roving 93 Table showing the number of yards a loom will weave per day 94 Table showing the per cent waste of different qualities of short staple cotton 95 Table showing the number of gallons of oil required for difTerent number of spindles per day 96 Table showing the number of revolutions of the front roller of different roving frames per minute 97 Table showing the usual production per day of the live spindle frame 98 Table showing the usual production per day of the mule 98 Table showing the usual production per day of the cap, or Danforth's frame 99 Table showing the usual production per day of the dead spindle frame 99 Table showing the usual production per day of the ring spindle frame ICQ Table showing the usual production per day of | looms ]01 Table showing the number of picks per minute of different width looms 102 Note H, showing the cost per pound for manufacturing, also thiB rate of wages al- lowed in all the calculations, and number of operatives 103 Note I, showing the cost per yard for manufacturing, and also the rate of wages, and number of operatives allowed 105 Note P, showing the style of the factory building lOS CONTENTS. ix BELTING. PAGE, Table showing the velocity of belts 114 Table showing the width of belts to transmit different number of horse power 115 Table showing the required width of belts to drive different kinds of spindles 116 Table showing the width of counter belts to drive different kinds of machinery. .. . 119 Table showing the width of counter belts to drive large size board planing machines 122 Note E, showing an experiment on belting. 123 CORN AND FLOUR MILLS. Table showing the area of all the openings in the inward discharging turbine wheel, to drive 4^ feet stones, grinding corn 128 Table showing the area of all the openings in the outward discharging turbine wheel, to drive 4^ feet stones, grinding wheat 132 Table showing the dimensions of the overshot and breast wheel to 4.j feet stones grinding corn » 134 CUT-NAIL MACHINES. Tables showing the dimensions of the overshot and breast wheel to drive cut-nail machines 139 FURNACES. Table showing the dimensions of the overshot and breast wheels to drive blast, &c., for furnaces 144 MISCELLANEOUS MACHINERY. # Tables showing the actual and calculated power required to drive large size circular saws 148 Table showing the actual and calculated power required to drive upright saws 148 Table showing the actual and calculated power required to drive planing machines. 149 Tables showing the power required to drive 4^ feet stones grinding corn and wheat. 149 Table showing the power required to drive the blast, &c., for furnaces and cut-nail machines 150 PADDLE WHEELS. Table showing the number of miles that boats move by the wheels 154 Table showing the number of revolutions of the wheels due to the speed of the boat. 155 Problems « , 161 0 EXPLANATION OF TERMS USED IN THIS WORK. A Horse Power is considered in all the calculations in this work to be equal to 33,000 pounds raised one foot high per minute. A Hank or Skein is equal to 840 yards. ^ Co-efficient of Discharge is that number which must be multiplied by the square root of the head to obtain the velocity of the water when it leaves the opening. GENERAL EXPLANATION OP THE DIFFERENT TABLES. It will be observed that there is connected with each table an explanation, showing the mode of performing or taking out a calculation ; there are also examples given, to show the mode in detail of taking out a calculation. At the end of the work there are a large number of Problems givei^ which refer to the difJerent tables to obtain elements, which when combined, give the solution of the Problem ; the design of the following observations, is to explain more fully some of the tables. The actual quantity of water passing into a straight canal in a given time, the bottom of which being level, and the sides perpendicular, will not differ materially from that found by calculation in Table No. 1 ; but if these three ele- ments are variable, the result obtained by calculation will not be so certain ; hence, the different results which could have been obtained from this, and carried into those Prob- lems given to illustrate the application of the different tables have been omitted, because it was feared that there would GENERAL EXPLANATION not be a sufficient degree of accuracy attending them, to correspond with those results which are predicated upon mathematical truths, which are linked in the series of the different calculations. Unless the location is very favorable, the results obtained by this table can only be considered as an approximation to the true result. Tables No. I and 2, show the number of cubic feet of water passing in a stream per second ; Table No. 3, shows the number of horse power which this quantity of water will produce when applied to different falls ; this quantity of water may be applied to the overshot, breast, Parker's, or the outward and inward discharging turbine wheels, all of which probably produce about the same effect. It must be borne in mind that this table shows the effective power ; that is, the usual per cent loss of the foregoing wheels has been deducted from that which is due to the quantity of water ^plied to the whole fall. Table No. 5, shows the amount of back-water ; when the width of the race, and the quantity of the water dis- charged from the wheel per second are known, as the Mill- wright always knows the horse power of the wheel, he can easily find the number of cubic feet of water that will be discharged into the wheel pit per second : for instance, sup- pose the fall of a breast or the diameter of an overshot wheel to be 72 feet, and 20 horse power; in order to find the number of cubic feet of water discharged from this wheel per second, turn to Table No. 3; find 12 in the column marked " Diameter," below this number in the table find 20, or the nearest number to it, which is 19.99 ; now oppo- site to this number in the column marked No. Feet/' will OF THE DIFFERENT TABLES. xiii be found 22 cubic feet ; hence it will be seen, that it the fall of the breast or the diameter of the overshot is known, and also the power of the wheel, the number of cubic feet of water discharged can be readily found. It will be noticed that the fall of the breast or the diameter of the overshot wheel is about 3 feet less than the whole fall ; hence in case the quantity of water discharged from the turbine or Parker's wheel should be required, it would be necessary to deduct 3 feet from the whole fall : for instance, suppose the power of a turbine wheel to be 30 horse, and the whole fall to be 15 feet, deduct 3 feet, which gives 12 feet effective fall — find 12 in the column marked Diameter,'' in Table No. 3 ; below this number in the table find 30, or the nearest number to it, which is 29.99 ; opposite to this number in the column marked " No. Feet," will be found 33 cubic feet discharged per second. Table No. 8, shows the number of cubic feet of water discharged per second through gates under different heads ; for instance, suppose the head to an overshot wheel to be 2 feet or 24 inches, the length of the gate being 12 feet, and it is open 3 inches ; now the length of the gate, which is 12 feet or 144 inches, multiplied by 3 inches, gives 432 inches — now find 24 in the column marked Head,'' opposite to this number in the column marked " No Feet," will be found 5.46, which multiplied by 4.32, gives 23.58 cubic feet discharged per second : suppose this quantity of water to be applied to an overshot wheel, 16 feet in diameter ; required, the horse power ; turn to Table No. 3 — find 23.58, or say 24 in the column marked ^'No. Feet," opposite to this num- ber in the table, and under 16 in the column marked " Di- xiv GENERAL EXfLANATiON ameter," will be found 29.08 horse power. Again, requir- ed, the proper length of an overshot wheel to receive 24 cubic feet of water per second ; in the previous statement it was found, that 24 cubic feet of water applied to an overshot wheel 16 feet in diameter per second, would produce 29.08 horse power ; now turn to Table No. 9 — find 16 in the coU umn marked " Diameter,' ' opposite to this number in the table find 29.08, or the nearest number to it, which is 28. 1^ over this number and in the column marked Length," will be found 9 feet, the required length of the wheel ; the co- efficient of discharge in these calculations is 5.5. Table No. 9, shows the horse power of the overshot and breast wheels, which are calculated to run 5 feet per second, the depth of the buckets being 12 inches, and the head about 2 feet ; these wheels are calculated to produce about 66 per cent of the whole power of the site. It will be noticed that the breast wheel is calculated to produce as great effect as the overshot; there is no doubt but the breast wheel, when properly constructed and well calculated, can, and does produce as great effect as the over- shot. When those elements which are involved in a series of calculations are considered in detail, they not only show that the breast wheel is equal to, but more efficacious than the overshot ; they show that the head required to obtain the relative velocity, may be some twelve to fifteen inches less on the breast than on the overshot wheel. In order to fully illustrate this position, suppose the breast wheel to be at rest ; let the top of the buckets be just in line with the openings of the gate ; now, as the buckets are twelve inches deep, the water will fall twelve inches OF THE BIFFERENT TABLES. before it arrives to the bottom of the bucket ; as the wheel moves five feet per second, and the buckets do not fill so fast as the wheel moves, the distance through which the water falls after it passes through the gate will never be less than one foot ; now it does not require but two feet head to impel the water eight feet per second, hence one foot head is sufficient to give the usual relative velocity of the water to breast wheels. The water in entering the buckets of the overshot wheel changes its direction, and therefore the depth of the bucket does not much, if any, increase the velocity of the water^ consequently one foot head to the breast wheel accomplishes the same end as two feet to the overshot. The diameter of the breast wheel should exceed that of an overshot about three feet on the same fall. Table No. 12, shows the effective power of the outward and inward discharging turbine wheels; for instance, suppose the effective head or the total head when the wheel is in operation to be 16 feet, then the horse power of the outward discharging (if the area of all the openings were 100 inches) would be 21, and the horse power of the inward discharging would be 12.1. It must not be understood that the relative effect of these wheels under the same head, and discharging the same quantity of water in the same time, is as 21 to 12.1 j but that the quantity of water which these wheels discharge in the same time under a given headj and having the same area of openings, is as 21 to 12.1 ; this difference in the quantity of discharge is due to the motion which the water receives while passing through the wheel ; the outward dis- charging wheel receives the water at the centre, which XVI GENERAL EXPLANATION escapes at the periphery — but the inward discharging re- ceives the water at the circumference, which vents at the centre ; hence it will be readily seen, that the centrifugal force which the water receives while passing through these wheels, acts with, and in opposition respectively to the force of discharge due to the head. Table No. 10, shows the per cent loss of power of a stream when it is transmitted by the overshot or breast wheel ; that is, if they are calculated according to this work. This table shows that the per cent loss of power of an over- shot wheel 9 feet in diameter, or a breast wheel 9 feet fall, is 52 per cent ; but if the diameter or fall of the wheel is 30 feet, there will be only 23 per cent loss ; hence a difference of 29 per cent in favor of the latter wheel : when the diam- eter or fall of the wheel is 14 feet, the loss is 38 per cent, which deducted from 100, gives 62 per cent effective power, which is probably about the effective power of Parker's and the two turbine wheels ; they may exceed 62 per cent in effect, but suppose they do not, then it would appear that these wheels produce greater effect from a given quantity of water than the overshot wheel 14 feet in diameter on the same fall : an overshot wheel 14 feet in diameter requires a fall of about 17 feet, hence these wheels are more efficacious on a fall of 17 feet than the breast or overshot. In the present instance the overshot and breast wheels are calculated to produce a maximum effect ; but there are many overshot and breast wheels in operation whose velocity much exceeds five feet per second, having more than two feet head, and the depth of the bucket much exceeding 12 inches ; hence the loss power in such cases, will exceed the OF THE DIFFERENT TABLES. xvii amount represented in Table No. 10, in proportion as those elements differ from those represented in Note A ; hence the cause of these wheels frequently being more efficacious on falls of 22 to 24 feet. The power should be taken from the overshot and breast wheels on the side to which the water is applied, then the journals of the wheel will sustain the weight of the wheel, and the weight of the water on the wheel ; but if the power is taken from the opposite side to which the water is applied, then the journals of the wheel will sustain the weight of the water on the wheel, and the resistance of the power which is nearly or quite equal to the weight of the water ; hence in this case the journals of the wheel sustain the weight of the wheel, and nearly twice the weight of the water, because the journals are as it were a fulcrum sustaining the weight and power. Table No. 5, Steam Power, shows the horse power of the condensing and non-condensing engines ; there are three va- riable elements in the problem of calculating the power of an engine ; to wit, the diameter of the cylinder, the velocity of the piston, and the effective pressure of the steam upon the piston ; as only two can be represented in the table, one of the three must be omitted, or considered a constant num- ber : in this table the velocity of the piston is constant, which is calculated to move 100 feet per minute ; hence if the piston move 300 feet, the power of the engine will be in- creased three-fold, or the number found in the table due to 100 feet must be multiplied by 3. The probable per cent loss of different engines is given, to show the mode of ascer- taining the required diameter of the cylinder to drive the Xviii GENERAL EXPLANATION different kind of machinery represented in the different problems : it is optional with the engineer in making his cal- culations what per cent loss to allow. Table No. 3, Manufacturing, shows the calculated and actual power required to drive different number and kind of spindles with looms ; the actual power required, was obtain- ed by noting the number and kind of spindles in operation in several factories which were driven by overshot wheels, having about two feet head, and running about five feet per second, whose power was calculated and carefully compared with the amount of the power of the wheels used : by this means an approximation to the actual power required was obtained ; the calculated power, or the power of the wheel, exceeds the actual power about 25 per cent. On account of there being so many variable elements brought into action in a series of calculations showing the power required to drive a given amount of machinery, there has an opin- ion arisen among mechanics, that it is quite impossible to arrive at any definite conclusions as regards the amount of power required to drive a given amount of any kind, more especially cotton machinery ; now it is quite evident that the average power required to drive the machinery in two factories, each containing the same amount and kind of ma- chinery, and turning off the same amount of work in the same time, will not differ materially ; still there may be a great difference in the amount of water which two such fac- tories situated on the same fall would require, which differ- ence however arises from the mode of transmitting the power (which is due to the gravitation of the water) to the machinery. It is not uncommon to see overshot and breast OF THE DIFFERENT TABLES. xix wheels (more particularly the breast wheel) working under a head of four or five feet, the velocity of the wheels being sonae seven or eight feet per second, the depth of the bucket some 16 inches, and the whole head and fall not exceeding 16 feet : in such cases theory shows, and observations and ex- periments confirm, that there is not 50 per cent of the power of the site transmitted to the machinery ; hence the differ- ence in the quantity of water or power used is due to the mode of transmitting it : such palpable errors as the forego- ing are often overlooked, and the difference in the amount of power or quantity of water expended, has been too often attributed to the mode of arranging the shafting, and the workmanship and condition of the machinery. It is quite evident that the difference in the amount of power required to drive the shafting, arising from its mode of arrangement, when compared with the power required to drive the whole machinery, is inconsiderable; hence this element may in the ordinary calculations be omitted. In this table the No. of the yarn, the amount and kind of the machinery, and the production, have been considered. It may be proper to re- mark that the power required to drive the same machinery will vary in a certain ratio with the amount which it turns off ; the difference in the amount which the same kind of ma- chinery produces is not material, but the calculations are such as to correspond with the greatest production of the different kind of machinery. The filling is calculated to be spun on the Cap or Dan- forth, the ring and dead spindle frames in these calculations. The dead and ring spindle frames turn off about 25 per cent more than the mule when spinning filling ; as filling is XX GENERAL EXPLANATION about half of the whole production of the factory ; the in- creased production when the filling is spun on the frame, above the amount when the filling is spun on the mule, will be about 12 per cent, hence there will be about 12 per cent more attendant machinery : now the attendant machinery for a given number of spindles, including looms, will require about two thirds of the whole power ; hence the increased power due by direct proportion is about 8 per cent ; it will be safe to allow 7 per cent. The power required to spin a given amount of filling on a frame will exceed the power re- quired to spin the same on the mule about 25 per cent ; since the spinning requires one third of the whole power, or per cent, half of the spinning will require about 16 per cent ; one fourth of 16 per cent is 4 per cent, hence the whole difference is about 11 per cent, which agrees with the amount allowed in the table : in the same manner the amount of power required to drive the different number and kind of spindles was found. The Tables ranging from No. 4 to 9 show the length of the overshot and breast wheels required to drive different number and kind of spindles on different numbers of yarn — the column marked ^'Fall," shows the fall of the breast wheel, or the diameter of the overshot, both of which are cal- culated to have about 2 feet head, the depth of the bucket being about 12 inches, and the velocity of the wheel about 5 feet per second ; this table shows the length of the bucket in the wheel. It will be noticed that when the diameter of the overshot or the fall of the breast wheel is 12 feet, the length will be 72 feet to drive 10,000 mule and frame spin- dles on No. 10 to 25 yarn ; now 72 feet may be divided into OF THE DIFFERENT TABLES. any convenient length, say 12 feet, which will give 6 wheelS;^ or 18 feet, which will give 4 wheels. Table No. 12, shows the attendant machinery required for different number and kind of spindles on different numbers of yarn ; it will be noticed that on No. 5 to 10 yarn, the fine speeder spindles are omitted, as they are seldom if ever used on such coarse work ; many manufacturers prefer the non- twisting speeder: the number of spindles can be found by dividing the number of speeder spindles found in the table by 2.5. — Example, for 1000 spindles on No. 16 yarn, 50 fine speeder spindles are required, which divided by 2.5, gives 20 non-twisting speeder spindles ; if the fly frame is preferred, multiply the number of speeder spindles found in the table by 2, the result will give the number of fly frame spindles ; this ratio appears to be too great, but it agrees well in practice. It will be noticed that this table is calcu- lated for mules and frames ; if the filling is spun on the ring or dead spindle frame, add about 12 per cent to the attendant machinery ; if the filling and warp is spun on the Danforth frame, add 40 per cent to to the attendant machinery. The number of yarn ranges from 5 to 10, 10 to 20, &;c., but the calculations were made for No. 8, No. 16, No. 24, and No. 35 yarn. Table No. 13, Manufacturing, shows the number of re- volutions of a driven shaft per minute, when it is driven by different sized pulleys ; over each table will be found the number of turns per minute which the driving shaft is calcu- lated to run ; if the line shaft makes 100 turns per minutCj and the driving pulley on the same is 10 inches in diameter, then if the diameter of the pulley on the shaft to be driven xxii GENERAL EXPLANATION by this is 10 inches it will make 100 turns, if it is 12 inches, 14, 16, 18, 20, 22, or 24, it will respectively make 83, 71, 62, 56, 50, 45, and 42 turns per minute, which will be seen by examining the table ; if the pulley on the driven shaft is 10 inches in diameter, and the pulley on the driving should be 10, 12, 14, ]6, 18, 20, 22, or 24 inches, the driven shaft would respectively make 100, 120, 140, 160, 180, 200, 220, and 240 turns per minute ; it will be noticed that the calcu- lations are made for the driving shaft to run from 96 to 124 turns per minute ; now suppose a shaft was running 240 turns per minute, and it was driven by a pulley 24 inches in diameter, what must be the diameter of a pulley to drive the shaft say 180 turns ?— find 240 in the table marked " 100 Revolutions," opposite to this number in the column marked Driving Pulleys," will be found 24 inches, which is the driving pulley ; above 240 will be found 180 turns; opposite to this number, in the column marked Driving Pulleys," will be found 18 inches, the diameter of the pulley required; again, suppose the driven pulley on this shaft, which is cal- culated to run 240 turns, is 10 inches, what must be the di- ameter of this pulley to drive the shaft 100 turns ? — opposite to 240 find 100, over this number, in the column marked Driven Pulleys," will be found 24 inches ; it will be noticed that the ratio of variation in the diameter of the pul- leys is 2 inches ; if it is desirable not to alter the revolutions only the number due to one inch, take half the difference which 2 inches makes : for instance, suppose the driven shaft makes 100 turns per minute, what must be the diam- eter of the driven pulley to drive it 110 turns per minute ? — it will be noticed that a 10 inch pulley drives it 100 turns, OF TflE DIFFERENT TABLES. , ? and a 12 inch pulley drives it 120 turns per minute ;^henef it will require a pulley 11 inches in diameter. /i | Table No. 2, Belting, shows the required width pf'^he\i0 to transmit different number of horse power — the coliimnr^at the top of the table shows the diameter of the smallest drum, which must always regulate the width of the belt. There are five elements involved in the problem of cal- culating the power which a belt is capable of transmitting ; to wit, the angle of the belt, the diameter of the smallest drum, and the distance between their centres, the velocity and width of the belt. In ordinary calculations the angle of the belt may be neglected — as this element is inconsiderable when compared to the whole power of the belt — and also the distance between the centre of the drums, when it exceeds 15 or 20 feet : hence, the only variable elements involved in the problem are the width and velocity of the belt, and the diameter of the smallest drum ; as only two variable ele- ments can be represented in the table, the velocity of the belt must be considered constant, which is calculated to move 1500 feet per minute ; the power of a belt increases in a certain ratio with its velocity ; hence, the calculations in this table will be applicable to all belts whose velocity ex- ceeds 1500 feet, leaving a surplus power in the belt, corres- ponding with the ratio due to the increased velocity of the belt over and above 1500 feet per minute. It is found, by a great number of observations, that the proper velocity of large belts is about 2000 feet per minute. Ii>RRATA. Page 19, Example Second, for 20, read 50 cubic feet. 24, « it 10, « 20. 39, f( 4210 " 4200 pounds. 68, First, 16, " 17.2 feet. (( 77, (( t< centre " counter. 94, Second (( 31, 30 yards. 102, t( 112, " 104 picks. 168, Problem No. 24, (< water " wheel. WATER POWER. MECHANICAL PRINCIPIA. WATER POWER. The following table shows the number of cubic feet of water passing in streams per second. The column marked Velocity" shows the number of inches that a block of wood, or any floating body, thrown into the middle of a stream, passes over per second ; the column marked " No. of Feet'' shows the number of cubic feet of water passing in the stream per second ; the column marked " Area" shows the area of the stream, which is one foot — the quantity of water passing in a stream varies as the area of the stream — hence if the area of a stream is multiplied by the number of cubic feet of water found in the table due to one foot, the result will give the number of cubic feet of water due to that area. Example. Required, the number of cubic feet of water passing in a stream per second — the width of the stream being 20 feet, the depth of the stream being 2 feet (which multiplied by 20 gives 40 feet as the area of the stream), and the velocity of a floating body thrown into the middle of the stream being 24 inches per second — find 24 in the column marked " Veloci- ty opposite to this number, in the column marked "No. of Feet," will be found 1.63, which multiplied by 40 (the area of the stream) gives 65.2 cubic feet of water passing in the stream per second. — Answer, 12 MECHANICAL PRINCIPIA. No. 1. Velocity. No. of Feet Area. Velocity. No. of Feet. Area. 8 .47 42 O HA 10 .61 44 OIK O.IO 12 ,75 46 O O 1 0.31 14 .89 48 •J /< CJ o.4o 16 1.04 oU O 18 1.18 52 3.76 OA 1.33 54 o no 3 yj 22 1.48 00 /( AO 1.63 ro i)0 4.24 26 1.78 60 4.39 28 1.93 62 4.55 30 2.08 64 4.70 32 2.24 66 4.86 34 2.38 68 5.02 36 2.54 70 5.17 38 2.69 72 5.33 40 2.84 The following table shows the number of cubic feet of water passing over dams per second, the water on the dam being any depth from 1 to 60 inches, the length of the dam being 1 foot. The quantity of water passing over dams va- ries as the length — hence if any length is multiplied by the number of cubic feet found in the table due to 1 foot, the result will give the number of cubic feet due to that length. The depth of the water on platform dams with the ordinary inclination should be taken at the lowest point, or where the water leaves the dam. The column marked " Depth'* shows the depth of the water on the dam — the column marked "Length" shows the length of the dam, which is one foot. Example. Required, the number of cubic feet of water passing over a dam per second, the depth of the water on the dam being 16 inches, and the length of the dam being 40 feet — find 16 in the column marked "Depth;" opposite to this number, in the column marked " No. of Feet," will be found 5.24 cubic feet, which multiplied by 40 feet (the length of the dam) WATER POWER. 13 gives 209.6 cubic feet of water passing over the dam per second . — Ansiver. Example. Required, the number of cubic feet of water passing over a dam per second, the depth of the water on the dam being 3 inches, and the length of the dam being 80 feet — find 3 in the column marked " Depth opposite to this number, in the column marked "No. of Feet," will be found .42, which multiplied by 80 gives 33.6 cubic feet passing over the dam per second. — Answer. No. 2. Depth. Length. No. of Feet. Depth. Leugth. No. of Feet. 1 1 .08 31 1 14.11 2 1 .23 32 1 14.81 3 1 .42 33 1 15.51 4 1 .66 34 1 16.23 5 .92 35 19.91 1.20 36 17.67 7 L51 37 18.43 8 1.85 38 19.18 9 2.21 39 19.93 10 2.57 40 20.71 -.11 2.99 41 21.41 12 3.40 42 22.29 13 3.83 43 23.06 14 4.28 44 23.88 15 4.75 45 24.68 16 5.24 46 25.53 17 5.72 47 26.36 18 6.24 48 27.10 19 6.79 49 28.00 20 7.32 50 28.97 21 7.88 51 29.81 22 8.44 52 30.62 23 9.04 53 31.56 24 9.60 54 32.45 25 10.22 55 33.26 26 10.84 56 34.26 27 11.47 57 34.95 28 12.01 58 36.00 29 12.77 59 36.95 30 13.43 60 37.80 14 MECHANICAL PRINCIPIA. The following table shows the horse power that different number of cubic feet of water per second will produce, when applied to overshot wheels of different dianaeter, or to breast wheels of different falls — the column marked "No. of Feet," shows the number of cubic feet of water to be applied to the wheel per second, the column marked " Diameter," shows the diameter of the overshot wheel, or the fall of the breast wheel. Example. Required, the number of horse power that 20 cubic feet of water per second would produce, if applied to an overshot wheel 12 feet in diameter — find 20 in the column marked " No. of Feet," opposite to this number in the table, and under 12 in the column marked " Diameter," will be found 18.18 horse power. — Answer, Example. Required, the horse power that 30 cubic feet of water per second would produce, if applied to a breast wheel, the fall being 15 feet — find 80 in the column marked " No. of Feet," opposite to this number in the table, and under 15 in the column marked " Diameter," will be found 34.08 horse power. — Answe7\ Hence, if the horse power of the wheel is known, (the overshot, breast and turbine,) and also the head or fall, the number of cubic feet of water discharged from the wheel into the pit per second can be found. Suppose the fall to be 15 feet — then find 15 in the column marked " Diameter," under this number in the table find the horse power of the wheel — opposite to this number in the column marked " No, of Feet," will be found the number of cubic feet of water discharged into the wheel pit per second, WATER POWER. 15 No. 3. of Ft. DIAMETER. 6 ;z; 6 7 8 9 10 11 12 13 6 2.72 3.18 3.63 4.04 4.51 4.99 5.45 5.90 7 3.18 3.71 4.24 4-72 5.27 5 83 6.36 6.88 8 3 63 4.24 4.84 5.44 6.03 6.66 7.27 7.87 9 4 08 4.77 5.45 6.12 6.79 7.49 8.18 8.85 10 4.54 5.30 6.06 6.81 7.55 8.33 9.09 9.84 11 4.99 5.83 6.66 7.49 8.30 9.16 9.99 10.82 12 5.45 6.36 7.27 8.17 9.06 9.99 10.90 11.80 13 5.90 6.89 7.87 8.85 9.81 10 82 11.81 12.79 14 6.35 7.42 8.48 9.53 10.57 11.66 12.72 13.77 15 6.81 7.95 9.09 10.21 11.32 12.49 13.63 14.76 16 7.26 8.48 9.69 10.89 12 08 13.32 14.54 15.14 17 7.72 9 01 10.30 11.57 12.83 14.16 15 45 16.72 18 8.17 9.54 10 90 12.25 13.59 14.99 1636 17.71 19 8.62 10.07 11.51 12.93 14.34 15.82 17.27 18.69 20 9.08 10.60 12.12 13.62 15.10 16.66 18.18 19.68 21 9.53 11 13 12.72 14 30 15.85 17.49 19.08 20.66 22 9.99 11.66 13.33 14.98 16.61 18.32 19.99 21.64 23 10.44 12.19 13.93 15.66 17.36 19.15 20.90 22.63 24 10.89 12.72 14.54 16.34 18.12 19.99 21.81 23.61 25 11.35 13.25 15.15 17.02 18.87 20.82 22.72 24.60 26 11.80 13.78 15.75 17.70 19 63 21.65 23.63 25.58 27 12.26 14.31 16.36 18.38 20.38 22.49 24.54 26.56 28 12.71 14.84 16.96 19.06 21.14 23.32 25.45 27.55 29 13.16 1537 17.57 19.74 21.89 24.15 26.36 28.53 30 13.62 15 90 18.18 20.43 22. 65 24.99 27.27 29.52 3J 14.07 16.43 18.78 21.11 23.40 25.82 28.17 30.50 32 14.53 16.96 19.39 21.79 24.16 26.65 29.08 31.48 33 14.98 17.49 19.99 22.47 24.91 27.48 29.99 32.47 34 15 44 18.02 20.60 23.15 25.67 28.32 30.90 33.45 35 15.90 18.55 21 21 23.83 26.42 29.15 31.81 34.44 36 16.34 19.08 21.81 24.51 27.18 29.98 32.72 3542 37 16.79 19.61 22.42 25.19 27.93 30.82 33.63 36.40 38 17.25 20.14 23.02 25.87 28.69 31.65 34.54 37.39 39 17.70 20 67 23.63 26.55 29.44 32.48 35.45 38.37 40 18.16 21.20 24.24 27.24 30.20 33.32 36.36 39.36 41 18.61 21.73 24.84 27.92 30.95 34.15 37.26 40.34 42 19.06 22.26 25.45 28.60 31.71 3498 38.17 41.32 43 19 52 22.79 26.05 23.28 32 46 35.81 39.08 42.31 44 1997 23.32 26 66 29.96 33.22 36.65 39.99 43.29 45 20 43 23.85 27.27 30.64 33 97 37.48 40.90 44 28 46 20-88 24.38 27.87 31.32 34.73 38.31 41.81 45.26 47 21.33 24.91 28.48 32.00 35.48 39.15 42.72 46.24 48 21.79 25.44 29.08 32.68 36.24 39.98 43.63 47.23 49 22.24 25.97 29.69 33.36 36.99 40.81 44.54 48.21 50 22.70 26.50 30.30 34 05 37.75 41.65 45.45 1 49.20 16 MECHANICAL PRINCIPIA. ]Vo. 3. — Continued. £ I ««-• 1 O I DIAMETER. o i 5z ' 14 15 16 17 18 19 20 21 6 6.36 6.81 7.26 7.72 8.18 8.54 9.09 9.55 7 7.42 7.97 8.47 9.01 9.54 10.08 10.61 11.14 8 8.48 9.09 9.68 10.30 10.91 11.52 12.12 12.73 9 9.54 10.22 10.90 11.59 12.27 12.9a 13.64 14.32 10 10.60 11.36 12.12 12.88 13.64 14.40 15.16 15 92 11 11.66 12.49 13.^3 14.16 15.00 15.84 16.67 17.51 V2 12.72 13.63 14 54 15.45 16.36 17.28 18.19 19.10 13 13.78 14.76 15.75 16.74 17.73 18.72 19.70 20 69 14 14.84 15.90 16 96 18.03 19.09 20.16 21.22 22,28 15 15.90 J 7.04 18.18 19.32 20.46 21 60 22.74 23.88 16 16.96 18.17 19.39 20.60 21.82 23.04 24.25 25.47 17 18.02 19.31 20.60 21.89 23.18 24 48 25.77 27.06 18 19.08 20.44 21.81 23.18 24.55 25.92 27.28 28.65 19 20.14 21.58 23.02 24.47 25.91 27.36 28.80 30.24 20 21.20 22.72 24.24 25.76 27.28 28.80 30.32 31.84 21 22.26 23.85 25 45 27.04 28.64 30.24 31.83 33.43 22 23.32 24.99 26.66 28.33 30.00 31.68 33.35 35.02 23 24.38 26.12 27.87 29.62 31.37 33.12 34.86 36.61 24 25.44 27.26 29.08 30.91 32 73 34.56 36.38 38.20 25 26.50 28.40 30.30 32.20 34.10 36.00 37.90 39 80 26 27.56 29.53 31.51 33.48 3546 37.44 39.41 41.39 27 28.62 30.67 32.72 34.77 36.82 38.88 40.93 42.98 28 29.68 31.80 33.93 36.06 38.19 40.32 42.44 44.57 29 30.74 32.94 35.14 37.35 39.55 41.76 43.96 46.16 30 31.80 34.08 36.36 38.64 40.92 43 20 45.48 47.76 31 32.86 35.21 37.57 39.92 42.28 44.64 46.99 49.35 32 33.92 36.35 38.78 41.21 43.64 46.08 48.51 50.94 33 34.98 37.48 39.99 42.50 45.01 47.52 50.02 52 53 34 36.04 38.62 41.20 43. 79 46 37 48.96 51.54 54.12 35 37.10 39.76 42.42 45.08 47.74 50.40 53.06 55 72 36 38.16 40.89 43.63 46.36 49.10 51.84 5457 57.31 37 39.22 42.03 44.84 47.65 50.46 53.28 56.09 58.90 38 40.28 43 16 46.05 48.94 51.83 54.72 57.60 60.49 39 41.34 44.30 47.26 50.23 53.19 56.16 59.12 62.08 40 42.40 45.44 48.48 51.52 54.56 57.60 60.64 63.68 41 43.46 46.57 49 69 52.80 55.92 59 04 62.15 65.27 42 , 44 52 47.71 50.90 54 09 57.28 60.48 63 67 66.86 43 ^45.58 48.84 52.11 5538 58.65 61.92 65.18 68,45 44 46.64 49.98 53.32 56.67 60.01 63.36 66.70 70.04 45 47.70 51.12 54-54 57. 96 61.38 64.80 68.22 71.64 46 48.76 52.25 55 75 59.24 62.74 66 24 69.73 73 23 47 49,82 53.39 56.96 60.53 64.10 67.68 71.25 74.82 48 50.88 54.52 58.17 61.82 65.47 69.12 72 76 76.41 49 51.94 55 66 59.38 63.11 66.83 70 56 74.28 78.00 50 53.00 56.80 60.60 64.40 68.20 72.00 75-80 79.60 WATER POWER. ]Vo. S*— Continued. 17 DIAMETER. 22 23 24 25 26 27 28 29 30 10.00 10.46 10.92 11.37 11.83 12.28 12.74 13.20 13.65 11.67 12.20 12.74 13.27 13.80 14.33 14.86 15.40 15.93 13.34 13.95 14.56 15.16 15.77 16.38 16 99 17.60 18.20 15.01 15.69 16.38 17.06 17.74 18.43 19.11 19.80 20.48 16.68 17.44 18.20 18.96 19.72 20.48 21.24 22.00 22.76 18.34 19.18 20.02 20.85 21.69 22.52 23.36 24.20 25.03 20.01 20.92 21 84 22.75 23.66 24 57 25.48 26.40 27.31 21.68 22.67 23.66 24 64 25.63 26.62 27.61 28.60 29.58 23.35 24.41 25.48 26.54 27.60 28.67 29.73 30.80 31.86 25.02 26.16 27.30 28.44 29 58 30.72 31.86 33.00 34.14 26.68 27.90 29.12 30.33 31.55 32.76 33.98 35.20 36.41 28.35 29.64 30.94 32.33 33.52 34.81 36.10 37.40 38.69 30.02 31 39 32.76 34.12 3549 36 86 38.23 39.60 40.96 31.69 33.13 34.58 36.02 37.46 38.91 40.35 41.80 43.24 33.36 34.88 36.40 37.92 39.44 40 96 42,48 44.00 45.52 35 02 36.62 38.22 39.81 41 41 43.00 44.60 46.20 47.79 36.69 38.36 40.04 41.71 43.38 45.05 46.72 48.40 50.07 38 36 40.11 41.86 43,63 45.35 47.10 48 85 50.60 52.34 40.03 41.85 43.68 45.50 47 32 49.15 50.97 52.80 54.62 41.70 43.60 45.50 47.40 49.30 51 20 53.10 55.00 56.90 43 36 45.34 47.32 49.29 51.27 53.24 55 22 57.20 59.17 45 03 47.08 49.14 51.19 53 24 55.29 57.34 59.40 61.45 46.70 48.83 50.96 53,08 55.21 57.34 59.47 61.60 63.72 48.37 50.57 52.78 54 98 57.18 59 39 61.59 63.80 66.00 50.04 52 32 54.60 56.88 59.16 61.44 63.72 66.00 68.28 51 70 54.06 56 42 58.77 61.13 63.48 65.84 68.20 70.55 53.37 55 80 58.24 60.67 63.10 65 53 67.96 70.40 72.83 55.04 57.55 60.06 62.56 65.07 67.58 70.09 72.60 75.10 56.71 59.29 61.88 64.46 67.04 69.63 72.21 74.80 77.38 58.38 61.04 63 70 66 36 69.02 71.68 74.34 77.00 79.66 60.04 62.78 65.52 68 25 70 99 73.72 76.46 79.20 81.93 61.71 64.52 67.34 70.15 72.96 75.77 78.58 81.40 84.21 63 38 66,27 69.16 72.0# 74.93 77.82 80.71 83.60 86.48 65.05 68.01 70.98 73.94 76 90 79.87 82.83 85.80 88.76 66.72 69.76 72.80 75.84 78 88 81.92 84.96 88.00 91.04 DO.OO 71.50 74.62 77 73 80.85 83.96 87.08 90.20 93.31 70.05 73.24 76.44 79.63 82.82 86.01 89.20 92.40 95.59 71.72 74.99 78.26 81 52 84.79 88.06 91.33 94 60 97.86 73.39 76 73 80.08 83.42 86.76 90.10 93 45 96.80 100.14 75.06 78.48 81 90 85.32 88.74 92.16 95.59 99.00 102.42 76.72 80 22 83.70 87.21 90.71 94.21 97.70 101.20 104.69 78.39 81.96 85 56 89.11 92.68 96.25 99.82 103 40 106.97 80.06 83.71 87.34 91.00 94.65 98.30 101.95 105.60 109.24 81.73 85.45 89.18 92.90 96.62 100.35 104.07 107.80 111.52 1 83.40 87.20 91.00 94.80 98.60 102.40 106.20 110.00 113.80 2* \ 18 MECHANICAL PRINCIPIA. The following table shows the required area of the canal which conveys the water from the reservoir to the flume at the wheel — the column marked Area," shows the area of the canal in feet, the column marked " Length," shows the length of the overshot or breast wheels. It matters not what may be the diameter of the overshot or the fall of the breast wheel. Example. The length of two wheels being 20 feet, and the depth of the canal being 4 feet, required, the width — find 20 in the col- umn marked Length," opposite to this number in the column marked ^^Area," will be found 34, which divided by 4, gives 8-^ feet, which is the width of the canal, because 8^ multiplied by 4 gives 34. — Answer, Example. The length of a wheel being 14 feet, required the area of the canal — find 14 in the column marked Length," oppo- site to this number in the column marked Area," will be found 24 feet area. — Answer, There are wheels 14 feet in length, which are supplied No. 4. Area. Length. Area. Length. Area. Length. 8 5 29 17 51 38 10 6 31 18 53 40 12 7 32 19 55 42 13 8 34 20 57 44 15 9 36 22 59 46 17 10 38 24 60 48 19 11 39 26 62 50 20 12 41 28 64 52 22 13 43 30 66 54 24 14 45 32 68 56 25 15 47 34 70 58 27 16 49 36 71 1 60 WATER POWER. 19 with water by pipes whose area does not exceed 14 feet, but in such cases, it requires from 4 to 6 inches head to impel the water through the pipes — hence, there are from 4 to 6 inches of the whole head lost. If circumstances will permit, the area of the canal should not be less than represented in the table. The following table shows the depth of water in inches, in wheel pits — or it shows the difference of the depth of the water when the wheel is at rest and in motion — the column marked " No. of Feet," shows the number of cubic feet dis- charged from the wheel into the pit per second, the column marked " Width," shows the width of the race or water course from the wheel pit, the bottom of which (in width) is supposed to be level. Example. Required, the depth of the water in a wheel pit, the num- ber of cubic feet of water discharged from the wheel per second being 20, and the race being 12 feet wide — find 20 in the column marked " No. of Feet," opposite to this num- ber in the table, and under 12 in the column marked Width," will be found 7 inches, the difference in the depth of the water when the wheel is at rest and in motion. — Answer, Example, Required, the depth of the water in a wheel pit, the num- ber of cubic feet of water discharged from the wheel per second being 20, and the race being 10 feet in width — find 50 in the column marked ''No. of feet," opposite to this Dumber in the table, and under 10 in the column marked ^' Width," will be found 16 inches, the difference in the depth of the water when the wheel is at rest and in motion. — Answer, MECHANICAL PRINCIPIA. WIDTH. o 6 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 6 7 6 5 5 4 4 4 4 3 3 3 3 3 2 2 2 2 7 7 6 6 5 5 4 4 4 3 3 3 3 3 3 3 3 8 9 8 7 6 6 5 5 4 4 4 4 3 3 3 3 3 3 9 9 8 7 6 6 5 5 5 5 4 4 4 4 3 3 3 3 10 10 9 8 7 6 6 6 5 5 4 4 4 4 4 4 3 3 11 11 9 8 7 7 6 6 5 5 5 4 4 4 4 4 4 4 12 12 10 9 8 7 6 6 6 6 5 5 5 5 4 4 4 4 13 12 10 9 8 7 7 6 6 6 5 5 5 5 5 4 4 4 14 13 11 9 8 8 7 7 6 6 6 5 5 5 5 5 4 4 15 13 11 10 9 8 8 7 7 6 6 6 5 5 5 5 5 4 16 14 12 10 9 9 8 7 7 6 6 6 5 5 5 5 5 5 17 14 12 11 10 9 8 8 7 7 6 6 6 5 5 5 5 5 18 15 13 11 10 9 9 8 7 7 7 6 6 6 5 5 5 5 19 15 13 12 11 10 9 8 8 7 7 6 6 6 6 5 5 5 20 16 14 12 1] 10 9 9 8 7 7 7 6 6 6 6 5 5 21 16 14 12 ] 1 10 9 9 8 8 7 7 7 6 6 6 6 5 22 17 15 13 11 10 10 9 9 8 8 7 7 6 6 6 6 6 23 17 15 13 12 1] 10 9 9 8 8 7 7 7 6 6 6 6 24 18 15 14 12 11 10 10 9 8 8 8 7 7 7 6 6 6 25 18 16 14 12 11 11 10 9 9 8 8 7 7 7 7 6 6 26 19 16 14 13 12 11 10 9 9 9 8 8 7 7 7 7 r> 27 19 17 15 13 12 11 10 10 9 9 8 8 8 7 7 7 7 28 20 17 15 14 12 12 11 10 9 9 9 8 8 7 7 7 7 29 20 17 15 14 13 12 11 10 10 9 9 8 8 8 7 7 7 30 21 18 16 14 13 12 11 10 10 9 9 8 8 8 8 7 7 31 21 18 16 14 13 12 11 11 10 10 9 8 8 8 8 7 7 32 21 18 16 15 14 12 12 u 10 10 9 9 8 8 8 7 7 33 22 19 17 15 14 13 12 11 11 10 9 9 9 8 8 8 8 34 22 19 17 15 14 13 12 11 11 10 10 9 9 9 8 8 8 35 23 20 17 16 14 13 12 12 ] 1 10 10 9 9 9 8 8 8 36 23 20 18 16 15 13 13 12 11 11 10 10 9 9 8 8 8 37 23 20 18 16 15 14 13 12 11 11 10 10 9 9 9 8 8 38 24 21 18 16 15 14 13 12 12 u 10 10 10 9 9 8 8 39 24 21 19 17 15 14 13 12 12 11 10 10 10 9 9 9 8 40 25 21 19 17 16 14 14 13 12 11 10 10 10 10 9 9 8 41 25 22 19 17 16 15 14 13 12 12 11 11 10 10 9 9 9 42 26 22 20 18 16 15 14 13 12 12 11 11 10 10 9 9 9 43 26 22 20 18 16 15 14 13 13 12 11 11 11 10 9 9 9 44 27 23 20 18 17 15 L5 14 13 12 11 11 11 10 10 9 9 45 27 23 20 18 17 16 15 14 13 12 11 11 11 10 10 10 9 46 27 23 21 19 17 16 15 14 13 12 11 11 11 U 10 10 10 47 28 24 21 19 17 16 15 14 13 13 12 11 11 11 10 10 10 48 28 24 21 19 18 16 15 15 14 13 12 12 11 11 10 10 10 49 28 24 22 19 18 16 15 15 14 13 12 12 11 11 11 10 10 50 29 25 22 20 18 17 16 15 14 13 12 12 12 11 11 10 10 — ^ WATER POWER. />r. V' (,i\S 21 The following table shows the number of reVolufibii^ that overshot and breast wheels make per rninutej, of 'different diameters, when running 5 feet per second — the -eblumn marked "Diameter/' shows the diameter of the wh/els in feet, the column marked " Revolutions," shows the iiumber of revolutions that the wheels make per minute. Example. Required, the number of revolutions that a breast wheel makes per minute, the diameter being 20 feet — find 20 in the column marked " Diameter," opposite to this number in the column marked " Revolutions," will be found 4.77 revo- lutions per minute. — Ansioer, Example. Required, the number of revolutions per minute that an overshot wheel makes, the diameter being 12 feet — find 12 in the column marked " Diameter," opposite to this number in the column marked " Revolutions," will be found 7.98 revolutions per minute. — Answer, Wo. 6. Diameter. Revolutions. Diameter. 1 Revolutions. Diameter. > Revolutions. 9 10.61 17 5.61 24 3.98 10 9 55 18 530 25 3.84 11 8.65 19 5.03 26 3.67 12 7.98 20 4.77 27 3.53 13 7.34 21 454 28 3.41 14 6.82 22 4.34 29 3.29 15 6.36 23 4.15 30 3.18 16 5 96 The following table shows the number of revolutions per minute, that the pinion which geers into the water wheel 22 MECHANICAL PRINCTPIA. makes of different diameters — since the circumference of the water wheels run five feet per second, and the pinion geering into the segments on the circumference of the same wheel, the diameter of the wheel will not alter or change the number of turns of the pinion per minute, if it is increased or diminished — the column marked " Diameter," shows the diameter of the pinion in feet, the column marked " Revolutions," shows the number of revolutions of the pinion and pinion shaft per minute. Example. Required, the diameter of a pinion, to go on the pinion shaft, that will drive the shaft 47 turns per minute — find 47 in thecolumn marked " Revolutions ; " opposite to this num- ber in the column marked " Diameter," will be found 2 feet, the diameter of the pinion. — Answer, Example. A shaft is making 31 turns per minute, the diameter of the pinion being 3 feet ; what must be the diameter of the pinion to drive the shaft 63 turns per minute ? — find 63 in the column marked " Revolutions," opposite to this number in the column marked " Diameter," will be found 1^ feet diameter.— -4 n^z^er. No. 7. .2 s 3. > Q 1 95i 631 2 471 2i 381 3 3li 3^ 27i 4 23i WATER POWER. 23 The following table shows the number of cubic feet of water discharged per second, under the different heads — the column marked "Head/' shows the number of inches head, that is, the perpendicular distance from the level of the water to the centre of the opening — the column marked " Area,'' shows the number of inches area of the opening, which is 100 inches ; the quantity of water discharged per second, when the head remains constant, varies as the area of the opening — hence, if any area is divided by 100, and multiplied by the number of cubic feet due to any given head represented in the table, the result will give the num- ber of cubic feet due to that area. Example. The head being 24 inches, and the area of all the open- ings being 360 inches, required, the number of cubic feet of water discharged per second — find 24 in the column marked " Head," opposite to this column marked " No. of Feet," will be found 5.46 cubic feet, which is due to 100 inches area ; which multiplied by ?f ^, or 3.,p0, gives 19.65 cubic feet. — Answer, Example. The head being 27 inches, and the area of all the open- ings being 400 inches, required, the number of cubic feet of water discharged per second — find 27 in the column marked Head. Area. No. of Ft. Head. Area. No. of Ft. 12 100 3.82 33 100 6.34 15 4.28 36 6.61 18 4.69 39 }) 6.87 21 5.04 42 ii 7.14 24 5.46 45 if 7.41 27 5.73 48 it 7.64 30 6.03 24 MECHANICAL PRINCIPIA. "Head," opposite to this number in the column marked ^*No. of Feet," will be found 5.73, which multiplied by 4.00, gives 22.92 cubic feet. — Answer. The following table shows the horse power of overshot and breast wheels — the column marked " Diameter," shows the diameter of the overshot, or the fall of the breast wheel, the column marked " Length," shows the length of the wheel ; the fall on the breast wheel must always be reckoned from the upper gate — when the head exceeds two feet, add one third of the excess to the fall — suppose the head to be 4 feet, the excess is 2 feet, one third of which is 8 inches ; as there are no fractions of feet in the table, call this 1 foot, when the excess exceeds 6 inches, call it 1 foot, when it is less than 6 inches, it may be omitted. The head from the upper gate should never exceed 2 feet, but it may or should be as much less as circumstances will permit. (See Note A.) Example. . Required, the horse power of an overshot wheel, the diam- eter being 22 feet, and the length being 10 feet — find 22 in the column marked Diameter," opposite to this number in the table, and under 10 in the column marked " Length," will be found 42.9 horse pov/er. — Answer, Example. Required, the horse power of a breast wheel, the fall be- ing 28 feet, and the length being 20 feet — find 28 in the column marked Diameter," opposite to this number in the table, and under 10 in the column marked " Length," will be found 109.2 horse power. — Answer, WATER POWER. No. 9. 1 Diameter. OD o:> in '-^ i--^ hi) bi' 'i--' k) ■CO QO ""-J Ol 4^ to t"" CO CO 00 Cjl to CO Oi iO to CO 00 4^ 00 iO CO 00 -^1 Cn 4^ tO i™"* i--'CO^bi^k)^CO^bi4i^k)i--'bo''--'l--'>--'i--'h-' 1—-' CO 00 CT5 Cri iO H-i O 00 i Ol 00 1—' O CO ZJX 00 J--'a5k)co6iH--6oiii^i^^cocoa5iob^ ^^;^^;:^^;:^^^^4i^OOOOOOOOOOOO^OlO^O^OiO^O^O^-'^-'^-* O^c^cotooco*-^or«>^i0^cooocr5>^coi— 'OOO-^Ori cx)k)-^^-'b^^-j^cooobok)a5^--'bii^ 00 C^On4i^4^4^>Ji^4:^4:^OOOOOOOOOOtO{OlOlOtOJOi--'h-' ^^|--^co•<^onl4^^ooGoc^o^ooH-JCOooc:)4->■^Ol-->cD--J bo l-^ 'bo in '■^ io If^ '-^ io ''^ io 4^ CO OiO;iOnCr!On>^:^»^4i^4i^4^00000JOOOOiOiOfOiOJOt-' OOa^4^^:)OOOC7:4^^S>OCO-^OnWj--'Ci3-OnOnCriOi4i^4^4^4i^>^i.OOOOOOOOOJtOJOiOJO ^fi-^:)oooc^Wl--JCo^^o^oooooo^4^^oo-^ bl00k)H--CO^b5i4^60H-'K-'60^0ri»ip=.k)H^ ^ '^oia5a5cnoncnonon4i»4i'>P=-hP^oooooooooo{OJOto O^OnCOOGOa^OOi--'COC:)pP^iOCO--IOnJOOOOOiOO ^^ ■ENGT -3^^3 0iCnC5CriOnOnCr»Oi4^>^4i'4^00 00 a500iOfO p^a5^--OOO^WOOOO^COOOOO^COO k)c:)i---bxh-'bico'4i^booo6ok)'<»f--'b:)J^ 00 00«-a'200ooiO ^-'COOiCOOOOO^JOO^-^h;^!— 'COOiOJOGOOiiOO^ co>--4i^^cotootI>o-^woo^oocoaij^ oo^to^io^k)-^jo^^Da5H-'ait^b^I--'c^U-'b^ oo l--'OOOCOCOOOa300 •>:?■<^•-J^C^a^C;^C^^Cn^^i.^fi>^;i..OO |— ^WOa^i0C0C^^;cob^coioj^^>--bob^ioj^ 1— ' CO 1— 'K-tOOOCOCOOOOOOO-^!^— I0^ci0n0ntnh;i>.4:i>00 - ft^^ft n 79 n 70ft n ft7l 9 I'M ft 1 0 7 ftftd. A 7dQ < 40 ft99 ft oy < .0 t %JV ft^d 0 770 ftzL7 0 09 1 0 i7.44: U 7>^1 1 0 1 ft^O 1 0^7 9 yo < .<4 7Q9 ft7 1 9 0^0 A ouo ooo.o Of^*^ ^? JuO. o o i-yr ftO^ A 07fi e 007 yy / .0 QoO n y ju.u 7^K 0 1 0 y 1 J o 1 00'^ 9 WA7 0*^ 1 7 J-U i U.'i oOo CiA'i ft 1 090 ooy 0^^ 0 yoo.y 1 OlO Q 1 U4'w.o ooiJ yoo u lUOD.U UJ i OftO 1 you. 1 yuj yy -i.^ 1 0ft9 A 1 UU4.0 j nnc: 1 uyo.o QO/I 1 1 Oft. ft yj.D 1 fV9ft ^ 1 1 99 0 y-io 1 OdO 1 1 9 yo / 1 1 ztft /I 1 1 4:0.'* y Do 1 O^-'J. ft 1 1 ul .0 070 y / u 1 f\i(^ n 1 1 7/1 Q 000 lofto n 1 1 ftft n 1001 UOl.I 1201.2 1012 1113.2 1214.4 1023 U25.3 1227.6 1034 1137.4 1240.8 1045 1149,5 1254.0 1056 1161.6 1267.2 1067 1173.7 1280.4 1078 1185.8 1293.6 1039 1197.9 1306.8 1100 1210.0 1320 0 STEAM POWER. 1 ^ ^ "/"/X 43 ExAMPLEo \ ' > \ Requiredj the number of cubic feet of water |>er day^ 5to supply an engine, the calculated power of which is 40 hdi^e power — find 40 in the column marked " Horse Bowe^," opposite to this number in the table, and under IS- rft the column marked Hours,'' will be found 528 cubic feet of water.— ^fi^wef. Example, Required, the number of cubic feet of water per day (12 hours), to supply an engine, the calculated power being 90 horse power— find 90 in the column marked "Horse Power," opposite to this number in the table, and under 12 m the column marked " Hours,^' will be found 1188 cubic feet. — Answer, The following table shows the mean pressure of steam upon piston, when acting expansively— the column marked Pressure,'' shows the pressure of the steam when it enters the cylinder, the column marked " Cut off," shows what portion of the whole length of the cylinder the piston has moved when the steam is cut off. Example, The effective pressure of steam upon piston, before it is cut off, or at the commencement of the stroke, is 60 pounds per inch ; the steam being cut off at the length of the stroke : required, the mean effective pressure— find 60 in the column marked Pressure," opposite to this number in the table, and under f in the column marked "Cut off," will be found 51.12 pounds pressure ; in ordinary calculations the fractions in this table may be omitted ; if the fraction exceeds half a unit, add one to the pressure; suppose the pressure was 51,7, then add one to 51 which gives 52, but if the 44 MECHANICAL PRmciPIA. pressure was 51.4, the fraction can be omitted, which gives 51 pounds pressure. — Answer. Example. The effective pressure at the commencement of the stroke is 120, the steam being cut off at ^ the length of the stroke ; required, the mean effective pressure — find 120 in the col- umn marked Pressure," opposite to this number in the table, and under f in the column marked " Cut off," will be found 102.24 pounds mean effective pressure. — Answer. No. 5. 6 CUT OFF. Press 1-8 2-8 3-8 4-8 5-8 6-8 7-8 10 4.16 6.07 7.54 8.52 9.19 9 67 9.92 11 4.57 6.67 8.29 9 37 10.10 10 63 10.91 12 4 99 7.28 9. 04 10.22 11.02 11 60 11.90 13 5.40 7 89 9.80 11.07 11.94 12.57 12.89 14 5.82 8.49 10 55 11 92 12 86 ia.53 13.88 15 6.24 9.10 11 31 12.78 13 78 14.50 14 88 16 6.65 9 71 12.06 13.63 14 70 15 47 15 87 17 7 07 10 31 12.81 14.48 15.62 16.43 16. 86 18 7.48 10.92 13.57 15.3a 16 54 17.40 17.85 19 7.90 1 1 .53 14.32 16.18 17.46 18 37 18.84 20 8.32 12.14 15.08 17.04 18 38 19.34 1984 21 8.73 12.74 15 83 17.^^9 19.29 20.30 20.83- 22 9.15 13 35 16.58 18.74 20.21 21.27 21. 82 23 9.56 13.96 1734 19..59 21.13 2224 22.81 24 9 98 14 56 18.09 20.44 22 05 23 20 23.80 25 10.40 15.17 18.85 21 30 22.97 24.17 24 80 26 1081 15.78 19.60 22 15 23 89 25.14 25 79 27 11.23 16.38 20.35 23.00 24.81 26.10 26.78 28 11.64 16.99 21.11 23 85 25.73 27.07 27-77 29 12.06 17.60 21.86 24 70 26.65 28 04 28.76 30 12.48 18.21 22 62 25.56 27.57 29 01 29.76 31 12 89 18.81 23.37 26.41 28.48 29.97 30. 75 32 13.31 19.42 24 12 27 26 29 40 30 94 31.74 33 13.72 20 O:^ 24.h8 28 11 30 32 31 91 32.73 34 14.14 20.63 25.63 28.96 31.24 32.87 33. 72 35 14.56 21 24 26.39 29.82 32.16 33.84 34 72 36 14.97 21. 8o 27.14 30 67 33 08 34.81 35 71 37 15.39 22.45 27 »9 31.52 34.00 35 77 36.7a 33 15.80 23.06 28.65 32 37 34.94 36.74 37 69 39 16.22 23.67 29.40 33 22 35.84 37.71 38-68 STEABI POWEK. 5. — Continued. 45 6 CUT OFF. ' Press 1-8 2-8 3 -8 4-8 5.8 6-8 7-8 40 16.64 24.28 30.16 34.08 36.76 38,68 . 39.68 41 17 05 24.88 30 91 34.93 37 67 39.64 40.67 42 1 7.47 25.49 31 66 35 78 38 59 40 61 41 66 43 1 7.b8 26 10 32 42 36 63 39 51 41 .58 42. 15 44 18.30 26.70 33 17 37.48 40.43 42.54 43.64 45 1 8 . 72 27.31 33 93 38.34 41.35 43 51 44 64 46 19.13 27 92 34.68 39 19 42.27 44.48 45.63 47 19 55 28.52 35 43 40. (»4 43 19 45 44 46 62 48 19.96 29.13 36.19 40.89 44.11 46.41 47.61 49 20 38 29. 74 36.94 41.74 45. 03 47.38 48.60 50 20 80 30 35 37 70 42.60 45.95 48.35 49.60 51 21.21 30 95 38 45 43 45 46.86 49.31 50 59 52 21 63 3 1 56 39. 20 44.30 47 78 50.28 51.58 53 22.04 32.17 39. 96 45.15 48.70 51.25 52.57 54 22 46 32 77 40 71 46.00 49 62 52.21 53 56 55 22.88 33 38 41. 47 46.86 50.54 53 . 1 8 5456 56 23.29 33.99 42.22 47. 71 51 46 54.15 55.55 57 23.71 34.59 42. 97 48.56 52 38 55 1 1 56. 54 58 24.12 35 20 43. 73 49.41 53. 30 56.08 57 53 59 24.54 35 81 44.48 50 26 54 22 57.05 58-52 60 24 96 36.42 45 24 51.12 55 14 58.02 59.52 61 25.37 37.02 45-99 51 97 56.05 58.98 60 51 62 25.79 37.63 46. 74 52 82 56.97 59.95 61-51 63 26.20 38.24 47 50 53.67 57.^9 60.92 62 49 64 26.62 38.84 48.25 54.52 58 81 61.88 63.48 65 27.(14 39.45 49 01 55 38. 59.73 62.85 64 48 66 27.45 40.06 49 76 56 23 60.65 63 82 65 47 67 27 87 40.66 50. 51 57. OS 61 57 64.78 66. 46 68 28.28 41.27 51.27 57.93 62 49 65.75 67 45 69 28 70 41. e8 52. ('2 58-78 63.41 66.72 68.44 70 29.12 42 49 52.78 59.64 64 33 67.69 69.44 71 29 53 43 09 53 53 60 49 65.24 68 65 70.43 72 29 95 43.70 54.28 61.34 66.16 69.62 71.42 / o 30.36 44.31 55.04 62 19 67.08 70 59 72.41 74 30.78 44.9 1 55.79 63 04 68.00 71.55 73.49 75 31. 20 45 52 5o 55 63.90 68.92 72 52 74.40 76 31 61 46.13 57.30 64.75 69.84 73.49 75 39 77 32.03 46 73 58.05 65 60 70.76 74.45 76.38 78 3244 47.34 58. HI 66.45 71.68 75.42 77.37 79 32.86 47 95 59.56 67.30 72.60 76 39 78.36 80 33.28 4S.56 60 32 68 16 73 52 77.36 79 36 81 33. 69 49.16 61.07 69 01 74 43 78 33 80.35 82 34.11 49.77 61.82 69 h6 75 35 79 29 81.34 83 34 52 50.38 62 58 70.71 76.27 80.26 82.33 84 3494 50.98 1 63 33 71.56 1 77.19 81.22 83 32 i 46 MECHANICAL PRINCIPiA. Wo. 5. — Continued. Pressure. CUT OFF. 1 -o O Q Q Q o-o A Q 4-0 0-0 fi Q O-O 7 Q / -0 85 Jo.oo 51.59 o4. Uy 70 /10 7Q 1 1 QO 1 Q oz ly Q/l QO 04.O/i 86 OD.l i CO on 64.84 70 07 7Q no /y.Uo QQ 1 fi OO. I 0 Q^i Q 1 00. ol 87 Q^^ 1 Q oD.iy CO Qn CC CO oo.oy 7/i 1 O 7Q dK. /y .yo Q/l 1 O 04. 1,4 Qfi QO OO.OU 88 OD.OU CQ /I 1 OO. 41 oO.oO 7/1 Q7 Qn Q7 ou.o / Qci nQ 00. uy Q7 OQ 0 / .,4y 89 Q7 no c/1 no C7 1 n 0 / .lU 7^^ QO Q 1 7Q 0 1. /y Qfi nfi oo.uo QQ OQ 00.<40 90 Q7 AA C /I fiQ 04.D0 ^17 on 0 / oO 7fi flQ 1 O.Oo QO 71 0-i . / 1 Q7 nQ 0 / .Uo QQ OQ 91 Q7 Qc; CC O*} Oo-Ol 77 QQ fiO 00.0,4 Q7 QQ 0 / .yy QO 07 92 QQ 07 0D.O4 oy ot) 7Q QQ /O.OO Qi ^A 04.04 QQ Qfi oo.yo Ql Ofi y 1 ..40 93 oO.Do CfJ /I c 7n 1 o 7Q OQ Q'^ /Ifi 00.40 QQ QQ oy. yo 00 O't 94 oj.LU CL7 nt;; 7n ft7 Qn nQ Qfi QQ OO.oO Qn QQ yu.oy QQ OJ. 95 0 / .DU 71 fiQ f l OJ Qn Q/l ou.y4 Q7 Qn 0 / .oU Ql Qfi y 1 .OO Q/L OA 9d QQ QQ 07 70 Ql 7Q Ol. / y QQ 00 QO QQ »/,4.0o Q£^ OQ 97 4U.oD f^ft Q7 7Q 1 Q iO'io QO C\A O/^.04 QQ 1 A oy .14 QQ 7Q yoe /y Qfi 00 98 /in 7^i 4U. / O f;Q A9. oy .40 7Q 8Q /o-oy QQ /IQ OO .4y on nfi yu.uo Qzl 7fi y4. / 0 Q7 01 99 Al 1 Q 41 • lo fjn no Du.uy 7/1 fi/1 <404 QJ. Q'l 04, o4 Qn QQ yu.yo Qf; 7Q yo. / o QQ on yo.,4u loo /1 1 fin 41 .DU fin 70 < 0 4U Q^^ on 0 1 on y i.yu Qfi 7n y 0. / u QQ on yy .^u 101 /10 01 fii Qn Ol .oU 7fi 1 /o.io Qfi nc; OO. uo QO Ql y,<5.oi Q7 fifi y / .00 1 nn 1 Q * UU. 1 J 102 /lO zLQ 4^4 4CJ o 1 .y 1 7f; Qn / o.yu Qfi on oo.yu QQ 7Q yo. io QQ fiQ yo.oo 1 ni 1 Q J-Ul . 1 0 103 4'i.04 fio c;o 77 fifi / / .00 Q7 7p; O / . / 0 Q'l fi^i y4.oo QQ fin yy .OU ino 1 7 104 /f^ Of; 7Q A^ /0.41 QQ fin oo.ou Qf^ ^1 yo.o / 1 nn ^fi lUU.OO 1 nQ 1 fi Uo. lO 105 4C> -Oo flQ 7Q Do. / «3 7Q 1 7 /y.i / QQ /Ifi oy .40 Qfi /IQ y o.4y 1 n 1 c;q lUl.Oo 1 (\A 1 fi .IU4.10 106 AA HQ 44. uy 04. o4 70 QO /y .y,4 QO Ql Q7 41 y / .41 1 no c;n 1U,4. OU 1 n^; 1 auo io 107 44. Oi 04. y4 Qn fi7 ou.o / Ql Ifi y 1.10 QQ QQ yo.oo 1 HQ A fi lUo.40 1 nfi 14 -lUO. 14 108 /lA QO 44 y.4 00.00 Q 1 AQ Ol.4o QO ni QQ Of^ yy .,40 1(\A /I Q 1U4.40 1 n7 1 Q ±U / .lo 109 /I 40.'54 OD 1 0 90 1 Q QO Qfi y/4.00 1 nn 1 7 1 nc /ifi 1U0.41/ 1 nQ 1 0 110 40. < O fifi 77 OO. / / QO Q/l 0'4.y4 QQ 70 1 n 1 no J-U 1 .uy 1 nfi Q7 lUO.o / 1 no 1 0 luy, 1,4 111 46.17 67.37 83.69 94.57 102.00 107.33 uo.u 112 46.59 67.98 84.44 95.42 102.92 108 30 111.10 113 47.00 68.59 85.20 96.27 103.84 109.27 112.09 114 47.42 69.19 85 95 97.12 104 76 110.23 113.08 115 47.84 69.80 86.71 97.98 105.68 111.10 114,08 116 48.25 70.41 87.46 98.83 106 60 112.17 115 07 117 48.67 71.01 88.21 99 68 107 52 113.13 116.06 118 49.08 71.62 88.97 100.53 108.44 11410 117.05 119 49.50 72.23 89-72 101.38 109.36 115.07 118.04 120 49.92 72.84 90.48 102.24 110.28 116.04 119.04 STSAM POWER. 4? The following table shov/s the horse power of the con- densing and non-condensing engines — the column marked Pressure," shows the effective pressure per square inch upon piston, the column marked " Diameter," shows the diameter of the cylinder in inches : the piston is calculated to move 100 feet per minute, the power of the engine varies as the velocity of the piston ; hence, if any velocity is divided by 100, and multiplied by the number of horse power found in the table due to 100, the result will give the number of horse power due to that velocity. Example. Required, the horse power of an engine, the diameter of the cylinder being 14 inches, the effective pressure being 50 pounds per square inch, and the velocity of the piston being 300 feet per minute — find 14 in the column marked Diam- eter," opposite to this number in the table, and under 50 in the column marked ^' Pressure," Vv^ill be found 23.32, which is the horse power of the engine when the piston moves 100 feet per minute ; as the piston moves 300 feet, multiply 28.32 by ^{^^ or 3,00, w^hich gives 69.96 horse powder. — Answer, Example. Required, the horse power of an engine, the diameter of the cylinder being 18 inches, the effective pressure per inch being 60 pounds, and the velocity of the piston being 275 feet per minute — find 18 in the column marked "Diameter," opposite to this number in the table, and under 60 in the col- umn marked " Pressure," will be found 46.26, which mul- tiplied by 2.75, gives 127.21 horse ^ower^—Ansroer, 48 MECHANICAL PRINCIPIA. No. G. leter. PRESSURE. DiaiYi 10 11 12 13 14 15 16 17 18 19 — 8 1.52 1.67 1.83 1.98 2.13 2.28 2.44 2 59 2.74 2.89 9 1.93 2.12 2.31 251 2.70 2.89 3.08 3.27 3.46 3.66 JO 2.38 2.62 2.85 3.09 3.33 3.57 3.80 4.04 4.28 4.52 11 2.88 3.16 3.45 3.74 4.03 4.32 4.61 4.89 5.18 5.47 12 3.43 3.77 4.11 4.45 4.79 5.14 5 48 5.82 6.17 6.51 13 4 02 4.42 4.82 5 22 5 63 6.03 6.43 6 83 7.24 7.64 14 4.66 5.13 5.59 6.06 6.52 6.99 7.46 7.92 8.39 8.86 15 5 35 5.89 6.42 6.96 7 49 8.03 8.56 9.10 963 10.17 16 6.09 6.70 7.31 7.92 8.53 9.14 9.75 10.35 10.97 11.57 17 6.87 7.50 8.25 8.94 9.63 10.31 11.00 11.68 12 37 13.06 18 7.71 8.48 9.25 10.02 10.79 11.56 12.33 13 11 13.88 14.65 19 8.59 9.45 1031 11.17 12.02 12.88 13.74 1460 15.46 16.32 20 9.52 10.47 11.42 12.37 13 32 14.28 15.23 16 18 17.13 18.08 21 10.49 11.54 1259 13.64 14.69 15.74 16 79 17.84 18.89 19.94 22 11.52 12.67 13.82 14.97 16.12 17.28 18.43 19.58 20.73 21.88 23 12.59 13.84 15.10 16.36 17.62 18.88 20.14 21.40 22.66 23.92 24 13.70 15.07 16.45 17.82 19.19 20.56 21.93 23.31 24.67 26.04 25 14 87 16.30 17.85 19 33 20 82 22.31 23.80 25.28 26.77 28 20 26 16.09 17.69 19.30 20.91 22.52 24.13 25.74 27.35 28.96 30.56 27 17.35 19.08 20.82 22.55 24 29 26.02 27.76 29.49 31.23 32.96 28 18.66 20.52 22 39 24.25 26 12 27.98 29.85 31.72 33.58 35.45 29 20.01 22.01 24.01 26.01 28.02 30.02 32.02 34.02 36.02 38.02 30 21.42 23.56 25.70 27.84 29 98 32.13 34.27 36.41 38..55 40.69 31 22 87 25.15 27.44 29.73 32.01 34.30 36.59 38.88 41.16 43.45 32 24.37 26.80 29 24 31.68 34 11 36.55 38.99 4143 43.86 46.30 33 25.91 28.50 31.10 33.69 36.28 38.87 41.46 44.06 46.65 49 24 34 27.51 30.26 33.01 35.76 38.51 41.26 44.02 46.77 49.52 52.27 35 29.15 32.07 34.98 37.90 40.81 43 73 46.64 49.56 52.47 55.39 86 30.84 33.92 37.01 40.09 43.18 46.26 49.34 52.43 55.51 58 60 37 32.58 35.83 30.09 42.35 45.61 48.87 52.12 55.38 58.64 61.90 38 34 36 37 80 41.23 44.67 48.11 51.54 54.98 58.42 61.85 65.29 39 3n.20 39.82 4344 47.06 50.68 54.30 57.92 GISA 65 16 68.78 40 38.08 41.88 45.69 49.50 53.31 57.12 60.92 64.73 68.54 72.35 41 40.01 44.00 48.00 52.00 56.00 60.00 04.00 68.01 72 01 76.01 42 41.98 46.18 50.37 54.57 58.77 62.97 67.17 71.36 75.56 79.76 43 44.01 48.40 52.80 57.20 61.61 06.00 70.40 74.81 79.21 83.61 44 46.07 50.68 55.29 59.89 64.50 69.11 73.72 78.32 82.93 87.54 45 48.19 53.01 57.83 62.65 67.47 72.29 77.11 81.92 86.74 91.56 46 50.36 55.39 60.43 65.46 70 50 75.54 80.57 85 61 90.64 95.68 47 5-2.57 57.83 63.08 68.34 73.60 78^85 84^11 89.37 94.63 99!88 48 54.83 60.31 05.79 71 28 76.76 82.24 87.73 93 21 98.69 104.18 49 57.14 62.85 68.57 74.28 79 99 85.71 91.42 97.14 102.85 108.56 50 59.. 50 65.45 71.40 77.35 83.30 89.25 95.20 101.15 107.10 113.05 51 (iJ.90 68.09 74.28 80.47 86.66 92.85 99.04 105.23 111.42 117.61 52 64.35 70.78 77.22 83.66 90.09 96.53 102.96 109.40 115.83 122.27 53 (56.85 73.53 8022 86.90 93..59 100.27 106.96 113.64 120.33 127.01 54 69.40 76.34 83 28 90.22 97.16 104.10 111.04 117.98 124.92 131.86 55 71.99 79.19 86.39 93 59 100.79 107.99 115.19 122 38 129.58 136.78 56 74.63 82.09 , 89.56 97.02 104.49 111.95 119.41 126.88 134. .34 141.80 57 77.32 85.05 92.78 100.52 108.25 115.98 123.71 131.45 139.17 146.91 58 80.06 82.84 88.06 96.07 104.07 112.08 120.09 128.09 136.10 144.10 152.11 59 91.12 99 41 107.69 115 98 124.26 132.55 140.83 149.12 157.40 60 85.67 94.24 102.81 11J.38 1 19.95 128.51 137.03 145.65 154.22 162.79 STEAM POWER. ]¥o» 6. — Continued. 49 leter. PRESSURE. fa .5 P 20 21 22 23 24 25 26 27 28 29 "~" 8 3 04 3.19 3-35 3 50 3 65 3-81 3 96 '±.11 4 26 A 4-41 9 3.85 4.04 4-24 4 43 4 '2 4-82 5 01 5.20 5.39 5-59 10 4.76 4-99 5-23 5 47 5-71 5 95 6 19 6 4*^ 6.66 6-90 11 0. t o 6. 05 6-33 6 62 6-9 1 7-20 7 49 7 77 8-35 12 6 85 7. 19 7-54 7 88 8 22 8-56 8 91 9.35 9.. 59 9-94 13 8.04 8.44 8-84 9 25 9.65 10-05 10 46 10.86 1 1 Ofi 1 l.^D 11 66 14 9.32 9.79 10-26 10.73 11.19 11-66 12 12 12 59 13 05 13 52 15 10.71 1 1 .24 11 78 12.31 12-85 13.38 13 92 14 99 1.5 52 16 12.18 12 79 13-41 14.01 14-62 15.23 15 84 16.45 17 06 17 67 17 13.75 14-44 15-13 15.82 16 51 17.19 17 88 18 57 19 26 19 94 18 1542 16- 19 16-96 17 73 18 51 19.28 21.59 22 36 19 17- 18 18-04 18-90 19 76 20 62 21.48 22 33 24-91 20 19-04 19-99 20 94 21.89 22.84 23.80 24 75 25 70 ^6 65 27 60 O I 20-99 22-04 23.09 24.14 25 - 1 9 26.24 27 29 28.34 29 39 30 44 22 23.04 24-19 25.34 26-49 27.65 28.80 29 95 31.10 32 2.5 33 41 23 2,5-18 26-43 27.69 28 95 30 21 31.47 32 73 33 99 36 51 24 27-41 28-78 30. 15 31.53 30 90 34*27 35 64 37 Ol 38 ^8 39-75 25 29-75 31-23 32.72 34.21 35.70 37.18 38 66 40 16 4 1 65 43-13 32- 17 33-78 35.39 37 00 38-61 40.22 41 83 4.3 44 ^5 05 46.65 27 34-70 36-43 38.17 39.90 41 64 43.37 45 11 46 84 48.58 50-31 28 37-31 39-18 41.04 42-91 44 78 46.64 48 51 50 37 52.24 54-11 29 40-03 42-03 44.03 46-03 4« 03 50.03 52 03 54 04 58-04 30 42 84 44-98 47.12 49 26 51 41 53 55 55 69 57.83 59 97 62- 12 31 45-74 48-02 50-31 59. (3Q 54 89 57.17 59 46 01 - /O 66-32 32 48-74 51-17 53-61 56.05 58 49 60.92 63 36 68 23 70.67 33 51-83 54-42 57-01 02 20 64.79 g7 3g 72.57 75- 16 34 55-02 57-77 60-52 6.3.27 66 03 68.78 71 53 77 03 79-78 35 58-31 61 22 64-14 69 97 72.88 /8./ 1 81.63 84-54 36 61-68 64 77 67-85 70.93 74-02 77.10 80 19 83 27 86 36 89-44 37 65-16 68-4 1 7l 67 74 93 78 19 81 4.5 84 70 87 96 94-48 38 68-73 72 16 75 60 79 04 8'^ 47 85 91 89 35 92 78 96 22 99-66 39 72-40 76 02 79-64 8.3.26 86 88 90 .50 94 12 101 36 104.98 40 76- 16 79-97 83.77 87 58 9! 39 95.20 99 01 102 81 106.62 110.43 41 80 01 84 0 1 88«01 92 01 90-0 1 100 01 104 01 112 01 1 16 01 42 83 96 88* 16 92.36 96 55 1 00 75 1 04 9.5 109 1.5 1 13 35 1 J 7 .54 121-74 43 88-01 92-41 96-81 101 21 10-5. 6 J 110 01 1 14 41 118 81 1 2-3 2 1 127 61 44 92- 15 9G'75 10 1 -36 105-97 110 58 115 19 133-62 45 96 38 101-20 106-02 110.84 115.66 1 20*48 12530 1.30J2 134 94 J 39 -76 45 100-72 105-75 11079 115-83 120.86 125.90 130.93 13-5.97 14101 146-04 47 105 14 110-40 115.66 120.91 126.17 131.43 136 68 141.94 147.20 1.52.46 48 109-66 115-14 120.63 126 11 131.59 137.08 142.56 148,04 153 53 159.01 49 114-23 119. 99 125 71 131.42 137.14 142.85 148..56 1.54.28 J 59.99 165-71 50 119-00 124-95 130.90 136.85 14-2.80 148.75 1.54.70 160.65 166.60 172. 55 51 123-80 129-99 1.36-18 142.37 148-56 154.75 11)0.94 167.13 173.32 179-51 52 128-70 135 14 14 1. 57 148.01 154-44 160.88 167.32 173 75 180.19 186-62 53 133-70 140 38 147-07 153-75 160.44 167- 12 173.81 180.49 187.18 J93.86 54 138 80 145 74 1.52.68 159.62 166.56 173-50 180.44 187.38 194. .32 201-26 55 143-98 151-18 158.38 165.58 172-78 179-98 187.18 194.38 201.58 208.78 56 149-27 156-73 164-19 171.66 179-12 186 .59 194.05 201.51 208.98 216.44 57 154 64 162-38 170 11 177-84 185-57 193.31 201.04 208.77 216,50 224.23 58 160.12 168-12 176.13 184-14 192-14 200.15 208.15 216.16 224.17 2.32.] 7 59 165.69 173-97 182.25 190.54 198-82 207.11 215.39 223.68 231.96 240-25 60 171.35 179.92 18S.49 197.06 205.62 214.19 222.76 231.33 239.90 248.46 50 MECHANICAL TRINCIPIA. No. 6. — Continued. PRESSURE. s Q 30 31 32 33 34 35 36 37 38 39 o 4.57 4 72 4.87 5 02 5.17 5.33 5.48 5.63 5.78 5.94 9 5.78 5 97 6 17 6 36 6.55 6.74 6.94 7.13 7.32 7.51 iO 7.14 7 37 7 61 7 85 8.09 8.33 8.56 8 80 9 04 9.28 11 8.64 8 93 9 21 9 .50 9.79 10.08 10.36 10 65 lO 94 11.23 TO 10.28 10 62 10 96 ll 31 11.65 11.99 12 34 12 68 13 02 13.36 13 12.06 12 46 12 87 13 27 13.67 14.07 14.47 14 88 15 28 15.68 14 13 99 14 46 14 92 15 39 15.86 16.32 16.79 17 26 17 72 18.18 15 16.06 16 60 17 13 17 67 18,20 18.74 19.27 19 81 20 34 20 88 16 18.28 18 89 19 50 20 11 20,72 21.33 21.03 22 54 23 15 23.76 17 20 63 21 32 22 01 22 69 23*38 24.07 24.76 25.44 26*13 26.82 18 23.13 2.3 90 24 67 25 44 26-22 26.99 27.76 28.5.3 29*30 30-07 19 25.77 26 63 27.49 28.35 29.21 30.06 30.92 31.78 32.64 33.50 20 28.56 29 .51 30.46 31.41 32^36 33.32 34.27 35 22 36-17 37.12 21 31.49 32 52 33.58 34.63 35.68 36 73 37.78 38.83 39.88 40.93 22 34. 56 35 71 36.86 38.01 39.16 40.32 41 .47 42.62 43.77 44.92 23 37.77 39 02 40.28 4 J 54 42.80 44.06 45.32 46.58 47.84 49.10 24 4 1 .12 42 49 43.86 45.23 46.60 47.98 49.35 50,72 52.09 53.46 25 44.62 46 1 1 47.60 49.08 50^57 52.06 53.55 55.03 56.52 58.01 26 48.26 49 87 51.48 53.09 54.70 56.31 57.92 59,52 61.13 62-74 27 52.05 53 78 55.52 57 25 58.99 60.72 62 46 64 19 (55 93 67.66 28 5.5.97 57.84 59.70 61.57 63.43 65.30 67. 17 69,03 70 90 72.77 29 62.04 64.04 66.04 68.05 70. 05 72.05 74 05 76 05 78.05 30 64 26 6640 68. 54 70.68 72.83 74.97 77.11 79-25 81 39 83.53 31 68.61 70 89 73.18 75 47 77.75 80.04 82 33 84-62 86 90 89-19 32 73.11 75.54 77.98 80 42 82.85 85.29 87 73 90.17 92 61 95-04 33 77.75 80 34 82. 93 85.52 88.12 90.71 93 .30 95-89 98.48 101-07 U'4 82.53 85 29 88.04 90 79 93.54 96.29 104 54 35 87.46 90 38 93.29 96 21 99.12 102 04 104 9.5 107 87 1 10 78 IT} 7n 36 92.52 95 61 98.69 101 78 104.86 1(*7 95 1 14.1 1 117 on 120-28 37 97.74 100 99 104.25 107 51 1 10.77 114 03 117 28 120 54 127-06 38 103.09 106 53 109.97 1 13 40 1 16.84 120 28 123.71 127 15 130-59 134.02 39 108.60 112 22 1 1 5.84 119 46 123.08 126,70 130.32 133 94 137-56 141.18 40 114.24 1 18 04 121 .85 125 66 129.47 133.28 137.08 140 89 J4C.01 4] 120.01 124.01 128.01 132 01 136.02 140 02 144.02 148 02 1.56.02 42 125-94 130. 14 134. 34 138 54 142.73 1^16 93 151.13 155 33 1-59-53 163-72 43 132. 01 1 36. 41 140.81 J45 21 149.62 154 02 1.58.42 162 82 167-22 171-62 44 142. 8.3 247.44 1.52 05 156.65 161.26 165.87 170 48 175. 08 179-69 45 144.58 149.40 1.54.21 159.03 1(33!85 168^67 173.49 178!31 183.13 187-95 46 151.08 156.11 161.15 166.19 171.22 176.26 181.29 186,33 191.37 196-40 47 157.71 162.97 168.23 173 49 178.74 184.00 189.26 194..52 199.77 205-03 48 164.49 16998 175.46 180.94 186.43 191.91 1!'.7.39 202.88 208 36 213.84 49 171.42 177.14 1S2.85 188.56 194.23 199.99 205.71 211,42 217.13 222-85 50 178.50 184.45 190.40 196.35 202.30 208.25 214.20 220,15 226.10 232.05 51 185.70 191 89 198.08 204.27 210.47 216.66 222.85 229.04 235,23 241-42 52 193.06 199.49 205.93 212.38 218.80 225.23 231,67 238.10 244.54 250.98 53 200.55 207.23 21392 220.60 227 29 233 97 240,66 247.34 254.03 260-71 54 20820 21.5.14 222.08 229.02 235.96 242.90 249.84 256-78 263.72 270.66 55 215.98 223. 18 230.38 237.58 244.77 251.97 259.17 266.37 273.57 280.77 56 223.90 2.31.37 238.83 246.29 2.53.76 261.22 268.68 276.15 283.61 291.08 57 231.97 239.70 247.43 2.55.16 262.90 270.63 278.36 286.09 293.83 301-56 58 240.18 248.18 2.56.19 264.20 272.20 280.21 288.21 296.22 304.23 312.23 59 248.53 2.56.81 265.10 273.38 281.67 289.95 298.24 .306,52 314.81 323.09 60 257.03 265.60 274.17 2rf2.74 291.30 299.87 308.44 317.01 325,58 334.14 STEAM POWER. 61 No* 6. — Continued, PRESSURE. Diam 40 41 42 43 44 45 46 47 48 49 8 6.09 P. 24 6.39 6.54 6.70 6-85 7.01 7.16 7.31 7.46 9 7.71 7 90 8.09 8 28 8.48 8-67 886 9.05 9.25 9. 44 10 9.52 9.75 9.99 10 23 10.47 10-71 10.94 11.18 11 42 11.66 11 11.52 11.81 12 09 12 33 12.67 12-96 13.24 13.53 13.82 14.11 12 13.71 14.05 14.39 14.73 15.07 15-42 15.76 16.10 16.45 16.79 13 16.08 16.49 16.89 17.29 17.69 18-09 18.50 18.90 19.31 19 71 14 18.65 19.12 19.58 20.05 20.52 20-98 21.45 21.92 22.38 22.85 15 21.42 21.95 22.49 23.02 23-56 24-09 24.63 25.16 25.70 26.23 16 24.37 24.98 25.59 26.21 26-81 27-42 28.03 28.64 29.25 29.86 17 27.51 28.19 28.88 29.57 30-26 30-95 31.64 32.32 33.01 33.70 18 30.84 31.61 32.38 33.15 33-93 34-69 35.47 36.24 37.01 37.78 19 34-36 35.22 36.08 36.94 37-80 38-66 3951 40.37 41.23 42.09 20 38-08 39.03 39.98 40.93 41-88 42.84 43.78 44.74 45.69 46.64 21 41-98 43 03 44.08 45.13 46- 18 47-23 48.28 49.33 50.38 51.43 22 46-08 47.23 48.38 49.53 50-68 51-84 52. 99 54.14 55.29 56.44 23 50 36 51.61 52.87 54. 13 55 39 56-65 57.91 59.17 60.43 61.69 24 54 83 56.20 57.57 58.94 60-31 61-68 63.06 64.43 65.80 6717 25 59-50 60.98 62. 47 63.96 65-45 66-93 68.42 69.91 71.40 72.88 26 64-35 65-96 67.57 69.18 70.79 72.40 74.00 75.61 77 22 78.83 27 69-40 7M3 72.87 74.60 76-34 78.07 79.81 81. 54 83.28 85-01 28 74. 63 76 50 78.36 80.23 82.09 83.96 85.83 87.69 89 56 91-42 29 1 80-06 82 06 84.06 86.06 88.06 90.06 92.06 94.07 96.07 98.07 30 85.68 87-82 89.96 92.10 94.24 96.40 98.53 100.67 102.81 104.95 31 91-48 93-76 96.05 98.34 100.62 102.91 105.20 107.49 109.77 112 06 32 97.48 99-91 102.35 104.79 107.22 109.66 112.10 114.54 1 16.97 119 41 33 103 66 106-26 108.85 111.44 114.03 116.63 119.22 121.80 124.40 126.99 34 110.05 112-80 115.55 118.30 121.05 123.80 126.55 12931 132.06 134 81 35 116.62 119-53 122 45 125.36 128.28 131.19 134.11 137.02 13994 142.85 36 123.37 126-45 129.54 132.62 135.70 138.79 141.87 144.96 148.04 151. 13 37 i 130.32 133 -57 136-83 140.09 143.35 146.61 149 86 153 12 156.38 159. 64 38; 137.46 140-90 144-33 147.77 151.21 154-64 158.08 161 52 164.95 168 39 39 144 80 148-42 152.04 1.55.66 1.59.28 162-90 166.52 17014 173.76 177.38 40 152.32 156-12 159-93 163.74 167.55 171-36 17897 182.78 186-59 41 160.02 164-02 168.02 172.02 176.02 180-02 184.02 188-02 192.02 196.02 42 167.92 172.12 176.32 180.52 184.72 188-91 193.11 197 31 201.51 205.71 43 1 176.02 180.42 184.82 189.22 193.62 198-02 202.42 206.82 211.22 215. 62 44 184.30 188.91 193.51 198.12 202.73 207.34 211.94 216. 55 221.16 225.77 45 I 192.77 197.59 202.41 207.23 212.05 216.87 221.69 226.51 231.33 236.14 46 1 201.44 206.48 211.51 216.55 221.58 226.62 231.66 23669 241 73 246.76 47 i 210.29 215. 54 220.80 226.06 231.32 238.57 241.83 247 09 2.52.35 257-60 48 1 219-33 224.81 230.29 235.78 241.26 246.74 2.52.23 257.71 263.19 268-68 49 228-56 234.28 239.99 245.71 251.42 257.13 262.85 268-56 274.28 279-99 50 238-00 243.95 249.90 255.85 261.80 267.75 273.70 279-65 285 60 291-55 51 247-61 2.53-80 2.59.99 266.18 272.37 278.56 284.75 290 94 297.13 303.33 52 257-41 263-85 270.28 276.72 283.15 289.59 296.02 302.46 308.89 315.33 53 267 40 274-08 280.77 287.45 294.14 300.82 307.51 314. 19 320.88 327.56 54 277.60 284-54 291.48 298.42 305.36 312.30 319.24 326-18 333.12 340.06 55 287-97 295.17 302.37 309. 57 316.77 323.97 331.17 33837 345.57 352.77 56 298. 54 306.00 313.47 320.93 328,39 335.86 343.32 350-78 353.25 365.71 57 309.29 317.02 324.76 332.49 340.22 347.95 355.69 363-42 371.15 378.88 58 320.24 328.25 336.25 344.26 352.26 360.27 368.28 376-28 384 29 392.29 59 331.38 339.66 347.94 356.23 364.51 372.80 381.08 389.37 397.65 405.94 60 342.71 351.28 359.85 368.41 376.98 385.55 304.12 1 40269 411.25 419.82 52 MECHANICAL PRINCIPIA. No* 6. — Continued. PRESSURE. Diarn 50 51 52 53 54 55 56 57 58 59 a 7.61 < .76 <-r net 7.92 0.07 8 22 8.37 0-52 o-d8 o.8,"{ 8-98 9 9.63 9.83 10.02 10.21 10 4 1 JU Oy 10.79 10-98 1 1 . 17 11 .37 10 11.90 12.14 12. 37 12.61 12 8.5 13-09 1 3 • .3.3 13 56 1,3.80 14.04 11 14.41 14.69 14.97 1.5 .5.5 15-84 Id 10 JO. IZ, 16-41 IR 71 JO. / J 16.99 12 17.13 17.47 17.82 18.1b 18 51 18-84 19-19 19. ,54 19.87 20.22 13 20.11 20. .51 20.91 21. .31 21.72 22-12 22. 52 22.92 23.32 23.73 14 23.32 23.78 04 OK ZO 24 7 1 lo 25 - 6-5 26.11 26-58 27 05 27.51 15 26.77 27.31 28.38 oi 29-4.5 29-98 30 -,52 31.05 3 1 .59 16 30.47 31.08 31.69 32 29 33.5 1 34- 12 34.73 3.5.34 35-93 17 34.39 35 07 00. /O 00 4o 37.14 ^7 38.51 39.21 39-89 40.58 18 38.55 39 32 43 63 43. 18 43,95 44-72 45,49 19 42. 95 43 81 44.0 / 4.5 53 46.39 47 25 48-11 48-96 49 83 20 47. 60 48 55 49. .50 50 4.5 51 .40 52 36 0.1 .-51 54-26 K'^ Q1 5o.lo 21 52.48 53 .53 5.5 63 56.68 57 73 on- ni •59-83 60 87 61 ,92 22 57.60 58 75 61 0.5 62 21 63 36 04.01 6.5 . 66 7^ no 67 96 23 62.95 64 20 66 72 67 98 70-, 50 71 .76 70 ^1 74 28 24 68.54 69 91 72 6.5 74 O'^ /5.o9 7^1 7R /O. /O 78. 13 80 88 25 74 37 75.86 80 3.^^ 8181 8.3.30 84.78 80 -*7 87.76 26 80.44 82 05 8.5 27 86 88 88.48 ?^ 91.70 93-31 94.92 27 86.7.5 88.48 93 69 9.5.42 9/. 16 98-89 100-6.3 10'^. 36 28 93 29 95. 16 97.02 93.89 1 00.7.5 102.62 104-49 106-3.5 1 10 08 29 100.07 102.07 104.07 106.07 iuo.i)7 1 10-08 112-08 I lo.08 118.08 30 107.10 109 24 111.38 1 15 66 117 81 119-95 122 09 124-23 31 114.35 116 63 121 21 i^>>.4y ioe; 7S 132 64 134.94 *?9 121.85 ]24.2t'^ 1^0.72 129.16 131. .59 134.03 J.50-47 l.>8.91 141 .34 143.78 33 129. .59 132. 18 1.34.77 13 / .36 1 39 9.5 142-54 145-14 1 47 7.3 1,50.32 1,52. 91 34 1 37.56 140 3 1 143.06 J40.O1 148.57 1 ^1 07 156-82 162.32 35 145.77 148 69 151.60 1.54.. 52 157.43 160-35 163 26 17^ 80 lo9.09 170 01 J 1 z.yji 36 154.21 157 29 160.38 166.. 5.5 169.63 170 70 178 88 101 07 37 ] 62.90 166. 1.5 169 41 1 i^.o7 175.93 179.19 100 f1 18,5.70 188.96 192-22 38 171.83 17.5.26 1 78 70 182.1.3 185. ,57 189 01 900 ^0 19.5.88 199.32 202. 75 39 181.00 184. ()2 188.24 191.86 195.48 199.10 206 34 2l3-,58 40 190.40 194.21 198.02 201 82 20.5.63 onn A A ZU:j.44 -41-1-24 217.06 220.86 224 67 4J onn no 204. 03 208.03 212.03 216.03 OOrt fit 224-03 228.03 232 03 2H6.03 42 209.91 218.30 222.50 226.70 0'~>ri on 235.09 oof» 00 243.49 247.69 43 ZZv \J,i 228.83 23.3.23 237.63 242.03 246.43 25f).8.3 25.5.2.3 259 63 44 230. 38 234 98 239.59 244.20 248.81 25.3.41 2.58-02 Of!0 fit zuz-yio 267.24 271.84 45 240. 96 245.78 250 60 255.42 260 24 265 06 269.88 274.70 279., 52 234.34 46 251 80 256.84 261.87 266.91 27r94 276.98 282-02 287.05 292^09 297^12 47 262 86 268.12 273.37 278.63 283 89 289.15 294.40 299.66 304.92 310.18 48 274.16 279.64 285.13 29061 296.09 301.. 58 307.06 312..54 318-03 323.51 49 285.71 291.42 297.13 302.85 308.56 314 23 319 99 325.70 331-42 ,337.13 50 297.50 303.45 309.40 315 35 321.30 327.25 .333.20 .3,39.15 345.10 351-05 51 309 51 3] 5.70 321.89 328.08 3.34.27 .340.46 346-65 .3.52.84 3.59.03 .365-22 52 321.77 328.20 334.64 .341.07 347.51 353.94 360-38 .366.81 ,373.25 379-68 53 334.25 ,340.94 34762 3.54 31 360.99 367.68 374 35 .381-05 387.73 394 42 54 347.00 3.5394 360.83 367.82 374.76 381.70 388.64 395-58 402.. 52 409-46 55 3.5997 367.16 374.36 381.56 388.76 395.96 403.16 410-36 417.56 424.76 56 373.18 380.64 388 10 395.57 403.03 410.49 417.98 425-42 432.88 440,37 57 386.62 .39435 402.03 409 81 417..54 425.28 433.01 440.74 448.47 456-21 58 400.30 408.31 416.31 424.32 432.32 440.33 448.34 456.34 464.35 472 35 59 414.22 422.50 430.79 439.07 447 36 4.55.64 463.93 472.21 480.. 50 488.78 60 428.39 436.96 445.53 454.09 462.66 471.23 479.80 483.37 496.93 5.5.50 STEAM POWER. 53 ]¥o. 6. — Continued, 1 PRESSURE. Diara 60 61 62 63 64 65 66 67 68 69 ~— 8 9.13 9.29 9.44 9.59 9-74 9.89 10.05 10.21 10.36 10.51 9 11.. 56 11.75 11.94 12.14 12.33 12.53 12.72 12,91 13.10 13.29 10 14.28 14.52 14.75 14.99 15.23 15 47 15.71 1.5.94 16.18 16.42 31 17.28 17.56 17.85 18.14 1843 18.72 19.01 19.29 19.58 19.87 12 20.56 20.91 21.24 21.. 59 2193 22.27 22.62 22.96 23.30 23.64 33 24.13 24.53 24.94 25.34 25.74 26.14 26.54 26.94 27.35 27.75 34 27.98 28.45 2^.91 29.38 29-84 30.31 30.78 31.24 31.71 32.18 15 32.13 32.66 33.20 33.73 34.27 34.80 35.34 35.87 36.41 36.94 16 36.-56 37. 17 37.78 38.39 39 00 39.61 40.22 40 83 41.44 42.05 17 41.26 41. 95 42.64 43.. 33 44.02 44.71 45.39 46.08 46.77 47.46 18 46.26 47.01 47.81 4 8.. 58 49.35 .50.12 50 89 51.66 .52.43 53.21 39 51.54 52.41 53.26 54.12 54.98 55.84 56.70 57 56 .58.42 59.28 20 57.12 58.07 .59 02 .59.97 60.92 61.88 62.83 63.78 64.73 65.68 21 62.97 64.02 65.07 66 12 67.17 68.22 69.27 70.32 71.37 72.42 22 69.12 70.27 71.42 72.. 57 73.73 74.88 76.03 77.18 78.33 79.48 23 1 75.54 76.79 78. a5 79.31 80.. 57 81.83 83.09 84.35 85.61 86.87 24 82.25 83.02 84.99 86 36 87.73 8.9.10 90.47 91.84 93.21 94.59 25 i 89.25 90.73 92.22 93.71 95.20 96.68 98.17 99.66 101.15 102.63 26 ' 96..53 98.14 99.75 101.36 102.90 104.57 106.18 1(»7.79 109.40 111.01 27 104.10 105.84 107.. 57 109.31 111.04 112.77 114.51 116.24 117.98 119.72 28 i 111.95 113.81 115 63 117.55 119 41 121.28 123.14 125.01 126.88 128.74 29 i 120.09 122.09 124.09 126.09 128.09 130.09 132.09 134. iO 136.10 138.10 30 1 128..52 130.68 132 80 134.94 137.08 1.39.23 141.37 14351 145.65 147.79 31 ' 137.22 139.51 141.79 144.08 146 36 148.65 150.94 1.53 22 1.55.51 1.57.80 32' 146 22 148.65 1.51.09 1.53.. 53 15.5.96 158.41 160.84 103.28 165.72 168.15 33 1.55.50 158.09 J 60 69 163.28 165.87 . 168.46 171.05 173.65 176.24 178.83 34 165.08 167.82 170.58 173.33 176.08 178.83 181.58 184.33 187.08 189 83 35 174.93 177.84 180.76 183.67 186.59 189.50 192.42 195.33 198.25 201.16 36 185.05 188.14 191.22 194.31 197.39 200.47 203.56 206.64 209.73 212.81 37 195.43 198.73 201 99 205.25 208.51 211.77 215.02 218.28 221.54 224.80 38 1 206.19 209.63 213.06 216.50 219.94 223.37 226.81 230.25 2.33.68 237.12 39 1 217.20 220.82 224.44 22H.06 231.68 235.30 238.92 242.54 246.16 249.78 40 228.48 232.29 236.09 239.91 243.71 247.52 251.32 2.55.13 258.94 262.75 41 240 03 244.03 248.03 2.52.03 256.03 260.03 264.03 268.04 272.04 276.04 42 251.89 2.56.09 260.28 204.48 268.68 272.88 277.08 281.27 285.47 289.67 43 264. 03 268.43 272.83 277.23 281.63 286.03 290.43 294.84 299.24 303.64 44 276-45 281.06 2^5.67 290-27 294.88 299.49 304.10 308.70 313.31 317.92 45 2='9.16 293.98 298.80 303.62 .308.44 313 26 318.08 322 89 327.71 332.53 46 302.16 307.20 312 23 317.27 322.31 327.34 332.38 337.41 342 45 347.49 47 31.5.43 320-69 325 95 .331.20 336.46 341.T-3 346.98 352.23 357.48 362.75 48 328.99 334.48 339 96 345.44 350.93 .3.56.41 361.89 367 38 372.86 378.34 49 342 85 348.. 56 354. 28 359.99 305.70 371.42 377.13 .382.85 388.56 394.27 50 .3.57 00 362.95 368-90 374.85 380 80 386.75 392.70 39H.65 404.60 410.55 51 371.41 377.60' 383.79 389.98 .396.17 402.36 408.55 414.75 420 94 427.13 52 38(:«.12 .392.55 398-99 405.43 411.86 418.30 424.73 431.17 4,37 60 444.04 53 401.10 407.79 414.47 421.16 427.84 434.53 441.21 447.90 454.58 461 .27 54 416.40 423.34 430.28 437 22 444.16 451.10 4.58.04 464.98 471.92 478.86 55 431.98 439 16 446-36 453. .56 460.78 467.96 475.16 482..35 489.55 496.75 56 447.81 455.27 462-74 470.20 477.67 485 13 492.59 500.06 ,507.52 514.98 57 463.94 471.67 479-40 487.14 494.87 .502.60 510.33 518.07 525 80 533.53 58 480.36 4S8.37 498.37 504.3-1 512.39 .520.. 39 528.40 .536.40 .544.41 5.52.42 59 497.07 .505.35 513.63 .521.92 530.20 .538.49 546.77 555 06 56334 571.63 60 1 514.07 522 i A 531.20 539.77 548.34 556.91 565.48 1 574.04 582.61 591.18 54 MECHANICAL PRINCIPIA. No« 6. — Continued. PRESSURE. s 70 71 72 73 1 74 75 76 77 78 79 8 lOoo 10.81 10.96 11.12 11.27 11.42 11-57 1 1.72 11.88 12'03 9 13.49 13.68 13.87 14.06 14 26 14.45 14 64 14.84 15.03 15.22 10 16. ()6 16 89 17 IQ 1 l.l.i 17.37 17.61 17.85 18.08 18 32 18.56 J.0 oil 11 20. 16 20. 45 20.73 21 02 21 60 21 88 22. 17 22 46 22.75 12 23.99 24 33 24 67 25.01 25.36 25.70 26.04 26 38 26.73 27 07 13 28.15 23 9.5 29.36 29 76 30 16 30-56 30 95 31.37 31 77 14 32.64 .1.M 1 33.58 34 04 34 51 34 98 35 44 35 9 1 36.37 36 84 15 37.48 38.02 38.55 39.09 39 62 4i) 1(» 40 69 41 .23 41 76 16 42.06 4.3.26 43.87 44 48 45 QC) 45 71 46 31 46-92 47 53 AQ TA 17 48.14 50 2 1 50.89 51 58 52 27 52.96 53 64 f^A "i'i 18 53 98 i)4.74 56 29 57.06 57 83 5^\60 59.37 60.14 19 60.13 60-98 6] 85 62 71 63.57 64 43 65.29 66. 1.5 67.01 67-86 20 66.64 68 54 69 49 70.44 7 ! 40 7^* 35 73.30 74.25 7.5.20 21 73.46 74.. > 2 7'"^ fi7 / O.i) / 76 62 77. 67 78 72 79 76 80 81 Ol CO 82-91 22 80.64 81 .79 84 09 85 24 86 40 87 55 88 70 9 1.01 23 88.13 89.38 on (^A 91 90 93 16 94 42 95 68 no'on 98.20 99.46 24 95.96 97.33 98 70 100 07 101.44 102 ^1 104 18 lUO.DO 106.92 108-29 25 104.12 10.5.61 108 58 1 10.07 111 50 1 13 05 1 14.53 1 16.02 1 17.51 26 112.62 1 14 2.i 1^5 84 117 44 1 19.05 nno 07 12.5.49 127. 10 27 121.4.5 123.18 126 65 128.39 130 12 131 86 lo.j. 59 13.5.33 137.06 28 130.61 132. 47 134 34 136 21 138.07 139.94 gQ ^A'i A7 14.5.54 147.40 29 140.10 142. lO 141 10 146 10 148. 10 1-50. 1 1 152 11 154. 1 1 156.11 158.11 30 149.94 152-08 154 22 150 36 158.51 160-65 162 79 164.93 167.07 169.21 31 160.09 162. 37 166 95 169 2.3 1 7 1 . 52 17Q »1 176.09 178.38 180.67 32 170.59 173.02 177 90 180 33 182.77 187.64 190.08 192.52 33 181.42 184. 01 1 89 20 191 .79 194.38 196 97 199.56 202. 16 204.75 34 192.59 19.5.34 198 09 200 84 203. .59 206-34 21 1.85 2 14.60 217-35 35 204.08 2«)9 91 215 74 218 66 224.49 227.40 230.32 36 215.90 2v)iO 0(3 225 15 228 23 231 31 234 40 2.37.49 240.57 243.65 37 228.06 2.> 1.3 1 234 57 237 83 241.09 244 35 247 60 250.86 254. 12 257.38 38 240.56 24 3. 99 247 43 250 87 254 30 257 74 264.61 268.05 271.49 39 253.40 2-57.02 264 23 267 88 271 .50 07-10 o«o It 278.74 285.98 40 266.56 270.37 274 18 277 99 281 79 2*^5 60 293.21 297.02 300.83 41 280.04 284.04 288. {)4 296.04 300.04 .304.04 308.04 3 12.04 3 16.04 42 293.87 298.07 3'')2.27 .111*. 01) 314.86 319.06 323.26 327.45 331.65 43 308.04 .312. 44 3 16.84 321.24 325.64 330.04 334.44 3.38.84 343.24 347.64 44 322.53 327. 1.3 331. 74 336.35 34 5.. 57 3.50. 1 7 3.54.78 359.39 364.00 45 337 35 342.17 .346.99 351 81 356 63 3()i.45 366 27 371 .09 375.91 380.73 46 352^52 3.57.5r> 362 59 367.63 372.67 377.70 382.74 387! 77 392^81 397.*85 47 368 01 373.26 378.52 383.78 .389.04 394.29 399.55 404.81 410.06 415.32 48 383.83 3^931 394.79 400.28 405.76 411.24 416.73 422.21 427.69 433.18 49 399.99 405 70 411.42 417.13 422.85 428 .5!) 434.27 439.99 445.70 451.42 50 410.50 422 45 428 40 434.35 440.30 446 25 452.20 458.15 464.10 470.05 51 433.32 43951 445.70 451.89 458.08 464.27 470.46 476.65 482.84 489.03 52 450.47 456.91 463.34 469.78 476.21 482.65 489.09 495.52 501. 96 508.39 53 467.95 474.64 481.32 488.01 491.69 501.38 508.06 514.75 521.43 528.12 54 485.80 492.74 499.68 506.62 513 56 520.50 527.44 534.38 541. 32 548.26 55 503.95 511. 15 518.35 525.55 532.75 539.95 547.15 554.35 561.55 568.75 56 52245 52991 537.37 544.84 5.52 30 559.77 567.23 574.69 582.16 589.62 57 541.26 54900 5.56.73 564.46 572.19 579.93 587.66 595.39 603.12 610.85 58 560.42 568.43 576.43 584.44 592.45 600.45 608.46 616.48 624.47 632.48 59 579.91 588.19 596.48 604.76 613 05 621.33 629.62 637.90 646.19 654.47 GO 599.75 1 608.32 616.88 625.45 J 634.02 642.59 651.16 659.72 668.29 676.86 STEAM POWER. Mo. 6. — Continued. B a> PRESSURE. Diarr 80 81 82 83 84 85 86 87 88 89 8 12.18 1233 12.49 12.64 12-79 12.94 13.09 13.25 13.40 13.55 9 15.41 15.61 15.80 15.99 16.18 16.37 16.57 16.76 16.95 17,15 10 19.04 19.27 19.51 19.75 19.99 20.23 20.46 20.70 20.94 21.18 11 23.04 23.32 23.61 23.90 24.19 24.48 24.76 25.05 25.34 25.63 12 27.41 27.75 28.10 28.44 28.78 29.12 29.47 29.81 30.15 30.50 13 32.17 32.57 32.98 33.38 33.78 34.18 34.58 34.99 35.39 35.79 14 37.31 37.77 38.24 38.71 39.17 39.64 40.11 40.57 41.04 41.50 15 42.84 43.37 43.91 44.44 44.98 45.51 46.05 46.58 47.12 47.65 16 48.75 49.36 49.97 50.58 51.18 - 51.79 52.41 53 01 53.62 54. 23 17 55.02 55.71 56.39 57.08 57.77 58.46 59.15 59.83 60.52 61.21 18 61.68 62.45 63.23 64.00 64-77 e:5.54 66.31 67.08 67.85 68.62 19 68.72 69.58 70.44 71.31 72.16 73.02 73.88 74.74 75.60 76.46 20 76.16 77 11 78.06 79.01 79-96 80.92 81.87 82.82 83.77 84.72 O 1 83.98 85.01 86.06 87.11 88-16 89.21 90.26 91.31 92..36 93.41 oo Z4t 92.16 93.31 94.46 95.61 96-76 97.92 99.07 100.22 10137 102.52 23 100. 72 101.97 103.23 104.49 105.75 107.01 108.27 109.53 110.79 112.05 OA 109.66 111.04 112.41 113.78 115.15 116.52 117.89 119.26 120.63 122.00 y5 119.00 120.48 121 97 123.46 124.95 126.43 127.92 129.41 130-90 132.38 OR 128.71 130.32 131.92 133.53 135.14 136.75 138.36 13997 141.58 143.19 07 ^/ 138.80 140.53 142.27 144.00 145.74 147.47 149.21 150.94 152.68 154.41 149.27 151.13 153.00 154.86 156.73 158.60 160.46 162.33 164.19 166.06 29 160.12 162.12 164.12 166.12 168.12 170.12 172.12 174.13 176.13 178.13 30 171.36 173.50 175 64 177.78 179-92 182.07 184.21 186.35 188.49 190.63 31 182.96 185.24 187.53 189.82 192.10 194.39 196.68 198.96 201.25 203.54 32 194.96 197.39 199.83 202.27 204.71 207.14 209.58 212.01 214.45 216.89 33 207.34 209.93 212..52 215.11 217.71 220.30 222.89 225.48 228.07 230.67 34 220.10 222.85 225.60 228.35 231.10 233.86 236.61 239.36 242.11 244.86 35 233.24 236. 15 239.05 241.98 244.90 247.81 250.73 253.64 256.56 259.47 36 246.74 249.82 2.52.91 255.99 259.08 262.16 265.24 268.33 271.41 274 50 37 260.64 263.89 267.15 270.41 273.67 276.93 280.18 283.44 286.70 289.96 38 274.92 278.36 281.80 285.23 288.67 292.11 295 54 298.98 302.42 305.85 39 289.60 293.22 296.84 300.46 304.08 307.70 311.32 314.94 318.56 322.18 40 304.64 308.44 312.25 316 06 319.87 323.68 327.48 331.29 335.10 338.91 41 320.04 324 04 328.04 3.32.04 336.05 340.05 344.05 348.05 352.05 356.05 42 335.85 340.05 344.25 348.45 3.52.64 356.84 361.04 365.24 369.44 373.63 43 352.04 356 44 360.84 .365.24 369-65 374.05 378.45 382.85 387.25 391.65 44 3oo.d0 373.21 382.43 387.03 391.64 396.25 400.86 405.46 410.07 45 385.55 390.37 395.19 400.01 404.82 409.64 414.46 419 28 424.10 428.92 46 402.88 407.92 412.96 417.99 42303 428.06 433.10 438.14 443.17 448.21 47 420.58 425.84 431.09 436.35 441.61 446.87 452.12 457.38 462.64 467.89 48 438.66 444. 14 449.63 455.11 460.59 466.08 471.56 477.04 482..53 488.01 49 4.57.13 462.85 468.56 474.27 479.99 485,70 491.42 497.13 502.84 508.56 50 476.00 481.95 487.90 493.85 499.80 505.75 511.70 517 65 523.60 529. 55 51 495.22 501.41 507.60 513.79 519.98 526.17 532.36 538.55 544.74 550.93 52 514.83 521.26 527.70 534.13 540.. 57 547.00 553.44 559.87 .566.31 572.75 53 534.80 541.49 548.17 .554.86 561.. 54 568.23 574.91 581.60 588.28 594.97 54 555.20 562.14 569.08 576.02 582.96 589.90 596.84 603.78 610.72 617.66 55 575.95 .583.15 590.35 597.55 604.74 611.94 619.14 626.34 633.54 640.74 56 597.08 604.55 612.01 619.47 626.94 634.40 641.86 649.33 656.79 664.26 57 618.59 626.32 634.05 641.78 649.52 657.25 664.98 672.71 680.45 688.18 58 640.48 648.49 6.56.50 664.50 672.51 680.51 688.52 696.53 704.53 712.54 59 662.72 771 04 679.32 687.61 695.89 704.18 712.46 720.75 729.03 737.32 m 685.43 693.99 702.56 711.13 719.70 728.27 736.83 745.40 753.97 762.54 5G MECHANICAL PRINCIPIA. I^O, 6t — Continued. PRESSURE. 90 91 92 93 94 95 95 97 98 99 13.71 13.86 14.01 14.16 14.31 14-46 14-62 14.77 14.92 15- 07 17.34 17.53 17.72 17.9^ 18.11 18. 31 18.49 18. 69 18-88 19.07 21.42 21 65 21.89 22.13 22.37 22.61 22.84 23.08 23-32 23-56 25 02 26.20 26.49 28.78 27.07 27.36 27.64 27.93 28-22 28-51 30 84 31.18 3] 52 31.87 32.21 32.55 32.89 33-24 33-58 33-92 36.19 36.60 37.00 37.41 37.81 38.21 38.61 39-01 39-41 39-81 4 1 .97 42.44 42 90 43.37 4384 44.30 44-77 45 24 45-70 46.17 48.19 48.73 49.26 49.80 50 33 50.87 51 .40 51-94 52-47 53.01 54 84 55.45 .56.06 56.67 57 28 57.89 58.50 59. 11 59-72 60.33 61.90 62.58 63 27 63.96 64.65 65.34 66.02 66.71 67-40 68.09 6939 70.17 70 94 71 71 72 48 73.25 74.02 74 79 75-56 76.33 77.31 78.17 79 03 79.89 80.75 81.61 82.47 83.33 84-19 85.05 85.68 86.63 87.58 88.53 89.48 90.44 91.39 92.34 93 29 94.24 94.46 95.51 96 56 97.61 98.66 99.71 100-76 101. M 102.86 103-91 103.68 104.83 105.98 107.13 108.28 109.44 110.59 111.74 1 12-89 114 04 1 13.31 114.56 115.82 117.08 118.34 1 19.60 120-86 122.12 123 38 124.64 123.37 124.74 126.12 127 49 128 86 130.23 131.60 132.97 134.34 135.71 133.87 135.36 136.85 138.33 1 39.82 141.31 142 80 144.28 145-77 147.26 144.80 146.40 148.01 149.62 151. 23 1-52.84 154.45 156. 06 157-67 159.28 156.15 157.88 159.62 161.35 163.09 164.82 166*56 168.29 170 03 171 76 167.93 169.79 171.66 173 52 175.39 177! 26 179.12 180.99 182 85 184.72 180.13 182 13 184 13 186.13 188 14 190 14 192-14 194.14 196-14 198. 14 192.78 194 92 197.06 199 21 201.34 203-49 205 63 207.77 209. 91 212.05 205.83 208.11 210 40 212 69 214.97 217.26 219. 55 221.84 224-12 226.14 2] 9*33 221 76 224.20 226.64 229.07 231.51 233.95 236.38 238-82 241.26 233.26 2.35 85 238.44 241.03 243.62 246.22 248.81 251.40 253-99 256.58 247.61 250 36 253.11 2.55.87 258.62 261.37 264 12 266.87 269-62 272.37 262.39 265 3 1 268.22 271.14 274.05 276.97 279.88 282.80 285-71 288.63 277.-58 280.67 283.75 286.83 289 92 293.00 296.09 299.17 302-26 305.34 293.22 29(i 47 299.73 302.99 306 25 309.51 312.76 316.02 319.28 322.54 309.29 312.73 316.16 319.60 323.04 326 47 329.91 333 35 336.78 340-22 325.80 329. 42 333.04 336.66 340.28 343.90 347 52 351. 14 354.76 358-38 342.72 .346 52 350.33 354 J 4 357.94 361.76 365.56 369.37 373. 18 376-99 360.05 364. 05 368.05 372*05 376.05 380.05 384-05 388.05 392.05 396-05 377.83 38203 386.23 390.43 394.63 398 82 403 02 407.22 411.42 4 15-02 398 05 40045 404.85 409.25 413.65 418.05 422-4-5 426.85 431 25 435.(35 414. 68 419 29 423 89 428.50 433.1 1 437-72 442 32 446.93 451.54 456. J 5 433.74 438.56 443.38 448.20 4.53!02 457.84 462-66 467.48 472.30 477.12 453.24 4.58.28 463.32 468.35 473.39 478-42 483.46 488.50 493.. 53 498.57 473.15 478.41 483.67 488.92 494.18 499-44 504-70 509.95 515.21 520 47 493.49 498.98 504.46 509.94 51.5.43 520.91 52a- 39 531.88 .537.36 542.84 514.27 51999 525.70 531.42 537.13 542.84 548-56 5.54.27 559 99 565.70 535.50 541.45 547.40 .553.35 559.30 565.25 571.20 577.15 583.10 589.05 5.57.12 503 31 569 50 575.69 581.88 588.07 594.26 600.45 606.64 612.83 579.18 5H5.62 592.05 598.49 604.92 611.36 617.79 024.23 630.66 6,37.10 601.65 608 34 615.02 621.71 628.39 635.08 641.76 648.45 6.55.13 661.82 624.60 631.54 638.48 645 42 652 36 659.30 666 24 673.18 680.12 687.06 647.94 6.5.5.14 662.34 669.54 676.74 683.94 691.14 698.34 705.54 712.74 671.72 679.18 68665 694.11 701.57 709.04 716..50 723.96 731. 43 738.89 695.91 703.64 711 38 719.11 726.84 734.57 742.31 750-04 7.57.77 765.50 720.54 . 728.55 736.56 744.56 7.52.57 760.57 768.58 776.59 784.59 792.60 74560 753.88 762.17 770.45 778.74 787.02 795.31 803.59 811.88 820.16 771.11 779.67 788.24 796.81 805.38 813.95 822.51 831-08 839.65 848.22 STEAM POWER. 57 ]¥o« 5. — Continued. PRESSURE, Diarr 100 101 102 103 104 105 106 107 108 109 110 8 15.23 15.38 15.53 15.68 15.84 15.99 16.14 16.29 16.44 16.60 16.75 9 19.27 19.46 19.65 19.84 20.04 20.23 20.42 20.61 20.81 21.00 21.19 10 23.80 24.03 24.27 24.51 24.75 24.99 25.22 25.46 25.70 25.94 26.18 11 28.80 29.08 29.37 29.66 29 95 30.24 30.52 30.81 31.10 31.39 31.68 12 34.27 34 61 34.95 35.29 35.64 35.98 36.32 30.66 37.01 37.35 37.69 13 40.22 40.62 41.02 41.42 41.82 42.23 42.63 43.03 43.43 43.83 44.24 14 46.64 47.10 47.57 48 04 48.50 48.97 49.43 49.90 50.37 50.83 51.30 15 53.55 54.08 54.62 55.15 55 69 56.22 56.76 57.29 57.83 58.36 58.90 16 60.94 61.54 62.15 62.76 63.37 63.98 64.59 65.20 65.81 66.42 67.03 17 68.78 69. -4 6 70.15 70 84 71.53 7221 72.90 73.59 74.28 74.97 75.65 18 77.11 77.88 78.65 79 42 80.19 80 96 81.73 82.51 83.27 84.05 84.82 19 85.91 86.76 87.63 88.48 89.34 90.20 91.06 91.92 92.78 93.64 94.50 20 95.20 96 15 97.10 98.05 99.00 99.96 100.91 101.86 102.81 103.76 104.72 21 104.96 106.01 107.05 108.11 109.15 110.21 111.25 112.31 113.35 114.41 115.45 22 115.20 116.35 117.50 118.65 119.81 120.96 122.11 123.26 124.41 125.56 126.72 23 125.90 127.15 128.41 129.67 130 93 132.19 133.45 134.71 135.97 137.23 138.49 24 137.08 138.45 139.82 141.19 142.57 143.94 145.31 146.68 148.05 149.42 150.79 25 148.75 150.23 151.72 153 21 154.70 156.18 157.67 159.16 160.65 162.13 163.62 26 160.89 162.49 164.10 165.71 167.32 168.93 170.54 172.15 173.76 175.37 176.97 27 173.50 175.23 176.97 178.70 180.44 182.17 183.91 185.64 187.38 189.11 190.85 28 186.59 188.45 190.32 192.18 194.05 195.91 197.78 199.65 201.51 203.39 205.24 29 200,15 202.15 204.15 206.15 208,15 210.15 212.15 214.16 216.16 218.16 220.16 30 214 20 216.34 218.48 220.62 222.76 224.91 227.05 229.19 231. .33 233.47 235-62 31 228 70 230.9S 233,27 235.56 237.84 240.13 242.42 244.71 246.99 249.28 251-57 32 243 70 246.13 248.57 251.01 253.44 255.88 258.32 260.75 26.3.19 265.63 268.07 33 259.18 261.77 264 36 266.95 269.54 272.13 274.73 277.32 279.91 282.50 285.09 34 275.13 277.88 280.63 283.38 286.13 288.88 291.63 294.38 297.14 299.89 302.64 35 291.55 294.46 297.38 300.29 30321 306.12 309 04 311.95 314.87 317.78 320.70 36 308.43 311.51 314.59 317.68 320.76 323.85 326.93 330.02 333.10 336.18 339.27 37 325.80 329.05 332.31 3.35.57 338.83 342.09 345.34 .348.60 351.86 355.12 358.38 38 343.66 347.09 350.53 353.96 357.40 360.84 364.27 .367.71 371.15 374.58 378.02 39 362.00 365.62 369.24 372.86 376.4S 380.10 383.72 387.34 390.96 394.58 398.20 40 380.80 384.61 388.41 392.22 396.03 399.84 403.64 407.45 411.26 415.07 418.88 41 400.06 404.06 408.06 412.06 416.06 420.06 424.06 428.06 432.06 436.06 440.06 42 419.82 424.01 428.21 432.41 436.61 440.81 445-00 466.40 449 20 453.40 457.60 461.80 43 440.06 444.46 443.86 453.26 457.66 462.06 470.86 475.26 479.66 484.06 44 460 76 465.36 4G9.97 474.58 479.19 483.79 488.40 493.01 497.62 502.22 506.83 45 481.94 486.75 491.57 496.39 501.21 506.03 5J0.85 515.67 520.49 525.31 530.13 46 503 61 508 64 513.68 518.71 523.75 528.79 533 82 Ooo.ou KA'i SO 548.93 DDo-y / 47 525^73 530.98 535.24 '54L50 546.75 552.01 557.27 562.53 567.78 573!04 578-30 48 548.33 .553.81 559.29 564.77 570.26 575.74 581.22 586.71 592.19 597.67 603-16 49 571.42 577.13 582.84 588.56 594.27 599.99 605.70 611.41 617.13 622.84 628-56 50 595.00 600.95 600.90 6J2.85 618 80 624.75 630.70 636.65 642.60 648.55 654-50 51 619.03 625.22 631,41 637.60 643.79 649.98 656.17 662-36 668.55 674.74 680.93 52 643.54 649.97 656.41 662.84 669.28 675.71 682.15 688-58 695.02 701.45 707. 89 53 668.51 675.19 681.88 688.56 695.25 701.93 708.62 715-30 721.99 728.67 735.36 54 694.00 700.94 707.88 714.82 721.76 728.70 735.64 742-58 749.52 756.46 763.40 55 719.94 727.13 734.33 741.53 748.73 755.93 763.13 770-33 777.53 784.73 791.93 56 746.36 753.82 761.28 768.75 776.21 783.67 791.14 798.60 806.06 813..53 820.99 57 773.24 780.97 788.70 796.43 804.15 811.90 819.63 827.36 8.35.09 842.83 850.56 58 800.61 808.61 816-62 824.62 832.63 840.04 848.64 8.56-65 864.65 872.66 880.67 59 828.45 836.73 845.01 853.30 861 58 869.87 878.15 886.44 894.72 903.01 911.29 60 858.79 865.35 873.92 882.49 891.06 899.62 908.19 916.76 925.33 933.90 942.46 4 58 MECHANICAL PRINCIPIA. No. 5. — Continued, PRESSURE. i 1 Ill 112 113 114 115 116 117 118 119 120 — 8 iR on 17.0o 17 on 17 36 17 51 1 / .OO 17.81 17 97 18.12 18.27 9 21 38 Zi .Oo 21.77 21 96 22 16 22 3.5 22.54 22 75 22 93 23.12 JO 26 41 26 65 26 89 27 13 27 37 27 61 27.84 28 08 28 33 28.56 11 31 96 *?o 32 83 33 12 33 40 33.69 33 98 34.27 34.55 12 38 04 38 38 38-72 39 06 39 41 39 7.5 40 09 40 43 40 78 41 .12 13 44 64 45 04 45 44 45 85 46 25 46 65 47.05 47 45 47 86 48.26 14 51 77 52 23 52 70 53 16 53 63 54 10 54.56 55 03 55 50 55.97 15 59 44 oy.y / 60'51 61 04 61 58 62 11 62 65 6.3 18 03 72 64.26 16 67 64 68 25 68 86 69 47 70 08 70 69 71.29 71.91 72 51 /3.12 17 76 34 77 03 77.72 78 41 79.09 79 78 80.47 81.16 81 84 82.52 18 85 59 86.36 87.13 87.90 88 67 89 44 90.22 90 98 91 76 92.53 19 95*36 96 22 97*07 97.93 98.79 99 65 100.51 101.37 102 23 103.09 20 105*67 106.62 107.57 108.. 52 109.48 110 43 111.38 112.33 113 28 1 14.24 21 116 50 117.55 118.60 119.65 120.70 121.75 122.80 123.85 124 90 125.9.5 22 127*87 129.02 130.17 13L32 132 48 133 63 134.78 135.93 137 08 138.24 23 139 74 141.00 142 26 143.52 144.78 146.04 147.30 148.56 149 82 151.08 24 152* 16 153.53 154.90 156.27 157.65 1.59.02 160.39 161.76 163 13 164 50 25 ]65 11 166.60 168.08 169.57 171.06 172 55 174.03 175 52 177 01 26 178*58 180. 19 181.80 183.41 185.02 186 63 188.24 189 85 191 45 19.j.ut> 27 192 58 194.32 196.05 197.79 199.52 201.26 202.99 204.73 206 46 208 20 28 207* 11 908. QS 210.84 212.71 214.57 216.44 218.31 220J7 222 04 223.90 29 222*16 224-16 226.16 228.16 230.17 232.17 234.17 236.17 238 17 240.18 30 237 76 239*90 242.04 244.18 246.32 248.47 2.50.61 252.75 254.89 2.57 04 31 253 85 256-14 258.43 260.71 263.00 265.29 267.57 269.86 272.15 onn'1^ 32 270^50 272-94 275.38 277.81 280-25 282 69 285.12 287.56 290 00 .UO.OO 573 50 578.32 46 559.00 564.04 569.07 574^11 579.15 584^ 18 589*22 594 25 599.29 604.33 47 583.56 588.81 594.07 599.33 604.58 609.84 615.10 620.36 625^61 630.87 48 608.64 614.12 619.61 625.09 630.57 636.06 641.54 647.02 652 51 657.99 49 634.27 639.99 645 70 651.41 657.13 662.84 668.56 674.27 679.98 685.70 50 6G0.45 666 40 672.35 678.30 684-25 690.20 696.15 702.10 708.05 714.00 51 687.12 693.31 699.50 705.69 711-88 718 07 724.26 730.45 736.64 742.83 52 714.32 720.76 727.20 733.63 740-07 746..50 752.94 759.37 765.81 772.24 53 742.04 748.73 755.41 762.10 768-78 775.47 782.15 788.84 795.52 802.21 51 770.34 777.28 784.22 791.16 798.10 805.04 811.98 818.92 825.86 83280 55 799.13 806.33 813.53 820.73 827-93 835.13 842.32 849.52 856.72 863.92 56 828.45 835.92 843.38 850.85 8.58.31 865.77 873.24 880.70 888.16 895.63 57 858.29 866.02 873.76 881.49 889-22 896.95 904.09 912.42 920.15 927.88 58 888.67 896.68 904.68 912.69 920.70 928.70 930.71 944.71 9.52.72 960.73 59 919.57 927.86 936.14 944.43 9.52-71 961.00 9C9.28 977.57 985.85 994.14 60 951.03 9.59.60 968.17 976.74 985.30 993.87 1002.44 1011.01 1019.58 1028.14 STEAM POWER. 59 Note A. The probable per cent loss of power hy different engines. Accurately finished high pressure engines allow 15 per cent loss. Ordinarily finished high pressure engines allow 20 per cent loss. Accurately finished condensing engines allow 25 per cent loss. Ordinarily finished condensing engines allow 30 per cent loss. Note B, No. 8»3 Problem requires the diameter of a cylinder to produce 28 efTective horse power; but the horse power of the engines in the table is the theoretical power ; hence the effec- tive power must be increased to the theoretical power ; the ef- fective power in this problem is 20 per cent less than the theo- retical power ; suppose the theoretical power of an engine to be 50 horse power, and the loss power of the engine being 20 per cent, then, the effective power of the engine will be 40 horse power ; now 25 per cent of 40 added to 40 equals 50 ; hence 25 per cent of the effective power is equal to 20 per cent of the theoretical power; from this relation between the theoretical and eifective power the following statement is made. 1765 per cent of the effective power is equal to 15 per cent of the theoretical power. 25 per cent of the effective power is equal to 20 per cent of the theoretical power. 3333 per cent of the effective power is equal to 25 per cent of the theoretical power. 4286 per cent of the effective power is equal to 30 per cent of the theoretical power. 60 MFXHANICAL PRINCIPIA. Note C. The velocity of the piston in 83 Problem is 250 feet per minute, but the velocity of the piston represented in the table is 100 feet ; hence the velocity of the piston in No. 83 Prob- lem must be reduced to 100 feet per minute, which is done by dividing the effective power in 83 Problem by 2.50, be- cause 250 divided by 100 gives 2.50. COTTON MANUFACTURING. COTTON MANUFACTURING. The following table shows the usual cost of a brick factory after the foundation is finished, (see note P,) to contain different number of mule and frame spindles on No. 25 yarn with looms ; and also, the cost of the water wheel (overshot or breast,) engines, gearing and belting. Example. Required, the usual cost of a brick factory to contain 4000 mule and frame spindles, with looms on No. 25 yarn ; also, the cost of the water wheels to drive the same — find 4000 in the column marked " Spindles," opposite to this number in the column marked "Building," will be found 11324 dollars ; and also in the column marked " Wheels," will be found 1280 dollars. — Answer, Example. Required, the cost of an engine to drive 6009 mule and frame spindles on No. 25 yarn, with looms ; and also the cost of the belting and gearing — -find 6000 in the column marked "Spindles," opposite to this number in the column marked " Engine," will be found 7250 dollars ; and also in the column marked " Gearing," will be found 2556 dollars ; and in the column marked " Belting," will be found 1460 dollars. — Answer, 64 MECHANICAL PKINCIl'M. ]^o. 1. 13 uildi W h G g1 s • GG3.rin ^« Belting. lUOO 3056 350 1500 500 2G0 2000 5S12 660 2650 911 500 3000 85C8 970 3800 1319 740 4000 11324 1280 4950 1733 980 5000 14080 1590 6100 2142 1220 6000 16836 1900 7250 2556 1460 7000 19592 2210 8400 2965 1700 8000 2^-348 2520 9550 3376 1940 9000 25104 2830 10700 3787 2180 10000 27860 3140 11850 4198 2420 The following table shows the length of the building,, which is three stories high and of different widths ; to con- tain different number of spindles with looms : this table is calculated for the table which shows the attendant machinery for different number of spindles, in which there is double carding. Example. Required, the length of a building to contain 3000 spin- dles with looms, the width being 40 feet, and the building being three stories high — -find 3000 in the column marked " Spindles," opposite to this number in the table, and under Mo. 2. Spindls. WIDTH. 40 42 44 46 48 50 52 54 56 1000 42 40 38 36 34 33 32 31 30 2000 84 80 76 72 68 66 64 62 60 3000 126 120 114 108 102 99 96 93 90 4000 168 160 152 144 136 132 128 124 120 5000 210 200 190 180 170 165 160 155 150 6000 252 240 228 216 204 198 192 186 180 7000 294 280 266 252 238 231 224 217 210 8000 336 320 304 288 272 264 256 248 240 9000 378 360 342 324 306 297 288 279 270 10000 420 400 380 360 340 330 320 310 300 COTTON MANUFACTURING. 65 40 in the column marked " Width," will be found 126 feet. — Answer, Example. Required, the length of a building to contain 6000 spin- dles with looms, the width being 50 feet, and the building being four stories high — find 6000 in the column marked " Spin- dles," opposite to this number in the table, and under 50 in the column marked " Width," will be found 198 feet; now if three stories require 198 feet, four stories will by simple proportion require but 149 feet. — Answer. The following tables show the number of horse power requi- red to drive different number and kind of spindles with looms, on different numbers of yarn. The column marked " Frame Spindles," shows that the filling and warp yarn is spun on frames, which includes all kind of frames, except the cap or Danforth frame. When the warp and filling is spun on this frame, add one horse power to every 500 spindles. This frame produces more per spindle than others, consequently there will be more attendant machinery, hence the increase of power. The column marked " Calculated Power," shows the usual horse power of the engine or water wheel. The column marked *^ Actual Power," shows the actual power required, which is 25 per cent less than the power of the engine or wheel : hence there should be 25 per cent surplus power in the en- gine or wheel above what is required to drive the machinery. Example. Required, the horse power of an engine to drive 2000 mule and frame spindles with looms, the number of yarn being 25 — find 2000 in the column marked Mule and Frame Spindles," opposite to this number in the column marked Calculated Power," will be found 30 horse power. In the column marked Actual Power," will be found 22.5 horse power, the actual power required to drive 2000 mule and frame spindles with looms, on No. 25 yarn. — Answer, 4^ 66 MECHANICAL PRINCTPIA. No. 10 TO 20 Yarn. No. 20 to 30 Yarn. No. 30 to 40 Yarjt. Frame Calc A-Ctu cil Frame Calc Actual Fram'^ Calc Actual Spindles Pow. Power. Spindles Pow Power. Spindles Pow. Power. 1000 19 14.25 1 1000 17 12.75 1000 16 12 2O0O 38 28 50 1 2000 34 25.50 2000 32 24 3000 57 42.75 1 3000 51 38.25 3000 48 36 4000 76 57.00 1 4000 68 51.00 4000 64 48 5000 95 71.25 i 5000 85 63.75 5000 80 60 6000 114 85.50 1 6000 102 76.50 6000 96 72 7000 133 99.75 1 7000 119 89.25 7000 112 84 8000 152 114.00 i 8000 136 102.00 8000 128 96 9000 171 128.25 9000 153 114.75 9000 144 108 10000 190 142.50 10000 170 127.50 10000 160 120 No. 10 to 20 Yarn. No. 20 to 30 Yarn. No. 30 to 40 Yarn. Mule & Calcu Mule & Calcu Mule & Calou Frame laied Actual 1 Frame lated Actual Frame lated Actual Spindles Pow. Power. ; Spindles Pow. Power. Spindles Pow. Power. 1000 17 12.75 i 1000 15 11.25 1000 14 10.50 2000 34 25.50 i 2000 30 22.50 2000 28 21.00 3000 51 38.25 1 3000 45 33 75 3000 42 31.50 4000 68 51.00 ; 4000 60 45.00 4000 56 42.00 5000 85 63.75 ; 5000 75 56.25 5000 70 52.50 6000 102 76.50 ; 6000 90 67.50 6000 84 63.00 7000 119 89.25 j 7000 105 78.75 7000 98 73.51) 8000 136 102.00 1 8000 120 90.00 8000 112 84.00 9000 153 114.75 9000 135 101.25 9000 126 94.50 10000 170 127.50 10000 150 112 50 10000 140 105.00 No. 10 to 20 Yarn. No. 20 to 30 Yarn. No. 30 to 40 Yarn. Mule Calc. Actual Mule Calc. Actual Mule Calc Actual Spindles Pow. Power. Spindles Pow. Power. 1 Spindles Pow Power. 1000 16 12 1000 14 10.50 1000 13 9.75 2000 32 24 2000 28 21 00 2000 26 19.50 3000 48 36 3000 42 31.50 3000 39 29.25 4000 64 48 4000 56 42.00 4000 52 39.00 5000 80 60 5000 70 52.50 5000 65 48.75 6000 96 72 6000 84 63.00 6000 78 58.50 7000 112 84 7000 98 73.50 7000 91 68.25 8000 12« 96 8000 112 84.00 8000 104 78.00 9000 144 108 9000 126 94.50 9000 117 87.75 10000 160 120 10000 140 105.00 10000 130 97.50 COTTON MANUFACTURING. 67 Example. Required, the horse power of a water wheel, to drive 6000 mule spindles with looms, the number of the yarn being 36 — find 6000 in the column marked ^' Mule Spindles," opposite to this number in the column marked " Calculated Power,'^ will be found 78 horse power ; in the column mark- ed "Actual Power," will be found 58.5 horse power, the actual power required to drive 6000 mule spindles with looms, on No. 36 yarn. — Answer. The following tables show the required length of overshot and breast water wheels on different falls, to drive different number and kind of spindles with looms on different numbers No. 4. Mule Spindles with Looms No 10 to 25 Yarn. Fall. No. SPINDLES. looo' 2000 3000 4000 5000 6000^7000 8000 9000 10000 10 15.2 22.8 30.4 38.0 45.6 53.2 60.8 68.4 76 11 70 14.0 21.0 28.0 35.0 42 0 49.0 56.0 63.0 70 12 6.3 12 6 18.9 25.2 31.5 37.8 44.1 50.4 56.7 63 13 60 12.0 18.0 24 0 30.0 36.0 42.0 48.0 54.0 60 14 5.4 10.8 16.2 21 6 27.0 32.4 37.8 43.2 48.6 54 15 50 10.0 15.0 20.0 25.0 30 0 35.0 40.0 45.0 50 16 4.7 9.4 14.1 18.8 23.5 28.2 32.9 37.6 42 3 47 17 45 9.0 13.5 18.0 22.5 27.0 3J.5 36.0 40.5 45 ]8 4.2 8.4 12.6 16.8 21 0 252 29 4 33 6 37.8 42 19 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 360 40 20 3.8 7.6 11.4 15.2 19.0 22.8 26.6 30.4 34.2 38 21 3.6 7.2 108 14.4 18.0 21 6 25.2 28.8 324 36 22 3.4 6.8 102 13.6 17.0 20.4 23.8 27 2 30.6 34 23 3.3 6.6 9.9 13.2 16.5 19.8 23.1 26 4 29.7 33 24 3.1 6.2 9.3 12.4 15.5 18.6 21.7 24 8 279 31 25 3.0 6.0 9.0 12.0 15 0 18.0 21 0 24.0 27.0 30 26 2.9 5.8 8.7 11.6 14.5 17.4 20.3 23.2 26 1 29 27 2.8 5.6 8.4 11.2 14.0 16.8 19.6 22.4 252 28 28 2.7 5.4 8,1 10.8 13.5 16.2 18-9 21.6 24 3 27 29 2.6 5.2 7.8 10.4 13.0 15.6 18.2 20.8 23.4 26 30 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25 68 MECHANICAL PKINCIPIA. of yarn : the lengili of the wheel means the length of the buckets in the cZear, that is the length of the space in the wheel which the water occupies ; this must be particularly observed — the column marked " Fall," shows the fall of the breast, or the diameter of the overshot wheel ; the fall of the breast wheel is supposed to be two feet, (see Notes on Water Power,) the column marked No. of Spindles," shows the number of spindles with looms, to be driven. Example. Required, the length of an overshot wheel to drive 2000 frame spindles with looms, on any number of yarn from 10 to 25, the diameter of the wheel being 12 feet — find 12 in I¥o. 5. Mule Spindles with Looms No. 25 to 40 Yarn. No. SPINDLES. Fall. 1000 2000 3000 4000 5000'6000 1 7000 8000 9000 lOOOO 10 6.6 13.2 19.8 26.4 33.0 39.6 46.2 52.8 59.4 66.0 11 6.0 12.0 18.0 24.0 30.0 36.0 42.0 48.0 54.0 60.0 12 5.5 11.0 16.5 22.0 27.5 33.0 38.5 44.0 49.5 55.0 13 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 14 4.7 9.4 14.1 18.8 23.5 28.2 32.9 37.6 42 3 47.0 15 4.4 8.8 13.2 17.6 22.0 26.4 30.8 35.2 39.6 44.0 16 4.1 8.2 12.3 16.4 20.5 24.6 28.7 32.8 36.9 41.0 17 3.9 7.8 11.7 15.6 19.5 23.4 27.3 31.2 35.1 39.0 18 3.7 7.4 11.1 14.8 18.5 22.2 25.9 29.6 33.3 37.0 19 3.5 7.0 10.5 14.0 17.5 21.0 24.5 28.0 31.5 35.0 20 3.3 6.6 9.9 13.2 16.5 19.8 23.1 26.4 29.7 33.0 21 31 6.2 9.3 12.4 15.5 18.6 21.7 24.8 27.9 31.0 22 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0 23 29 5.8 8,7 11.6 14.5 17.4 20.3 23.2 26.1 29.0 24 2.8 5.5 8.2 11.0 13.7 16.5 19.2 22.0 24.7 27.5 25 2.6 5.2 7.8 10.4 13.0 15.6 18.2 20.6 23.4 26.0 26 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27 24 4.8 7.2 9.6 12.0 14.4 16.8 19.2 21.6 24.0 28 23 4.7 7.0 9.4 11.7 14.1 16.4 18.8 21.1 23.5 29 23 4.6 6.9 9.2 11.5 13.8 16.1 18.4 20.7 23. 0 30 2.2 4.4 6.6 8.8 11.0 13.2 15.4 17.6 19.8 22.0 COTTON MANUFACTURING. 69 the column marked " Fall," opposite to this number in the table, and under 2000 in the column marked " No. of Spin- dles," will be found 16 feet, the length of the bucket in the clear. — Ansiver, Example. Required, the length of an overshot wheel to 8000 mule and frame spindles with looms, on any number of 3^arn from 10 to 25, the diameter of the wheel being 22 feet — find 22 in the column marked " Fall," opposite to this number in the table, and under 8000 in the column marked " No. of Spindles," will be found 32 feet the length of the bucket in the clear, or two wheels 16 feet each in the clear. — Answer, No. 6. Mule and Frame Spindles with Looms No. 10 to 25 Yarn. No. SPINDLES. Fall. 1000 2000 3000 4000 5000 60007000 j_ 8000 9000 10000 10 8.7 17.4 26.1 34.8 43.5 52.2 60.9 69.6 78 3 87.0 11 8.0 16.0 24.0 32.0 40 0 48.0 56.0 64.0 72.0 80.0 12 7.2 14.4 21.6 28.8 36.0 43.2 50.4 57.6 64.8 72.0 13 6.7 13.4 20.1 26.8 33.6 40.3 47.0 ,53.7 60.4 67.2 14 6.2 12.5 18.7 25.0 31.2 37.5 |43.7 50.0 56.2 625 15 5.8 11.6 174 23 2 29.1 .34 9 j40.7 465 52.3 58.2 16 5.5 11.0 16.5 22.0 27.5 33.0 38 5 44.0 49 5 55.0 17 52 10 4 15.6 20.8 (26.0 31.2 36.4 41.6 46.8 52.0 18 4.9 9.8 14.7 19.6 |24.5 29.4 34.3 39.2 44.1 49.0 19 4.6 9.2 13. 8 18.4 23.0 27.6 |32.2 36.8 41.4 46.0 20 4.3 8.7 13.1 17.4 21.8 26.1 30.5 34.8 39.2 43.6 21 4.1 8.2 12.4 16.5 20.7 24.8 |28.9 33.1 37.2 41.4 22 3.9 8.0 12.0 16.0 !20.0 24.0 28.0 32.0 36.0 40.0 23 3.8 7.6 11.4 15.2 19.3 22.8 126.6 30.4 34.2 38.0 24 3.6 7.2 10.8 14.4 184 21.6 :25.2 28.8 32.4 36.0 25 3.4 6.8 10.2 13.6 17.4 20.4 23 8 27.2 30.6 34.0 26 3.3 6 6 9.9 132 16.5 19.8 23.1 26.4 29.7 33.0 27 32 6.4 9.6 12.8 16.0 19.2 ;22.4 25.6 28.8 32.0 28 3.1 6.2 9 3 12.4 15.5 18.6 [21.7 24.8 27.9 31.0 29 3.0 60 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0 30 2.9 5.8 8.7 11. 6 14.5 17.4 I2O.3 23.2 26.1 29.0 70 MECHANICAL PRINCIPIA. Example. Required, the length of a breast wheel to drive 2000 mule spindles with looms, on any number of yarn from 25 to 40, the fall being 10 feet — find 10 in the column marked Fall," opposite to this number in the table, and under 2000 in the column marked No. of Spindles,*' will be found 13.2 feet the length of the bucket in the clear ; if an iron and wood wheel are equal in length, the difference in the length of the buckets will be from one to two feet ; hence the length of the bucket in the clear must always be ob- served . — Answer, Mule and Frame Spindles with Looms No. 25 to 40 Yarn. No. SPINDLES. Fall. 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 10 7.6 15.2 22.8 30.4 38.0 45.6 53.2 60.8 68.4 76 11 7.0 14.0 21.0 28.0 35.0 42.0 49.0 56.0 63.0 70 12 6.3 12.6 18.9 25.2 31.5 37.8 44.1 .50.4 56 7 63 13 6.0 12.0 18.0 24.0 30.0 36.0 42.0 48.0 54.0 60 14 5.4 10.8 16.2 21.6 27.0 32.4 37.8 43 2 48.6 54 15 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50 16 4.7 9.4 14.1 18.8 23.5 28.2 32.9 37.6 42.3 47 17 4.5 9.0 13.5 18.0 22.5 27.0 31.5 36.0 40.5 45 18 4.2 8.4 12 6 16.8 21.0 25.2 29.4 •33 6 37.8 42 19 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40 20 3.8 7.6 11.4 15.2 19.0 22 8 26.6 30.4 34.2 38 21 3.6 7.2 10.8 14.4 18.0 21.6 25 2 28.8 32.4 36 2-2 34 6.8 10.2 13 6 17.0 20.4 23 8 27.2 30 6 34 23 3.3 66 9.9 13.2 16.5 19. 8 23.1 26.4 29.7 33 24 31 6.2 9.3 12.4 15.5 18.6 21.7 24.8 27.9 31 25 3.0 6.0 9.0 120 15.0 18.0 21.0 24 0 27.0 30 26 2.9 5.8 8.7 11.6 14.5 17.4 20 3 23.2 26 1 29 27 2.8 5.6 8.4 11.2 14.0 16 8 19.6 22.4 25.2 28 28 2.7 5.4 8.1 10.8 13.5 16.2 18.9 21.6 24.3 27 29 2.6 5.2 7.8 10.4 13.0 15.6 18 2 20 8 23.4 26 30 2.5 5.0 7.5 lO.O 12.5 15.0 117.5 20.0 22.5 25 COTTON MANUFACTURING. 71 It will be noticed that the number of yarn in these tables range, from 10 to 25, and 25 to 40 ; if a greater degree of accuracy is required, or the length of the wheel required, say for No. 30 yarn, it can be found by referring to the table showing the calculated and actual power required to drive different number and kind of spindles with looms on differ- ent numbers of yarn ; after the number of horse power is found, refer to the table showing the horse power of over- shot and breast wheel on different falls, and of different length. Mo. 8. Frame Spindles with Looms No. 10 to 20 Yarn. 1 ! No. SPINDLES. Fall. 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 10 103 20.6 30.9 41.2 51.5 61.8 72.1 82.4 92.7 103.0 11 93 18.6 27.9 32.2 46.5 55.8 65.1 74.4 83.7 93.0 12 8-6 17.2 25 8 34.4 43.0 51.6 602 68.8 77.4 86.0 13 8.0 16.0 24.0 32.0 40.0 48.0 156.0 64.0 72.0 80.0 14 7.3 14.6 21 9 29.2 !36.5 43.8 51.1 58.4 65.7 73.0 15 7.0 140 21.0 28.0 |35.0 42.0 49.0 56.0 63.0 70.0 16 6.4 12.8 19.2 25.6 32.0 38.4 44.8 51.2 57.6 64.0 17 6.0 12.0 18.0 24 0 |30.0 36.0 42,0 48.0 54.0 60 0 18 5.7 11.4 17.1 22.8 28.5 34.2 39.9 45.6 50.3 57.0 19 5.4 10.8 16.2 21.6 27.0 324 37.8 43 2 48.6 54.0 20 5 1 102 15.3 20.4 25.5 30.6 35.7 40,8 45.9 51.0 21 4.9 9.8 14.7 19.6 24.5 29.4 343 392 44.1 49.0 22 4.7 9.4 14.1 18.8 23.5 28.2 32.9 37 6 42.3 47.0 23 4.5 9.0 13 5 18 0 22.5 27.0 31.5 36.0 40.5 45.0 24 4.3 8.6 12.9 17 2 21.5 25.8 30.1 34.4 38.7 43.0 25 4.1 8.2 12.3 164 20.5 24.6 28.7 32.8 36.9 41.0 26 3.9 7.8 11.7 15.6 19.5 23 4 |27.3 31.2 35 1 39.0 27 3.8 7 6 11.4 15.2 19.0 22.8 126.6 30.4 i34.2 38.0 28 3.7 7.4 11.1 14.8 18.5 22 2 25.9 29.6 33.3 37.0 29 3.5 7.0 10 5 14.0 17.5 21.0 i24 5 28.0 131.5 35.0 30 3.4 6.8 10.2 13 6 17.0 20.4 |23.8 27.2 130.6 34.0 72 MECHANICAL PRINCIPIA. No. 0. Frame Spindles with Looms No. 25 to 40 Yarn. No. SPINDLES. Fall. 1000 2000 3000'4000 1 5000 6000 7000 8000 9000 10000 ■ 10 1 '8.7 17.4 26.1 34.8 43.5 52.2 60.9 69.6 78.3 87.0 11 8.0 16 0 24.0 320 40.0 48.0 56 0 64.0 72.0 80 0 12 |7.2 14.4 21.6 28 8 36.0 43.2 j50.4 57.6 64.8 72.0 13 ! 6.7 13.4 20.1 26.8 33.6 40.3 47.0 53.7 60.4 67.2 14 ! 6.2 12 5 18.7 25.0 31.2 37.5 43.7 50.0 56.2 62.5 15 ! 5.8 11.6 17.4 23.2 29.1 34.9 '40.7 46.5 52.3 58.2 36 5.5 11.0 16 5 22.0 27.5 33 0 38.5 44.0 49.5 55.0 17 i 5.2 10.4 15.6 20.8 26.0 '31.2 36.4 41.6 468 52.0 18 ' 4.9 9.8 14.7 19.6 24.5 29.4 34.3 39.2 44.1 49.0 19 4.6 9.2 13.8 184 23.0 27.6 32.2 36.8 41.4 46.0 20 |4.3 8.7 13 1 17.4 21.8 26.1 30.5 34.8 39.2 43.6 21 14.1 8.2 12.4 16 5 20.7 124.8 28.9 33.1 37.2 41.4 22 j 4.0 8.0 12.0 16.0 20 0 24.0 27.8 32.0 36.0 40.0 23 3.8 7.6 U.4 15.2 19.3 22.8 26.6 30.4!34.2 38.0 24 3.6 7.2 10.8 14.4 18.4 21.6 25.2 28.8 :32.4 36.0 25 3.4 68 10.2 13.6 17.4 20.4 23 8 27.2 30.6 34.0 26 3.3 6.6 9.9 13.2 16.5 19.8 23.1 26.4 '29.7 33.0 27 3.2 6.4 9.6 12 8 16.0 19.2 22.4 25.6 28.8 32.0 28 3.1 6.2 9.3 12.4 15.5 18.6 21.7 24.8 27.9 31 0 29 3.0 6.0 9.0 12 0 15 0 18.0 21.0 24.0 27 0 30 0 30 2.9 5.8 8.7 11.6 14.5 17.4 20.3 23.2 26.1 29.0 The following table shows the required area of all the openings in the outward discharging turbine wheel, to drive different number of spindles under different heads : the col- umn marked " Head," shows the number of feet head, the column marked " No. of Spindles," shows the number of spindles to be driven. — (See Note B.) Example. Required, the area of all the openings in an outward dis- charging turbine wheel, the head being 16 feet, to drive 3000 spindles with looms, on No. 20 yarn — find 16 in the column ''marked Head," opposite to this number in the table, and COTTON MANUFACTURING. 73 under 3000 in the column marked Spindles," will be found 200 inches area. — Answer, Example. Required, the area of all the openings in an outward dis- charging turbine wheel, the head being 20 feet, to drive 2000 spindles on No. 25 yarn, with looms — find 20 in the column marked Head," opposite to this number in the table, and under 2000 in the column marked " Spindles," will be found 103 inches area. — Answer. No- 10. The Outward Discharging Turbine Water Wheel Mules and Frames and Weaving on No. 18 to 25 Yarn. SPINDLES. Head 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5 558 744 930 1116 1302 1488 1674 1860 2046 2232 6 363 484 605 726 847 968 1089 1210 1331 1452 7 311 415 519 623 727 831 935 1039 1143 1247 8 245 327 409 491 573 655 737 819 901 983 9 190 253 316 379 442 505 568 631 694 757 10 163 217 271 325 379 433 487 541 595 649 11 137 183 229 275 321 367 413 459 505 551 12 122 163 204 245 286 327 368 409 450 491 13 107 143 179 215 251 287 323 359 395 431 14 95 127 159 191 223 255 287 319 351 383 15 83 111 139 167 195 223 251 279 307 335 16 75 100 125 150 175 200 225 250 275 300 17 68 91 114 137 160 183 206 229 252 275 18 62 83 104 125 146 167 188 209 230 251 19 57 76 95 114 133 152 171 190 209 228 20 52 69 86 103 120 137 154 171 188 205 21 48 64 80 96 112 128 144 160 176 192 22 45 60 75 90 105 120 135 150 165 180 23 43 57 71 85 99 113 127 141 155 169 24 39 52 65 78 91 104 117 130 143 156 25 37 49 61 73 85 97 109 121 133 145 26 35 47 59 71 83 95 107 119 131 143 27 32 43 54 65 76 87 98 109 120 131 28 31 41 51 61 71 81 91 101 111 121 29 29 39 49 59 70 79 89 100 109 119 30 28 37 46 55 64 73 82 91 100 109 74 MECHANICAL PRINCIPIA. The following table shows the required area of all the openings in the inward discharging turbine wheel, to drive different number of spindles under different heads — the col- umn marked Head," shows the number of feet head, the column marked " Spindles," shows the number of spindles to be driven. (See Note B.) Example. Required, the area of all the openings in an inward dis- charging turbine wheel, the head being 12 feet, to drive 2000 N®. 11. The Inwaud or Centre D/scharging Turbine Water Wheel Mules AND Frames and Weaving- on No. 18 to 25 Yarn. SPINDLES. Head 500 1000 1500 2000 2500 3000 1 3500 4000 45005000 5 1000 1333 1666 1999 2332 2665 2998 3331 3664,3997 6 714 952 1190 1428 1666 1904 2142 2380 2618'2856 7 543 624 805 986 1167,1348 1529 1710 1891 2072 8 431 574 717 860 1003 1146 1289 1432 1575 1718 9 352 469 586 703 820 937 1054 1171 1288 1405 10 294 392 490 588 686| 784 882 980 1078 1176 11 252 336 420 504 588' 672 756 840 924 1008 12 217 289 361 433 505 577 649 721 793 865 13 190 253 316 379 442; 505 568 631 694 755 14 169 225 281 337 393j 449 505 561 617 673 15 151 201 251 301 351 401 451 501 551 601 16 136 181 226 271 316, 361 406 451 496 541 17 123 164 205 246 287| 328 369 410 451 492 18 113 151 189 227 265 303 341 379 417 455 19 104 139 174 209 244 279 314 349 384 419 20 96 128 160 192 224 256 288 320 352 384 21 88 117 146 175 204' 233 262 291 320 349 22 82 109 136 163 190' 217 244 271 298 325 23 77 103 129 155 I81i 207 233 259 285 311' 24 72 96 120 144 168 192 216 240 264 288 25 67 89 111 133 155 177 199 221 243 265 26 63 84 105 126 147j 168 189 210 231 252 27 59 79 99 119 139 159 179 199 219 239 28 56 75 94 113 132 151 170 189 208 227 29 53 71 89 107 125 143 161 179 197 215 30 50 67 84 101 118' 135 152 169 186 203 COTTON MANUFACTURING. 75 spindles and weaving on No. 25 yarn — find 12 in the col- umn marked " Head/' opposite to this number in the table, and under 2000 in the column marked " No. of Spindles," will be found 433 inches area. — Ansiver, Example. Required, the area of all the openings in the inward dis- charging turbine wheel, the head being 24 feet, to drive 3000 spindles and weaving on No. 18 yarn — find 24 in the col- umn marked " Head," opposite to this number in the table, and under 3000 in the column marked " No. of Spindles," will be found 192 inches area. — Ansioer, The following table shows the attendant machinery for different number of spindles, and for different numbers of yarn. This table is calculated for double carding when the yarn is finer than No. 20. Example. Required, the attendant machinery for 2000 spindles on No. 25 yarn — find 2000 in the column marked Spindles," opposite to this number in the different columns will be found, 1 willower, 1 picker, 16 cards, 2 R. R. Heads, 2 drawing frames, 20 coarse speeder spindles, 80 fine speeder spindles, 56 spooler spindles, 2 warpers, 2 dressers, 56 looms. — Answer, Example. Required, the attendant machinery for 4000 spindles on No. 8 yarn — find 4000 in the column marked " Spindles," opposite to this number in the different columns will be found, 1 willower, 3 pickers, 48 cards, 8 R. R. Heads, 8 drawing frames, 256 coarse speeder spindles, (fine speeder spindles not required on so coarse work,) 112 spooler spindles, 2 warpers, 4 dressers, 96 looms. — Answer, 76 MECHANICAL PRINCIPIA. Mo- 12. No. 5 TO 10 Yarn. Average cost from different Mach. Shops Willowers. Pickers, two Beaters. Single Cardg. 30 in. Cards. R. R. Heads. 3 Heads each Drawg. Frams Spdr. Spindles. Do. fine Do. Mule and Frame Spindles. spooler Spindles. Warpers. | Dressers. | Looms. 10555 1 1 12 2 2 64 (( 1000 28 1 1 24 21035 1 2 24 4 4 128 (( 2000 56 2 2 48 31015 1 3 36 6 6 192 (( 3000 84 2 3 72 41395 1 3 48 8 8 256 4000 112 2 4 96 51875 I 4 60 10 10 320 5000 140 3 5 120 62255 1 5 72 12 12 384 (( 6000 168 3 6 144 72730 1 6 84 14 14 448 7000 196 4 7 168 83190 2 7 96 16 16 512 8000 224 4 8 192 93570 2 8 108 18 18 576 t< 9000 252 4 9 216 103650 2 8 120 20 20 640 <( 10000 280 5 10 240 No. 10 TO 20 Yarn. 10055 1 1 8 2 2 12 50 3 000 28 1 1 1 28 19710 1 2 16 4 3 24 100 2000 56 1 2 56 29065 1 2 24 6 4 36 150 3000 84 2 3 84 38720 1 3 32 8 5 48 200 4000 112 2 4 112 48075 1 3 40 10 6 60 250 5000 140 3 5 140 57730 1 4 48 12 7 72 300 6000 168 3 6 168 67310 1 4 56 14 9 84 350 7000 196 4 7 196 76965 1 5 64 16 10 96 400 8000 224 4 8 224 86945 1 6 72 18 12 108 450 9000 252 5 9 252 96200 1 6 80 20 13 120 500 10000 280 5 10 280 No. 20 TO 30 Yarn. 9345 ] 1 1 8 1 1 10 40 1000 28 1 1 I 28 18535 I 1 16 2 2 20 80 2000 56 2 2 1 56 2703 0 1 2 24 3 2 30 120 3000 84 2 3 84 36280 1 2 32 4 3 40 160 4000 112 2 4 112 44875 1 2 40 5 3 50 200 5000 140 3 5 140 54145 1 3 48 6 4 60 240 6000 168 4 6 168 63090 1 3 56 7 4 70 280 7000 196 4 7196 72360 1 3 64 8 5 80 320 8000 224 5 8 224 81080 1 4 72 9 6 90 360 9000 252 5 9 252 90350 1 4 80 10 7 100 400 10000 280 6 10,280 No. 30 TO 40 Yarn. 8855j 1 1 6 1 1 10 38 1000 28 1 1 25 16860 1 1 12 2 1 20 76 2000 56 1 2 50 25190 1 1 18 3 2 30 114 3000 84 2 2 75 33645 1 2 24 4 2 40 152 4000 112 2 3 100 41525 1 2 30 5 3 50 190 5000 140 3 3 125 49980 1 2 36 6 3 60 228 6000 168 3 4 150 58610 1 2 42 7 4 70 266 7000 196 4 5 175 66315 1 3 48 8 4 80 304 8000 224 4 5 200 74920 1 3 54 9 4 90 342 9000 252 5 6 225 83600 1 3 60 10 5 100 380 10000 280 5 7 250 COTTON MANUFACTURING. / "--^ ^ 77 If other speeders are preferred, the number of each kind can be found from the following statement Non-twisting speeder, 10 spindles; twisting ditto, 25 spindles; fly frame, 50 spindles: — all produding the same amount of work on the same No. of yarn. The following table shows the number of revolutions per minute that shafts make when driven by different size pul- leys ; two inches is the ordinary ratio of increase of the diameter of pulleys; the following table is calculated accord- ingly — opposite to each table will be found the number of revolutions per minute that the driving shaft is supposed to run ; the column marked " Driving Pulleys," shows the di- ameter of the pulleys which are to go on to the driving shaft; the column marked Driven Pulleys," shows the diameter of the pulleys which are to go on to the driven shaft. Example. The driving shaft runs 120 turns per minute, the driving pulley on it is 14 inches in diameter ; required, the diameter of the driven pulley on the centre shaft, so it will make 140 turns per minute — find 14 in the column marked " Driving Pulleys," opposite to this number in the table, find 140 over this number, and in the column marked " Driven Pulleys," will be found 12 inches. — Answer. Example. A frame shaft is driven 136 turns per minute by a pul- ley 12 inches in diameter ; required, the diameter of a pul- ley to drive the frame shaft 182 turns per minute — find 12 in the column marked "Driving Pulleys," (opposite to 114 revolutions,) opposite to this number in the table find 136, below this number in the same column will be found 182, opposite to which in the column marked " Driving Pulleys," will be found 16 inches, the diameter of the required pulley. —Answer. riving illeys. 10 12 14 16 18 20 22 24 10 12 14 16 18 20 22 24 10 12 14 16 18 20 22 24 10 12 14 16 18 20 22 24 10 12 14 16 18 20 22 24 MECHANICAL PRINCIPIA. Wo. 13. 96 Revolutions. DRIVEN PULLEYS. 10 12 14 16 18 20 22 24 96 80 68 60 53 48 44 40 115 96 82 72 64 58 52 48 134 112 96 84 75 67 61 56 153 128 109 96 85 77 69 64 172 144 123 108 96 86 78 72 192 160 137 120 106 96 87 80 211 176 150 132 117 106 96 88 230 192 164 144 128 115 104 96 98 Revolutions. 98 81 70 61 54 49 45 41 118 98 84 73 65 59 oo 137 114 98 86 76 68 ^7 157 131 112 98 87 78 71 vo 176 147 126 110 98 88 80 73 196 163 140 122 109 98 89 82 216 179 154 134 120 108 98 90 235 196 168 147 131 117 107 98 100 Revolutions. 100 83 71 62 56 50 45 42 120 100 85 75 67 60 54 140 116 100 87 78 70 63 oo 160 133 114 100 89 80 72 67 180 150 128 112 100 90 82 1 0 200 166 142 125 111 100 V 1 oo 220 183 157 137 122 110 100 92 240 200 171 150 133 120 109 100 102 Revolutions. 102 85 73 C4 57 51 ^ u A9 122 102 87 76 68 \)i OD 1 143 119 102 89 79 71 \)0 OJ 163 136 116 102 91 82 i t DO 184 153 131 115 102 OO 7<^ 204 170 145 127 113 102 Q'l iJO fit; 224 187 160 140 125 112 102 93 245 204 175 153 136 122 111 102 104 Revolutions. 104 1 86 65 57 52 47 43 J 24 104 69 78 69 62 56 53 145 121 104 91 80 72 66 61 166 138 118 104 92 83 75 70 187 156 133 117 104 93 85 78 208 173 148 130 115 104 94 87 228 190 163 143 127 114 104 95 249 208 178 156 138 124 113 104 COTTON MANUFACTURING. 79 No, 13. — Continued. 106 Revolutions. DRIVEN PULLEYS. Driving Pulleys. 10 12 14 16 18 20 22 24 10 12 14 16 18 20 22 24 106 127 148 169 190 212 233 254 88 106 124 141 159 176 194 212 75 91 106 121 136 151 166 181 66 79 93 106 119 132 145 159 58 70 82 94 106 117 129 141 53 63 74 84 95 106 116 127 48 58 67 77 87 96 106 115 44 53 61 70 79 88 97 106 108 Revolutions. 10 108 90 77 67 60 54 49 45 12 129 108 92 81 72 64 58 54 14 151 126 108 94 84 75 68 63 16 172 144 123 108 96 86 78 72 18 194 162 138 121 108 97 88 81 20 216 180 154 135 120 108 98 90 22 237 198 169 148 132 118 108 99 24 259 216 185 162 144 129 117 108 110 Revolutions. 10 110 91 78 68 61 55 50 45 12 132 110 94 82 73 66 60 55 14 154 128 110 96 85 77 70 64 16 176 146 125 110 97 88 80 73 18 198 164 141 123 no 99 90 82 20 220 183 157 137 122 110 100 91 22 242 201 172 151 134 121 110 100 24 264 220 188 165 146 132 120 110 112 Revolutions. 10 112 93 80 70 62 56 51 46 12 134 112 96 84 74 67 61 56 14 156 130 112 98 87 78 71 65 16 179 149 128 112 99 89 81 74 18 201 168 144 126 111 100 91 84 20 224 186 160 140 124 112 101 93 22 446 205 176 154 136 123 111 102 24 268 224 192 168 149 134 122 112 114 Revolutions. 10 114 95 81 71 63 57 52 47 12 136 114 97 85 76 68 62 57 14 159 133 113 99 88 79 72 66 16 182 152 130 114 101 91 83 76 18 205 171 146 128 114 102 93 85 20 228 190 162 142 126 114 103 95 22 250 209 178 156 139 125 113 104 24 273 228 195 171 152 136 124 114 80 r.IECHANICAL PRINCIPTA. No. 13. — Continued. 116 Retolutions. Driving Pulleys. DRIVEN PULLEYS. 10 12 14 16 18 20 22 24 10 116 96 82 72 64 58 52 48 12 139 116 99 87 77 69 63 58 14 162 135 116 101 90 81 73 67 16 185 154 132 116 103 92 84 77 18 208 173 149 130 116 104 94 87 20 232 193 165 145 128 116 105 96 22 255 212 182 159 141 127 115 106 24 278 232 199 174 154 139 126 116 118 Revolutions. 10 118 98 84 73 65 59 53 49 12 141 118 101 88 78 70 64 59 14 165 137 117 103 91 82 75 68 16 188 157 134 118 104 94 85 78 18 212 176 151 132 118 106 96 88 20 236 196 168 147 131 118 107 98 22 259 216 185 162 144 129 118 108 24 283 236 202 176 157 141 128 118 120 Revolutions. 10 120 100 85 75 66 60 54 50 12 144 120 102 90 80 72 65 60 14 168 140 119 105 93 84 76 70 16 192 160 137 120 106 96 87 80 18 216 180 154 135 120 108 98 90 20 240 200 171 150 133 120 109 100 22 264 220 188 165 146 132 120 110 24 288 240 205 180 160 144 131 120 122 Revolutions. 10 122 101 87 76 67 61 55 50 12 146 J 22 104 91 81 73 66 60 14 170 142 122 108 94 85 77 71 16 195 162 139 122 108 97 88 81 18 219 183 156 137 121 109 99 91 20 244 203 174 152 135 122 110 101 22 268 223 191 167 148 134 12i^ 111 24 292 244 209 183 162 146 133 121 124 Revolutions. 10 124 103 88 77 68 62 56 51 12 148 124 106 93 82 74 67 62 14 173 144 124 103 96 86 78 72 16 198 165 141 124 110 99 90 82 18 223 186 159 139 123 111 101 93 20 248 206 177 155 137 124 112 103 22 272 227 194 170 151 136 123 113 24 297 248 212 186 165 148 135 124 COTTON MANUFACTURING. 81 No. 13. — Continued. 126 Revolutions. DRIVEN PULLEYS. Driving Pulleys. 10 12 14 16 18 20 22 24 10 126 105 90 78 70 63 57 52 12 151 126 108 94 84 75 68 63 14 176 147 126 110 98 88 80 73 16 201 168 144 126 112 100 91 84 18 226 189 162 141 126 113 102 94 20 252 210 180 157 140 126 114 105 22 277 231 198 173 154 138 125 115 24 302 252 216 189 168 151 137 126 128 Revolutions. 10 128 106 91 80 71 64 58 53 12 153 128 109 96 85 76 69 64 14 179 149 128 112 99 89 81 74 16 204 170 146 128 113 102 92 85 18 230 191 164 144 128 115 104 96 20 256 213 182 160 142 128 116 106 22 281 234 200 176 156 140 127 117 24 307 255 219 192 170 153 139 128 130 Revolutions. 10 130 108 92 81 72 65 59 54 12 156 130 111 97 86 78 71 65 14 182 151 130 114 101 91 82 75 16 208 173 148 130 115 104 94 86 18 234 195 167 146 130 117 l06 97 20 260 216 185 162 144 130 118 108 22 286 238 204 178 158 143 130 119 24 312 260 223 195 173 156 141 130 The following table is calculated for factories situated in the Northern States — the column marked " Spindles/^ shows the number of spindles in the factory with looms, the column marked^" Tons/' shows the number of tons of Anthracite Coal consumed per year. The factories are supposed to be heated by steam. Example. Required, the number of tons of Anthracite Coal per year to heat a factory containing 2000 spindles with looms — find 5 82 MECHANICAL PRINCIPIA. 2000 in the column marked " Spindles," opposite to this number in the column- marked " Tons," will be found 32 tons ; this includes the coal required for making starch, and heating the dressing room. — Answer. Example. Required, the number of tons of Anthracite Coal per year to heat a factory containing 8000 spindles with looms — find 8000 in the column marked " Spindles," opposite to this number in the column marked " Tons," will be found 128 tons. — Answer. Spindles Tons. 1000 16 2000 32 3000 48 4000 64 5000 80 6000 96 7000 112 8000 128 9000 144 10000 160 The following table shows the number of cubic feet in the plain cylindrical return flue boiler required to heat fac- tories containing different number of spindles with looms. This table is predicated from those factories which consume the least amount of coal for a given number of spindles ; the column marked " Spindles," shows the number of spindles with looms which the factories contain. Example. A boiler is 3 feet in diameter and 13 feet long, the con- tents in cubic feet is 92, nearly what size factory will this boiler heat — find 92, or the nearest number to it in the column marked " Contents," opposite to this number in the COTTON MANUFACTURING. 83 column marked " Spindles," will be found 2000 spindles with looms. — Answer, Example. Required, the contents of a boiler to heat a factory con- taining 4000 spindles with looms — find 4000 in the column mai'ked " Spindles," opposite to this number in the column marked "Contents," will be found 184 cubic feet: if the diameter of this boiler was 2 feet, what would be the length, the area of the end of a boiler 2 feet in diameter is 3 feet nearly, divide 184 by 3, gives 61-J- feet, the length of the boiler, or two boilers say 30 feet each, and 2 feet in diame- ter. — Ansicer. Wo. 15. Spindles Contents. 1000 46 2000 92 3000 138 4000 184 5000 230 6000 276 7000 322 8000 368 9000 414 10000 460 The following table shows the number of operatives re- quired to operate different number of spindles, on different numbers of yarn with looms : this table is predicated from the statements in the Note (I.)— the column marked " Spin- dles," shows the number of spindles to be operated with looms, the column marked "No. of Yarn," shows the num- ber of the yarn. Example. Required, the number of operatives to operate 6000 spin- dles the number of the yarn being 35 — find 6000 in the 84 MECHANICAL PRlNCiriA. column marked Spindles," opposite to this number in the table, and under 35 in the column marked ''No. of Yarn," will be found 1G2 operatives, the number required to operate 6000 mule and frame spindles with looms on No. 35 yarn. — Answer. Example. Required, the number of operatives to operate 10000 spin- dles, the number of the yarn being 15 — find 10000 in the column marked " Spindles,'' .opposite to this number in the table, and under 15 in the column marked No. of Yarn," will be found 330 operatives. — Ansioer, No. ICI. Spindls. No. 5. No. 10. No. 15. No. 20. No. 25. No. 30. No. 35. No. 40. 1000 .36 35 33 32 30 29 27 26 2000 72 69 66 63 60 57 54 52 3000 i lOS 103 99 94 90 85 81 78 4000 i 144 138 132 126 120 114 103 104 5000 ! 180 172 165 157 150 142 135 130 6000 ! 216 207 198 189 180 171 162 156 7000 ; 252 241 231 220 210 199 189 182 8000 288 276 264 252 240 228 216 208 9000 324 310 297 283 270 256 243 234 10000 3G0 345 330 315 300 285 270 260 The following tables show the amount paid for labor per week, to operate different number of spindles with looms ; and the amount paid per week, including all expenses except the cost of cotton, to operate different number of spindles witli looms on different number of yarn. Example. Required, the amount paid per week including all ex- penses except the cost of cotton, to operate 4000 spindles with looms on No. 30 yarn — find 4000 in the column marked Spindles," opposite to this number in the table, and under " No. 30," will be found 550 (hWav^.—Ansirer. COTTON MANUFACTURING. 85 Example . Required, the amount paid per week for labor, to operate 2000 mule and frame spindles on No. 30 yarn with looms — find 2000 in the column marked " Spindles," opposite to this number in the table, and under No. 30," will be found 204 dollars. — Ansiver, No. 17. Amount Paid per Week, Lncluding all Expenses except the cost OF Cotton. Spindls. No. 5. No. 10. No. 15. No. 20. No 25. No. 30. No. 35. No. 40. 1000 174 167 160 153 146 139 132 124 2000 348 334 320 306 292 278 264 249 3000 522 501 480 459 438 417 396 373 4000 696 668 640 612 584 556 528 498 5000 870 835 800 765 730 695 660 622 6000 1044 1002 960 918 876 834 792 747 7000 ]218 1169 1120 1071 1022 973 924 871 8000 1392 1336 1280 1224 1168 1112 1056 996 9000 1566 1503 1440 1377 1314 1251 1188 1120 10000 1740 1670 1600 1530 1460 1390 1320 1245 Amount Paid to Operatives per Week. Spindls. No. 5. No. 10. No. 15. No. 20. No. 25. No. 30. No. 35. No. 40. lUOO 130 124- 119 113 108 102 96 91 2000 260 248 238 226 216 204 192 182 3000 390 372 357 339 324 306 288 273 4000 520 496 476 452 432 408 384 364 5000 650 620 595 565 540 510 480 455 6000 780 744 714 678 648 612 576 546 7000 910 868 833 791 756 714 672 637 8000 1040 992 952 904 864 816 768 728 9000 1170 1116 1071 1017 972 918 864 819 10000 1300 1240 1190 1130 1080 1020 960 910 The following table shows the cost per pound, for manu- facturing different numbers of yarn from different prices of cotton — the column marked " No. Yarn," shows the number of yarn, the column marked Hanks," shows the 86 MECHANICAL PRINCIPIA. number of hanks per spindle the frames are supposed to turn off per day, the column marked Price of Cotton/' shows the range of the cost of the same quality of cotton ; this table is calculated for a mill of 2000 frame spindles, either the cap frame, or the dead spindle frame, or the ring and traveler frame. (See Note H.) No. 1§. No. Yarn Hanks. o "X) CO 00 ^ cn _oi CO CO JS2 j-i j:^ ^ O 4^ ^1 O CO '--T to*— 'O0>--Ovj^a:co ) CO CO -a I O 4^ ^ . OO I-' F-* ^ Oi Oi Oi CO to to iO CO CO CO CO CTi CO 5 O bo 05 lo CTS bo io Cr« CO -|-'^oo^o^-'a:^2oo^oa5io ) 00 05 OS > io cn 00 io ) JO M) 00 CO Cn jpi" CO 00 t--. 05 iO M) to M) 1 CO to to h- ,c > CO 00 05 05 Cn 4^ I bo 'k- 0^ bo o *4i^ ^ h-- 'tOlOGO^i^^OO: — ? CO GO 00 ^ ' 4^ O 4^ :) to to -5 1— ' 05 en 4^ 05 CO CO ^ 05 CO 05 K-" K- 5 O CO 00 00 3 O CO 05 O :)tOK-05i-'Cnooo5i-' ^ 05 Cn to Cr» CO CO to to 4^ CO O CO 4^ 4^ to to to to to 05 O CO 05 CO to O CO CO 00 05 CO to CT5 to to 00 to ^ ^ 05 Cn ) to to t ( 4^ CO C > to cn bo to i ? to I— 00 ( - ' 5 00 •<» ^ 05 I— Example. Required, the cost per pound to make number 20 twist, when the cotton is worth 10 cents — find 20 in the column marked No. of Yarn," opposite to this number in the table, and under 10 in the column marked Price of Cotton," will be found 18.01 cents per pound. — Aiisiver, COTTON MANUFACTURING. 87 Example. Requiredj the cost per pound to make No. 28 twist, when cotton is worth 8^ cents — find 28 in the column mark- ed " No. Yarn,'^ opposite to this number in the table, and ynder 8^ in the column marked " Price of Cotton/' will be found 18.92 €ents per pound. The following tables show the cost per yard for manu- facturing different styles of goods — the column marked No. 19. Wdth No. Yarn O05*000»fs^CX)>|S>.00rfi.O Filng Warp t;^ooooooooo Wt. CJOi—ooOGOCnOOtnai OS Id bo I;^. I-* bo ^ bo io cn - "00 tn CO 05 05 00 O O • ^ OJ 05 05 ;Cn Crt C5 • 0 CD Cn CO CD O ii^ ^ 01 ZO CD lo a^-^ OD ejx 4^ ' bot-'J-'^ii^OH-'io^CD C;iCDCOWOOC;iOO^OOO eDCojoboOTJ-'Ooji^cDjo 00 'h-* '4:^ CO io CTi hi iz) If^ ■ •"-■crTi— oootooooocn 00 00-^-i-'-<^ooaooooi:oa5-cnoo 0 05 CD 0 Cri tji^ 'to OO^CJOW(^::>.CO^^».OOOiO■ 0 H-j iJi>.00rf^00Kj^O Filng <^ Jv'^ Cr> ilii. .K (~\ /-rs iK 1>5 J iw ^^m^ ^ J rr^ *-v Warp ('Y^ or^ (nr\ (Tl^ lTv KJJ W (JJ KJJ SArf "iLi^ Wt. 00 ZJX to >— ' CO CO Co OO^O4i^00OCr*l04^ I—* to CT> Co CO O" I—* CJT 00 ►fs-OOOH-'CS^rfi^OOlO K>|M 00 k) o ^ H-" J-' OS o 0:»t0COJN2aD00 00tn00O ^qa^OiO^Cn O^tnC^Cr^pi ocojsijbccTsjocotfxboh-' ^StOOCOO-^liOOCrsOO Uiji».C0C0^C04:».btOC0 00 ^o^CiOiCnc/itntnastrt Kobihf^obOhl^CTi^kjCn l--'COJOCn4i^Cr«OOJ04:i. 00 4i»-CnCoa5a54i>.*ii.C.nOJs3 I^^c^Ksob^ooobibo a54:i.»;:i.^OOCOOOOOOCO CO ;>cr5COlO(-'a50M)Cr» o OOOCOOjiip^COCojs'f-'ifi^ til C04^-<}Off^OOCAOC0j ^ COTTON MANUFACTURING. 89 Example. The number of the yam being 31, the number of picks in the filling and warp being 64 and 60 per inch, the weight of the goods being 5.8 yards per pound, the width of the goods being and the cost of the cotton being 8 cents, re- quired, the cost per yard — find 31 in the column marked No. Yarn," opposite to this number in the table, and under 8 in the column marked Price of Cotton," will be found 4.68 cents per yard, the total cost of manufacturing. — Answer. Wo. 21. to Wdth *^tOtOCOtCJs3iOi-*i-Jt— ' iSo. j Yam Warp tntnOiCntnOitnhfi-COf^ Wt. C-«^*^i4i'4^tOaJ4^(4i^to in CD ^ br ho io io ho 'cn io OS rf^ I—* 00 Co O O 4^ 1—' jo CO '---1 h-i H-i cri CO io H-i^COtnCiKl^CO^Oi^ as ^COh-'CoinjoCO^h-'ifs- COO^Otn-^ClOr— tOff^ Oi Oi hf^ o-i bo 10 b:> ic bo Iz) 'a:> OitOf— ►f^GO'-li-'OiCOl— ' 00 COOitOO^iji-OlCoI^^I ^arf^tOtnCOCrrlOCOC^iOO 00 loH ob^^;^^-'COt^c^i^— 'OlCO COCOOOi^i.Ohfi-COCOtOtn CO CO 4i>.c;iOiht^is2toc/»h-'' o b^obobicocoob^toCTi 5* 90 MECHANICAL PRINCIPIA. The foUowino; table shows the number of revolutions of the front roller per minute on different kinds of spinning ma- chines — the column marked " No. Yarn," shows the num- ber of the yarn, the columns marked Cap, Dead, Ring, Live, and Mule Spindles," shows the different kinds of spinning. Example. Required, the number of revolutions per minute of the front roller on the cap frame to spin No. 20 yarn — find 20 in the column marked No. Yarn," opposite to this num- ber in the column marked " Cap Spindles," will be found 100 revolutions. — Answer. Example. Required, the 'number of " Stretches " a self-operating mule will make per minute on No. 35 yarn — find 35 in the column marked " No. Yarn," opposite to the number in the column marked ''Mule Spindles," will be found 2f- stretches. — Answer, Mo. 22. No. Yarn. Cap Spindles Dead Spindles Ring Spindles Live Spindles Mule Spindles 5. 100 80 3 10 1 90 75 3 15 1 110 85 85 70 3 20 1 100 80 80 68 3 25 96 78 78 65 3 30 90 75 75 62 25 35 72 72 60 2i 40 i 68 68 56 2| The following table shows the range of drafts and doub- lings, which are preferred by different manufacturers. Example. Required, the range of draft that a card may have — find " Card," in the column marked machine, opposite, in the COTTON MANUFACTURING.' — V-^ column marked "Draft," will be found 40 to 80 draft, tins shows that some manufacturers draw 40 to 1, while otjieife draw 80 to 1. — Answer, /-^ I Example. - Required, the range of doublings on the drawing frame — find " Drawing," in the column marked " Machines," opposite in the column marked " Doublings," will be found 64 to 212 doublin2:s. — Answer. No. 23. Machines. Drafts. Doublings. Picker 1 to 2 1 to 3 Card 40 to 80 40 to 60 R. R. Head 2 to 5 4 to 10 Each Head Three Heads Drawing 4 to 8 64 to 216 Speeder 5 to 8 (C it Fine Ditto 6 to 8 1 to 2 Mule Filling 8 to ]1 <( U Frame Warp 7 to 9 Ct 4( The column in the following table marked Revolutions," shows the number of revolutions of the froRt roller per minute, the column marked Hours," shows that the frame is cal- culated to run 12 hours without stopping, the column mark, ed " Skeins," shows the number of skeins which the frame will turn off. Mo. 24. Revolus. Skeins. Hours. Revolus. Skeins. Hours. 50 3.5 12 90 63 12 55 3.8 12 95 66 12 60 42 12 100 7.0 12 65 4.5 12 105 7.3 12 70 4.9 12 110 7..7 12 75 5.2 12 115 8.0 12 80 5.6 12 120 8.4 12 85 5.9 12 125 8.7 12 92 MECHANICAL PRINCIPI^. Example. Required, the number of skeins that a frame will turn off in 12 hours, the front roller making 80 turns per minute — find 80 in the column marked " Revolutions," opposite to this number in the column marked " Skeins," will be found 5.6 skeins. — Answer. The following table shows the twist required per inch for different numbers of yarn — the column marked No. Yarn," shows the number of the yarn, the column marked ^' Filling," shows the twist required per inch for filling, the column marked " Warp," shows the twist per inch required for warp. Example. Required, the twist per inch for No. 20 filling — find 20 in the column marked " No. Yarn," opposite to this num- ber in the column marked "Filling," will be found 16 turns per inch, the twist required. — Answer. Example. Required, the twist per inch for No. 20 warp — find 20 in the column marked " No. Yarn," opposite to this num- ber in the column marked " Warp," will be found 19 turns per inch, the twist required. — Ansiver, IVo. 25. No. Yrn. Filling. Warp. No. Yrn. Filling. IWarp, 5 8 9.5 25 18 21 8 10 12 28 20 23 10 11 14 30 21 25 14 13 16 33 23 26 16 14 17 36 24 28 18 15 18 38 25 29 20 16 19 40 27 30 22 17 20 COTTON MANUFACTURING. 93 The following table shows the twist required for different numbers of roving. Example. Required, the twist per inch for No. 4 roving — find 4 in the column marked " No. Roving," opposite to this number in the column marked " Twist," will be found 2 turns per inch. — Answer, Example. Required, the twist per inch for No. 2^ roving — find 2.5 in the column marked " No. Roving," opposite to this num- ber in the column marked Twist," will be found 1.6 twist per inch. — Answer, The twist required for different No. of yarn and roving represented in these tables, has been collected from some of the best operating factories in the country. Mo. 26. No. Rvg Twist. No. Rvg Twist. 0.1 1.0 4.0 2.0 1.5 1.2 4.5 2.1 * 2.0 1.4 5.0 2.2 2.5 1.6 6.0 2.5 3.0 1.7 7.0 2.7 3.5 1.9 The following table shows the number of yards a loom would turn off per day (in 12 hours) if the loom did not stop during the 12 hours or day. The column marked " Picks," shows the number of picks the loom runs per minute, the column marked Thread," shows the number of thread or picks of filling per inch, the column marked " Yards," shows the number of yards the loom would turn off in 12 hours. 94 MECHANICAL TRINCIPIA. Example. Required, the number of yards turned off per day, the number of picks per inch in the filling being 72 — find 72 in the column marked Threads," opposite to this number in the column marked "Yards," will be found 31 yards. — Answer. Example. Required, the number of yards turned off per day, the number of picks per inch in the filling being 64 — find 64 in the column marked Threads," opposite to this number in the column marked "Yards," will be found 35 yards. — Answer. No. 27. Picks. Threads. Yards. Hours. 112 30 74 12 (( 38 59 12 tc 40 56 12 « 44 50 12 50 45 12 (( 56 40 12 60 37 12 (( 64 34 12 68 32 12 i< 72 30 12 it 76 29 12 (( 80 28 12 Several lots of difierent qualities of cotton were run through the pickers and cards and the per cent waste noted. From these experiments, together with the information ob- tained from the factories working the different qualities of cotton, the following table is predicated. The column mark- ed " Price," shows the price of the cotton, that is, when the best quality of short staple cotton is worth 10 cents per pound, the poorest quality will be worth 7^ oents per pound. COTTON MANUFACTURING. 95 Example. Required, the per cent loss of the poorest quality of short staple cotton when spun into yarn — find 7-J- in the column marked " Price," opposite to this number in the column marked Per Cent," will be found 15 per cent loss. — Answer. Example. When the best quality of short staple cotton is worth 10 cents per pound, what per cent loss will there be in a qual- ity which is worth 8^ cents — find 8^ in the column marked " Price," opposite to this number in the column marked " Per Cent," will be found 12^ per cent waste. — Answer. No. 2§. Per Cent Price. 10 10 104 94 Hi 9 m 84 13i 8 15 74 The following table shows the number of gallons of oil required for difierent number of spindles per day, (for ma- chinery only,) — the column marked ^' Gallons," shows the number of gallons required per day, the column marked Spindles," shows the number of spindles. Example. A factory contains 6000 spindles with looms ; required, the number of gallons of oil to supply the factory per day — find 6000 in the column marked Spindles," opposite to this number in the column marked " Gallons," will be found 4 gallons. — Answer. 96 MECHANICAL PRINCIPIA. Example. Required, the number of gallons of oil to supply a factory of 2000 spindles with looms for 100 days— find 2000 in the column marked " Spindles," opposite to this number in the column marked " Gallons," will be found If gallons, which multiplied by 100 gives 125 gallons. — Answer. No. 29. Spindles Gallons. 1000 i 2000 3000 2 4000 24 5000 34 6000 4 7000 4i 8000 5i 9000 51 10000 64 The following table shows the number of revolutions per minute of the front roller on different kinds of roving frames — the column marked No. Roving," shows the number of roving. Example. ' Required, the number of revolutions per minute of the front roller on the non-twisting or condensing speeder making No. 2 roving — find 2 in the column marked " No. Roving," opposite to this number in the column marked " Non-twist- ing Speeder," will be found 450 revolutions per minute. — Answer. Example. Required, the number of revolutions of the front roller per minute on the twisting speeder on No. 4 roving — find 4 in the column marked " No. Roving," opposite to this num- COTTON MANUFACTURING. 97 ber in the column marked " Twisting Speeders," will be found 165 revolutions. — Ansioer, Example. Required, the number of revolutions of the front roller per minute on the fly frame on No. 4 roving — fmd 4 in the column marked " No. Roving," opposile to this number in the column marked Fly Frame," will be found 118 revolutions. — Ansiver, Mo. 30. No. Roving. Non-tvvistg Speeders. Twistng Speeders Fly Frame. i| 450 200 140 190 135 2 185 130 2i 180 128 3 175 125 34 170 120 4 165 118 44 160 116 The following tables show the usual amount of yarn turned off per day by the different kinds of spinning. Example. Required, the number of pounds of No. 8 yarn that 2000 dead spindles will turn off per day — find 8 in the column marked No. Yarn," opposite to this number in the table, and under 2000 in the column marked No. Spindles," will be found 1236 pounds, the amount turned off per day. — Answer. Example. Required, the number of pounds of No. 86 yarn that 3000 mule spindles will turn off per day — find 36 in the column marked ^^No. Yarn," opposite to this number in the table, 98 MECHANICAL PRINCIPlA. and under 3000 in the column marked No. Spindles," will be found 270 pounds. — Answer, No. 31. No. Spindles. Live Spindle Frames. i> o. Yarn. 500 1000 1500 2000 2500 3000 3500'4000 1 5 450 900 1350 1800 2250 2700 31503600 8 278 556 834 1112 1390 1668 1946 2224 10 219 438 657 876 1095 1314 1533 1752 12 178 356 534 712 890 1068 1246 1424 14 151 302 453 604 755 906 10571208 16 129 258 387 516 645 774 903 1032 18 113 226 339 452 565 678 791 904 20 101 202 303 404 505 606 707 808 22 90 180 270 360 450 540 630 720 25 79 158 237 316 395 474 553 632 28 69 138 207 276 345 414 483 552 30 63 126 189 252 315 378 441 504 33 56 112 168 224 280 336 392 448 36 51 102 153 204 255 306 357 408 40 45 90 135 180 225 270 315 360 No. 32. No. Spindles. Mules. No , Yarn. 500 1000 1500 2000 2500 30003500 4000 5 400 800 1200 1600 2000 2400 2800 3200 247 494 741 988 1235 14821729 1976 10 1 195 390 585 780 975 1170 1365 1560 12 158 316 474 632 790 948 1106 1264 14 134 268 402 536 670 804 938 1072 16 115 230 345 460 575 690 805 920 18 101 202 303 404 505 606 707 808 20 90 180 270 360 450 540 630 720 22 80 160 240 320 400 480 560 640 25 70 140 210 280 350 420 490 560 28 61 122 183 244 305 366 427 488 30 56 112 168 224! 280 336 392 448 33 50 100 150 200 250 300 350 400 36 45 90 135 180 225 270 315 360 40 40 80 120 160 200 240 280 320 Example. Required, the number of pounds of No. 16 yarn that 2000 cap spindles will turn off per day — find 16 in the col- COTTON MANUFACTURING. 99 umn marked No. Yarn," opposite to this number in the table, and under 2000 in the column marked No. Spin- dles," will be found 848 pounds. — Answer, IVo. 33. No. Spindles. Cap, or Danforth's Frame- No. Yarn. 500 1000 'l500 '2000[2500 3000 3500 4000 14 250 500 750 1000 1250 1500 1750 2000 16 212 424 636 848 1060 1272 1484 1696 18 183 366 549 732 915 1098 1281 1464 20 160 320 480 640 800 960 1120 1280 22 141 282 423 564 705 846 987 1128 25 120 240 360 480 600 720 840 960 28 103 206 309 412 515 618 721 824 30 .93 186 279 372 465 558 651 744 No. 34. No. Spindles. Dead Spindle Frame. No. Yarn. 500 1000 1500 20002500 3000 3500 4000 5 500 1000 1500 2000 2500 3000 3500 4000 8 309 618 927 1236 1545 1854 2163 2472 10 244 488 732 976 1220 1464 1708 1952 12 197 394 591 788 985 1182 1379 1576 14 167 334 501 668 835 1002 1169 1336 16 144 288 432 576 720 864 1008 1152 18 126 252 378 504 630 756 882 1008 20 112 224 336 448 560 672 784 896 22 100 200 300 400 500 600 700 800 25 88 176 264 352 440 528 616 704 28 76 152 228 304 380 456 532 608 30 70 140 210 280 350 420 490 560 33 62 124 186 248 310 372 434 496 36 56 112 168 224 280 336 392 448 40 50 100 150 200 250i 300 350 400 Example. Required, the amount of No. 25 yarn that 4000 ring spindles will turn off per day — find 25 in the column marked " No. Yarn," opposite to this number in the table, and under 4000 in the column marked " No. Spindles," will be found 704 pounds. — Answer, MEOflANlCAL rRlNCIPlA. No. 35. No. Spindles. Ring Spindle Frames. No. Yarn. 500 1000 1500 20002500 i 3000 3500 4000 1 fl7 1 u < 004: 501 668. 835 1 009 1 1 loo yj 16 144 288 432 576 720 864 1008 1152 18 126 252 378 504 630 756 882 1008 20 112 224 336 448 560 672 784 896 22 100 200 300 400 500 600 700 800 25 88 176 264 352 440 528 616 704 28 76 152 228 304 380 456 532 608 33 70 140 210 280 350 420 490 560 30 62 124 186 248 310 372 434 496 36 56 112 168 224 280 336 3:)2 448 Example. Required, the amount of No. 30 yarn that 2000 live spindles will turn off per day — find 30 in the column mark- ed " No. Yarn,'' opposite to this number in the table, and under 2000 in the column marked No. Spindles," will be found 252 pounds. — Answer, The following table shows the usual number of pounds that f yard wide looms will weave per day on different num- bers of yarn. A ^ loom will turn off iV? and a ^ loom more than a -f- loom per day: the column marked Threads," shows the number of threads or " Picks " in the filling per inch, the column marked " No. of Looms," shows the num- ber of looms required to produce the amount in the table. Example. Required, the number of pounds of goods that 50 looms will weave per day, the number of picks in the filling per inch being 64 — find 64 in the column marked Threads," opposite to this number in the table, and under 50 in the column marked " Looms," will be found 250 pounds. — Answer, COTTON MANUFACTURING. 101 If they were f looms the production would be which gives 16 pounds nearly, which added to 250 gives 266 pounds. If they were looms the production would be -^i^/-, which gives 21 pounds nearly, which added to 250 gives 271 pounds. EXABIPLE. Required, the number of pounds of goods that 30 looms will weave per day, the number of picks in the filling per inch being 30 — find 30 in the column marked " Threads," opposite to this number in the table, and under 30 in the column marked " Looms," will be found 750 pounds. — Answer, Mo. 36. No. OF Looms on | Goods. Thrds 20 30 40 50 60 70 80 90 100 30 500 750 1000 1250 1500 1750 2000 2250 2500 38 280 420 560 700 840 980 1120 1260 1400 40 200 300 400 500 600 700 800 900 100 44 180 270 360 450 540 630 720 810 900 50 140 210 280 350 420 490 560 630 700 58 120 180 240 300 360 420 480 540 600 .50 112 168 224 280 336 392 448 504 560 64 100 150 200 250 300 350 400 450 500 68 94 141 188 235 282 329 376 423 470 72 90 135 180 225 270 315 360 405 450 76 80 120 160 200 240 280 320 360 400 80 70 105 140 175 210 245 280 3!5 350 The following table shows the usual number of picks per minute of looms weaving different width of goods and differ- ent numbers of yarn; the column marked No. Yarn," shows the number of the yarn^ the column marked " Width," shows the width of the goods. ~ Example. Required the number of picks per minute of a loom, weaving No. 25 yarn — find 25 in the column marked *^No. 102 MECHANICAL PKINCIPIA. Yarn," opposite to this number in the table, and under J in the column marked ^' Width," will be found 112 picks per minute. — Answer, Example. Required, the number of picks per minute of a f loom, weaving No. 10 yarn — find 10 in the column marked "No. Yarn," opposite to this number in the table, and under | in the colum'n marked "Width," will be found 112 picks per minute. — Answer. No. 8T. WIDTH. No. Yarn. 3-4 7-8 4-4 5 110 98 96 10 108 106 104 15 118 116 114 20 114 112 110 25 112 110 108 30 112 110 108 36 110 108 106 Note H. The tables showing the cost per pound for manufacturing different No. of yarn from different prices of cotton, was pre- dicated from the following estimates. An estimate showing the cost per pound for manufacturing No. 12 twist or warp yarn, the price of the cotton being 6 cents per pound. The factory is supposed to contain 2000 framo spindles ; the cap or Danforth frame, or the dead spindle frame, or the ring and traveler frame ; as it is found by a very accurate cal- culation, that the cost per pound for manufacturing on these frames does not differ materially. The cost of manufactur- ing on the live spindle frame is found by a calculation predi- COTTON MANUFACTURING. 103 cated upoil actual results, to exceed the cost of manufacturing on the foregoing frames about 7 per cent per pound. 2 Card Strippers 2.50 5.00 6 Drawing Tenders 2.50 (C 15.00 1 Speeder Tender 3.00 6( 3.00 2 Fine do. Tenders 3.00 C6 6.00 1 Sweeper 2.00 iC 2.00 1 Card Grinder 5.00 (C 5.00 1 Overseer 8.00 a 8.00 12 Frame Piecers 2.50 a 30.00 4 Ditto Doffers 2.50 cc 10.00 6 Reel Tenders 2.50 ii 15.00 1 Second Overseer 3.00 cc 3.00 1 Overseer 8.00 cc 8.00 1 Yarn Bundler 3.00 cc 3.00 1 Ditto Baler 4.00 cc 4.00 1 Ditto Repairer 6.00 cc 6.00 1 Watchman 7.00 cc 7.00 1 Clerk 8.00 cc 8.00 1 Manager 15.00 15.00 Insurance say 10.00 Fires cc 4.00 Oil cc 12.00 Freight and Cartage cc 15.00 Ordinary Repairs cc 10.00 50.00 66.00 43.00 7058 Pounds of Cotton, (15 per cent waste gives 6000 Pounds of Yarn the produc- tion per week) at 6 cents per pound gives 423.00 474.00 6000)633.00 $633.00 10.55 cents the cost per pound. 104 MECHANICAL PRINCIPIA. It will be observed that all ordinary expenses are inclu- ded in this estimate except commission and cost of power. The value of the waste, which amounts to about 20 dollars per week, will probably fully cancel those small incidental expenses which have not appeared in detail in the estimate. An estimate showing the cost per pound for manufactur- ing No. 40 twist or warp yarn, the price of the cotton being 6 cents per pound. 1 Picker Tender i ^3.00 per week each $3.00 1 Card Stripper 4.00 u 4.00 1 Lap double Tender 2.00 6( 2.00 2 Drawing Tenders 2.50 6i 5.00 1 Speeder Tender 2.00 C( 2.00 1 Fine do. Tender 3.00 i( 3.00 1 Sweeper 2.00 2.00 1 Second Overseer 5.00 (i 5.00 1 Overseer 8.00 a 8.00 9 Frame Piecers 2.50 a 22.50 2 Ditto Doffers 2.50 u 5.00 4 Reel Tenders 2.50 cc 10.00 1 Second Overseer 3.00 a 3.00 1 Overseer 8.00 u 8.00 1 Yarn Baler 4.00 a 4.00 1 Repairer 6.00 (C 6.00 1 Watchman 7.00 7.00 1 Clerk 6.00 a 6.00 1 Manager 15.00 (C 15.00 Insurance say 6.00 Fires 3.00 Oil 6.75 Freight and Cartage U 5.00 Ordinary Repairs U 8.00 34.00 48.50 38.00 COTTON MANUFACTURING, 105 1230 Pounds of Cotton (12 per cent waste gives 1063 pounds of yarn the produc- tion per week,) at 6 cents per pound gives 63.78 92.53 $ 213.03 1062)213.03 20.04 cents cost per pound. Note L An estimate showing the cost per yard for manufacturing yard- wide goods, the yarn being No. 14 ; the number of threads per inch in the warp being 42 ; the number of threads per inch in the filling being 40 ; the weight of the goods being three yards per pound ; and the price of the cotton being 6 cents per pound. The factory is supposed to contain 2000 spindles, 1111 mule spindles, producing 4 hanks per spindle per day, and 889 frame spindles, producing 5 hanks per spindle per day, and 56 yard-wide looms. 2 Picker Tenders $2.50 per week each $5.00 2 Card Strippers 2.50 5.00 6 Drawing Tenders 2.00 cc 12.00 1 Speeder Tender 2.50 u 2.50 2 Fine do. Tenders 2.50 6i 5.00 1 Sweeper 2.00 iC 2.00 1 Card Grinder 4.00 CC 4.00 1 Overseer 8.00 « 8.00 5 Frame Piecers 2.50 cc 12.50 2 Frame Doffers 2.00 cc 4.00 2 Mule Piecers 2.50 cc 5.00 2 Ditto 2.00 cc 4.00 2 Ditto 1.50 cc 3.00 1 Mule Doffer 2.50 a 2.50 43.50 6 106 MECHANICAL rRINCiriA. 5.00 3.00 14.00 8.00 61.00 370 Cuts at 18 cts. (one extra Weaver at 3.40) 70.00 2 Reeders 2.50 cc 5.00 2 Cloth Trimmers 2.50 16 5.00 1 Cloth Baler 3.00 6i 3.00 1 Overseer 8.00 C( 8.00 1 Repairer 8.00 i( 8.00 1 Watchman 7.00 66 7.00 1 Clerk 8.00 66 8.00 1 Manager 20.00 66 20.00 Insurance say 15.00 Fires 66 5.00 Oil 66 15.00 Freight and Cartage 66 12.00 Ordinary Repairs 66 16.00 Shuttles, Harnesses, Reeds, Starch, &c. " 19.00 4608 Pounds of Cotton (18 per cent waste 91.00 43.00 gives 3779 pounds of yarn, or 11337 yards of goods per week ; the produc- tion of 2000 spindles, and 56 looms per week,) at 6 cents per pound gives 276.48 358.48 $ 596.98 11337)596.98 5.26 cents per yard. An estimate showing the cost per yard to manufacture yard- wide goods the number of the yarn being 40 ; the num- ber of thread per inch in the filling being 80 ; the number of 2 Spooler Tenders 2.50 1 Warper Tender 3.00 2 Dresser Tenders 7.00 1 Overseer 8.00 COTTON MANUFACTURING. 107 threads in the warp being 76 per inch ; and the weight of the goods being 4.25 yards per pound. The factory is sup- posed to contain 2000 spindles, 1037 mule spindles producing 3-J- hanks per spindle, per day ; and 963 frame spindles pro- ducing 3^ hanks per spindle, per day ; 50 yard-wide looms ; the price of the cotton being 6 cents per pound. 1 Picker Tender $3.00 pel weeK eacn 1 Card Stripper 3.00 a 1 Lap doubler Tender 2.00 a 9 on 2 Drawing Tenders 2.00 u d on 1 Speeder Tender 2.00 a 1 Fine do. Tender 2.50 (6 2.50 1 Overseer 8.00 6( 8.00 2 Mule Piecers 2.50 cc ^ nn 2 Ditto 2.00 a A nn 2 Ditto 1.50 n O A A O.UU 4 Frame Piecers 2.50 6C 10.00 2 Frame DofFers 2.00 (C 4.00 2 Spooler Tenders 2.50 i( 5.00 1 Warper Tender 2.50 6i 2.50 2 Dresser Tenders 7.00 & 3.00 " 10.00 1 Overseer 8.00 Ci 8.00 17 Weavers 3.50 (C 59.50 2 Reeders 2.00 ic 4.00 1 Cloth Trimmer 2.50 (C 2.50 1 Cloth Baler 3.00 cc 3.00 1 Overseer 8.00 cc 8.00 1 Repairer 6.00 cc 6.00 1 Watchman 7.00 cc 7.00 1 Clerk 6.00 cc 6.00 1 Manager 15.00 cc 15.90 24.50 51.50 77.00 34.00 108 MECHANICAL PRINCIPIA. Insurance .... say Fires " Oil Freight and Cartage ... Ordinary Repairs ... Shuttles, Harnesses, Reeds, Starch, &c. 1188 Pounds of Cotton (15 per cent waste gives 1010 pounds of yarn, or 4292 yards the production per week of 2000 spindles) at 6 cents per pound gives 4292)320.28 7.46 cents cost per yard. On this style of goods a weaver will turn off nearly as many yards per day on two looms as on three, hence it would not required over 40 looms for 2000 spindles on this style of goods. Note P. The cost of the factories represented in the table which refers to this note, is based upon the modern style of building, the principal features of which are as follows : The thicknesses of the several brick walls are — the first story 20 inches, the second story 16 inches, the third and fourth stories 12 inches : the heights of the several ceilings in the clear are — the first story 12 feet, the second story 11 feet, the third and fourth stories 10 feet. The large girders are placed from 7 to 8 J- feet apart, the floors are laid with two 1^ plank and one 3 inch plank ; the windows are placed from 7 to S\ feet apart and generally contain 24 lights 8 by 10 ; fire-proof roof, generally tin ; the stair-case or entrance 12.00 4.00 12.00 8.00 12.00 14.00 71.28 133.28 $ 320.28 COTTON MANUFACTURING. 109 detached from the factory, which is generally 16 by 18 feet; brick are supposed to be worth 4^ dollars per thousand de- livered on the site ; the cost of different kinds of lumber is predicated upon the usual prices in the city of New York ; the cost of the foundation up to the water sill is not included in these estimates. BELTING. BELTING. The following table shows the velocity of belts — the column marked Revolutions Shaft/' shows the number of revolutions v/hich the line or driven shaft is supposed to make per minutej the column marked " Diameter Drum," shows the diameter of the drum on the line or driven shaft. Example. The line shaft is required to make 120 turns per minute, and it is desired to have the belt run 1800 feet per minute; required, the diameter of the driven drum — find 120 in the column marked Revolutions Shaft,'^ opposite to this num- ber in the table find 1800, or the nearest to it, which is 1884 feet, over this number in the column marked " Diameter Drum,'' Vv'ill be found 5 feet, the diameter of the drum. — Ansiver. Example. The line shaft makes 100 turns per minute, the diameter of the driven drum is 4 feet ; required, the number of feet the belt moves per minute—find 100 in the column miarked Revolutions Shaft," opposite to the number in the table, and under 4 in the column marked Diameter Drum," will be found 1256 feet, — Ansiver. 6* 114 MECHANICAL PRINCIPIA. No. 1. Revolutions Shaft. DIAMETER DRUM. 2 3 3i 4 5 6 100 / OO 1099 1256 1413 lo /U 1 /J / 1884 110 690 863 1036 1208 1381 1554 1727 1899 2072 120 753 942 1130 1318 1507 1695 1884 2072 2260 130 816 1020 1224 1428 1632 1836 2041 2245 2449 140 879 1099 1318 1538,1758 1978 2198 2417 2637 150 942 1177 1413 16481884 2119 2355 2590 2826 160 1004 1256 1507 1758 2009 2260 2512 2763 3014 170 1067 1334 1601 1868 2135 2402 2669 2935 3202 180 1130 1413 1695 1978 2260 2543 2826 3108 3391 190 1193 1491 1789 2088 2386 2684 2983 3281 3579 200 1256 1570 1884 2198 2512 2826 3140 3454 3768 The following table shows the required width of belts to transmit different number of horse power. The apparent de- gree of accuracy in this table is not obtained for any practi- cal use, but to show the theoretical power of belts ; when the belts exceed 12 inches in width the fractions may be omitted. This table is predicated upon the velocity of the belts being from 25 to 30 feet per second, which is the ordinary velocity ; if the power to be transmitted exceeds 20 horse, and cir- cumstances will not allow the centre of the drums to be over 15 feet apart, the power should be transmitted by gearing. (See Note E.) Example. Required, the width of a belt to transmit 20 horse power from a water wheel, the diameter of the smallest drum being 6 feet — find 20 in the column marked Horse Power,'' opposite to this number in the table, and under 6 in the col- umn marked Diameter," will bo found 12 inches, the width of the belt-— Answer, BELTING. 115 Example, Required, the width of a belt to transmit 100 horse power from an engine, the diameter of the smallest drum being 5 feet — find 100 in the column marked " Horse Power," op- posite to this number in the table, and under 5 in the column marked Diameter," will be found 72 inches, which can be divided into four 18 inch belts or any desired width. — Answer, No. 2, DIAMETER. II 2 3 4 5 6 7 8 9 10 1 1.8 1.2 0.9 0.72 0.6 0 514 0.45 0.4 0.36 2 3.6 2.4 1.8 1.44 1.2 1028 0.90 0.8 0.72 3 5.4 3.6 2.7 2.16 1.8 1-542 1.35 1.2 1.08 4 7.2 4.8 3.6 2.88 2.4 2056 1.80 1.6 1.44 5 9.0 6.0 4.5 3.60 3.0 2-570 2.25 2.0 1.80 6 10.8 7.2 54 4 32 3.6 3 084 2 70 2.4 2.16 7 12.6 8.4 6.3 5.04 4.2 3-598 3.15 2,8 2.52 8 14.4 96 7.2 5.76 4.8 4112 3.60 3.2 2.88 9 16.2 10.8 8.1 6.48 5.4 4-626 4.05 3.6 3.24 10 18.0 12.0 90 7.20 6.0 5-140 4.50 4.0 3.60 12 21.6 14.4 10.8 8.64 7.2 6168 5.40 4.8 4.32 14 25.2 16.8 12.6 10.08 8.4 7-196 6.30 5.6 5.04 16 28.8 19.2 14.4 11.52 9.6 8-224 7.20 6.4 5.76 18 32.4 21.6 16.2 12.96 10.8 9-252 8.10 7.2 6.48 20 36.0 24.0 18.0 14.40 12.0 10-280 9.00 8.0 7.20 25 45.0 30.0 22.5. 18.00 15.0 12-850 11.25 lO.O 9.00 30 540 36.0 27.0 21.66 18.0 15 420 13 50 12.0 10.80 35 63.0 42.0 31.5 25.20 21.0 17-990 15 75 14.0 12.60 40 72.0 48.0 36.0 28.80 24.0 20 560 18.00 16.0 14.40 45 81.0 54.0 40.5 32.40 27.0 23-130 20.25 18.0 16.20 50 90.0 60.0 45.0 36.00 30.0 25-700 22.50 20.0 18.00 55 99.0 66.0 49.5 39.60 33 0 28-270 24.75 22.0 19.80 60 108.0 72.0 54.0 43.20 36.0 30 840 27.00 24.0 21.60 65 117.0 78.0 58.5 46.80 39.0 33-410 29.25 26.0 23.40 70 126.0 84.0 63.0 50.40 42.0 35-980 31.50 28.0 25.20 75 1350 90.0 67.5 54.00 45.0 38 550 33.75 30.0 27.00 80 144.0 96.0 72 0 57.00 48.0 41120 36.00 32.0 28.80 85 153.0 102.0 76.5 61.20 51.0 43-690 38.25 34.0 30.60 90 162.0 108.0 81.0 64.80 54.0 46 260 40.50 36.0 32.40 95 171.0 114.0 85.5 68.40 57.0 48.830 42,75 38.0 34.20 100 180.0 1200 90.0 72.00 60 0 51.400 45.00 40.0 36.00 116 MECHANICAL PRINCIPIA. It is immaterial whether the smallest drum is the driving or the driven drum ; if the diameter of the smallest drum remains constant the width of the belt will remain constant, if the diameter of the other drum should be increased inde- finitely. The following table shows the required width of large belts to drive different number and kind of spindles with looms— the columns marked Mules/' " Mules and Frames," and "Frames," show the number and kind of spindles to be driven, the column marked " No. Yarn," shows the number of yarn which the spindles are supposed to spin, the column marked Diameter," shows the diameter of the smallest drum. No. 3. Frame DIAMETER. 8 Spindles No. Yarn. 3 4 5 • 6 7 1000 30 to 40 13 10 8 64 4} 2000 (( t( 26 20 16 13 11 9 3000 <( i( 39 30 24 19 16 14 4000 (( (t 52 40 32 26 22 18 5000 ({ (( 65 50 40 32. 27 23 6000 tC (( 78 60 48 39 33 28 Wo. 4. DIAMETER. Mule 6 Spindles No. Yarn. 3 4 5 7 8 1000 10 to 20 13 10 8 7 6 5 2000 ec (e 27 20 16 13 11 10 3000 40 30 24 20 17 15 4000 (( n 54 40 32 27 23 20 5000 67 50 40 34 28 25 6000 81 61 49 40 34 30 BELTING. 117 No. 5. ! DIAMETER. Mule ■ S pilidlBs No. Yarn. 3 ! 4 5 6 7 8 1000 1 2000 3000 4000 5000 6000 20 to 30 oo-ji^ccioi--* Fall. 1— » lO CO h-t )— > f— 1 1— • UiImMm'Hw ►*'h'K:)lMioh' ,MMkj>-.,^|Wht+-' tJH »Hw t— '1— '1— 1|— 't— '1— ii— 't— i o:>o:'oo(oioco4i^oia5ao ^lMrfi|w*.lMioH KJh-iiMeAj bOlh-. 05 oocooococococooK-^-^^^^^}i^4i^t^^c:,^JC£)^-'^^ •^H MlH' tHw koH >f4-' toH koH lolM K5|i- loH •-. ^rfHwt^|MjHwioH»oHb3h'boH«NwiHw toH^H'-'kolt-'kJli-'^lw ►Hi-' *Jco bsh" koH rf^w loh'ioh' ^totoHrf^w u/f-i wiM to 00 (^H •t'lw koH tf^-" boH boh-toH M-' UH iHw MISCELLANEOUS MACHINERY. MISCELLANEOUS MACHINERY. The following tables show the actual and calculated power required to drive the different machines represented. The column marked 4^ Feet Stones, Corn," shows the number of Ai feet stones grinding corn to be driven, the col- umn marked " Actual Power," shows the actual power required, the column marked " Calculated Power," shows the usual power of the engine or water wheel. Example. Required, the calculated power to drive 3 large size cir- cular saws — find 3 in the column marked Circular Saws," (in No. 1 Table,) opposite to this number in the column marked Calculated Power," will be found 15 horse power. — Answer, Example. Required, the calculated power to drive 4 large size board planing machines — find 4 in the column marked " Planing Machines," (in No. 3 Table,) opposite to this number in the column marked " Calculated Power," will be found 24 horse power. — Ansioer, 148 MECHANICAL TKINCIPIA. Wo, 1. Circular Jalclatd Actual Saws. Power. Power. 1 5 4 2 10 8 3 15 12 4 20 16 5 25 20 6 30 24 No. 2. Upright Calclatd Actual Saws. Power. Power. 1 7 5 2 14 10 3 21 15 4 28 20 5 35 25 6 42 30 Example. Required, the calculated power to drive 3 run of 4-^ feet stones grinding corn — find 3 in the column marked " 4-^ feet Stones, Corn," opposite to this number in the column marked " Calculated Power," will be found 48 horse power. — Ansiver, Example. Required, the calculated power to drive 2 run of 4^ feet stones grinding wheat, with all the attendant machinery — find 2 in the column marked 4^ Feet Stones, Wheat," op- posite to this number in the column marked " Calculated Power," will be found 28 horse power. — Answer. EXABIPLE. Required, the calculated power to drive the blast, &c., to a furnace which makes 5 tons of No. 1 Iron per day — MISCELLANEOUS BIACHINERY. 149 find 5 in the column marked " Tons of Iron," opposite to this number in the column marked Calculated Power," will be found 35 horse power. — Answer. Example. Required, the calculated power to drive 12 cut-nail ma- chines of different size, with attendant machinery (grind- stones, plate-cutter, blast, &c.) — find 12 in the column mark- ed " Nail Machines," opposite to this number in the column marked " Calculated Power," will be found 24 horse power. — Answer, No. 3. Planing Calclatd Actual Machins Power. Power. 1 6 5 2 12 10 3 18 15 4 24 30 5 30 25 6 36 30 No. 4. Stones 4 J feet. Actual Calclatd Corn, Power, Power. 1 14 16 2 28 32 3 32 48 4 56 64 5 70 80 No. 5. Stones 1 4h feet Actual Calclatd Wheat, Power. I Power. 1 12 14 2 24 28 3 36 42 4 48 56 5 60 70 150 MECHANICAL PRINCIPJA. No. 6. No. 1 Actual Calclatd Iron. Power. Power. I G 7 id 12 14 3 18 21 4 24 28 5 30 35 6 36 42 7 42 49 8 48 56 9 54 63 10 60 70 ]¥o. T. Nail Actual Calclatd Machins Power Power. 6 9 12 7 10 14 8 12 16 9 13 18 30 15 20 11 16 22 32 18 24 13 19 26 PADDLE WHEELS. PADDLE WHEELS. The following table shows the number of miles per hour that a steamboat moves, when the diameter of the wheel and the number of revolutions which it makes per minute are known — the column marked " Revolutions," shows the number of revolutions that the paddle wheel makes per minute, the column marked "Diameter," shows the diam- eter of the paddle wheel in feet. Example. Required, the number of miles per hour that a boat is moving, the diameter of the wheels being 30 feet, and the wheels making 20 revolutions per minute — find 20 in the column marked " Revolutions," opposite to this number in the table, and under 30 in the column marked " Diameter," will be found 21.43 miles per hour. This would be the ve- locity of the boat if the water did not yield. — Answer. Example. The diameter of the paddle wheel being 26 feet, and the number of revolutions per minute being 14, required, the number of miles the boat is moving per hour — find 14 in the column marked " Revolutions," opposite to this number m 8 154 MECHANICAL PRINCIPIA. the table, and under 26 in the column marked Diameiur," will be found 12.99 miles per hour. — Answer, Wo. 1. DIAMETER. 24 25 26 11 12 13. 14. 15, 16 17. 17. 18. 19. 20. 21. 22, .49 12.99 .38 13.92 28 14.85 1715.78 0616.71 9617.64 .8518.56 .7419.49 63 20.42 53 21.35 .42 22.28 31 23.21 .2124.13 27 13.49 14.46 15.42 1639 1735 18.32 19.28 20.25 21.21 22.18 23.14 24.11 25.07 28 29 13.99 14 14 99 15 15.99 16 16.99 17 17.99 18 19.00 19 20.00 20 21.0021 22.00|22 23.00 23, 24.0024 30 31 32 33 ,7522, ,7923 ,8224, 86!25 25.00:25.90,26 26.0026.9427 .49 67 ] .85: 03 ^ 34 16 99 18.21 19.42 20.64 21|21.86 40,23.08 58i24.29 7625.51 .9426.73 1527.94 3029.16 4830.38 ,6631.59 The following table shows the number of revolutions of the paddle wheel due to the actual velocity of the boat ; that is, the number of revolutions due to the per cent slip of the wheel is deducted from the whole number of revolutions of the wheel per minute — the column marked Revolutions/' shows the number of revolutions which the paddle wheel makes per minute, the column marked Per Cent," shows the per cent slip of the paddle wheel. Example. A paddle wheel makes 20 revolutions per minute, and the slip (or the yielding of the water) of the wheel is 20 per cent ; required, the number of revolutions due to the ve- locity of the boat — find 20 in the column marked " Revolu- tions," below this number in the table, and opposite to 20 in the column marked " Per Cent," will be found 16 revolu- tions ; that is, if the water did not yield, the wheel would PADDLE WHEELS. 155 not make but 16 revolutions per minute to impel the boat with the same velocity which 20 revolutions per minute would when there is 20 per cent slip. — Answer. Example. A paddle wheel makes 16 revolutions per minute, and the slip is 16 per cent ; required, the number of revolutions due to the velocity of the boat — find 16 in the column mark- ed Revolutions," below this number in the table, and opposite to 16 in the column marked " Per Cent," will be found 13 revolutions. — Answer, -So. 2. oooc:)^^^^ooooCT)tf^^soGoa:>^^i^^ooGoo:l^^^ Per Cent. OOOOCOCDCnOOOt— 1— 'I— '1— 'iOiOJOCOCOC^t^ii. COCOCDOOOH-'t-' 1— Js3M)COWOOtfi>4^4i^^>ti>>CaCnOia5a5 1— ' CD REVOLUTJ to o :oNS. JO to 4^ lO JO 156 MECHANICAL PRINCIPIA. It would appear from the following statement that there is a fixed relation existing between the per cent loss of power of the steamboat paddle wheel (due to the yielding proper- ties of the water), and the relative velocity of the circumfer- ence of the wheel and the velocity of the boat. Let there be a large gear wheel secured on each end of the paddle wheel shaft, nearly equal in diameter to the pad- dle wheel ; let these gear wheels work into racks which rest on surfaces at or below the surface of the w^ater ; let the racks be indefinite in length, and void of gravity, and allow- ed to move freely on the surface on which they rest ; let the racks be held in their position by a chain connected to the end of each rack, and passing over carrying pulleys ; on the other end of the chains let there be weights suspended, so that when the gear wheel makes 12 turns per minute the weights will be just in equilibrium ; then the velocity of the boat will be equal to the velocity of the circumference of the gear wheel. Now let the gear wheel make 16 tTirns pei; minute, then the velocity of the boat will be greater than the velocity due to 12 turns per minute, but less than the velocity due to 16 turns per minute, and the velocity^of the racks or weights will be equal to the relative velocity. It is a well established law, that the momentum of matter in motion is equal to its weight, multiplied by its velocity ; if the weight remains constant the momentum will vary as the velocity, hence the momentum in this case varies as the velocity of the weights. It is a well known law, that the power required to put matter in motion is equal to the momentum of the matter when in •motion, thefefore the power required to put these weights in motion varies as the relative velocity ; again, the momentum of these weights does not tend in any manner to impel the boat, therefore the power transmitted from the engine to these weights is lost to that end. Now the water acts against the paddle wheels in the same manner as the racks act against the gear wheels. It is PADDLE WHEELS. 157 a well known law, that action and reaction is equal in oppo- site directions ; that is, the water reacts against the paddle wheel with the same force that the wheel acts against the water ; if the water does not yield there is no momentum implied, because there is no motion implied, but if the water yields then there is momentum implied ; and if the water yields with a velocity equal to the velocity of the boat, then will the power spent in putting the water in motion be equal to the power spent in putting the boat in motiong because action and reaction is equal in opposite directions. PROBLEMS. PROBLEMS. No. 1. The effective fall at Matteawan, New- York, being 29 feet, the length of the dam being 100 feet, and the depth of the water on the dam at low water mark being 3 inches ; required, the nunsber of cubic feet of water passing over the dam per second — find 3 in the column marked Depth,^' (in Table No. 2, Water Power,) opposite to this number in the column marked " No. Feet," will be found .42, which multiplied by 100 gives 42 cubic feet of water passing over the dam per second. — Ansioer. No. 2. Required, the number of horse power that 42 cubic feet of water per second will produce if applied to an overshot wheel 29 feet in diameter — find 42 in the column marked ^' No. Feet," (in Table No. 3,) opposite to this number in the table, and under 29 in the column marked Diameter," will be found 92.4 horse power. — Answer. No. 3. Required, the length of an overshot wheel 29 feet in di- ameter to transmit 92.4 horse power — find 29 in the column marked " Diameter," (in Table No. 9, Water Power,) op- 8* 162 MECHANICAL PRINCIPIA. posite to this number in the table find 92.4, or the nearest number to it which is 90.4 ; over this number in the column marked "Length," will be found 16 feet, the length of the wheel. — Ansioer. No. 4. Required, the area of the canal to convey the water from the dam to the wheel — find 16, the length of the wheel, in the column marked "Length," (in Table No. 4, Water Power,) opposite to this number in the column marked " Area," will be found 27 feet ; if the water in the canal is 4 feet deep, the canal will be nearly 7 feet wide, because 4 multiplied by 7 is nearly equal to 27 feet. — Answer. No. 5. Required, the depth of the water in the wheel pit, the width of the race being equal to the length of the wheel, which is 16 feet — find 42 cubic feet of water in the column marked "No. Feet," (in Table No. 5, Water Power,) op- posite to this number in the table, and under 16 in the column marked " Width," will be found 10 inches, the dif- ference in the depth of the water when the wheel is at rest and in motion. — Answer, No. 6. Required, the width of the belt to transmit 92 horse power, the diameter of the smallest drum being 6 feet — find 92 or the nearest number to it in the column marked " Horse Power," (in Table No. 2, Belting,) opposite to 95 in the table, and under 6 in the column marked " Diameter," will be found 57 inches, or three belts 19 inches each. — Answer, No. 7. Required, the number of mule and frame spindles with looms on No. 36 yarn that 92 horse power is capable of dri- PROBLEMS. 163 ving — find 92 or the nearest number to it which is 94.5, in the column marked "Actual Power," (in Table No. 3, Manufacturing,) opposite to this number in the column marked " Mula and Frame Spindles," will be found 9000 spindles with looms. — Answer, No. 8. Required, the attendant machinery for 9000 mule and frame spindles, the number of the yarn being 36 — find 9000 in the column marked " Mule and Frame Spindles," (in Table No. 12, Manufacturing,) opposite to this number in the different columns will be found, 1 willower, 3 two beater pickers, 54 thirty-inch cards, 9 railway heads, 4 drawing frames three heads each, 90 coarse speeder spindles, 342 fine speeder spindles, 252 spooler spindles, 5 warpers, 6 dressers, 225 looms. — Answer, No. 9. The factory being three stories high and 50 feet wide, required, the length to contain 9000 spindles with looms — find 9000 in the column marked " Spindles," (in Table No. 2, Manufacturing,) opposite to this number in the table, and under 50 in the column marked " Width," will be found 297 feet, the length of the building. — Answer, No. 10. Required, the number of operatives to operate 9000 spin- dles on No. 36 yarn — find 9000 in the column marked " Spindles," (in Table No. 16,) opposite to this number in the table, and under 35 in the column marked " No. Yarn^" will be found 243 operatives. — Answer. No. 11. Required, the amount paid per week to operate 9000 spindles with looms on No. 36 yarn per week, (including all 164 MECHANICAL PRINCIPIA. expenses except the cost of the cotton.) — find 9000 in the column marked Spindles," (in Table No. 17,) opposite to this number in the table, and under 35 in the. column mark- ed No. Yarn," will be found 1188 dollars.^^n5w;er. No. 12. Required, the contents of a boiler to heat a factory con- taining 9000 spindles with looms — find 9000 in the column marked ^'Spindles," (in Table No. 15, Manufacturing,) opposite to this number in the column marked " Contents," will be found 414 cubic feet ; if the boiler is 4 feet in diam- eter the length will be nearly 33 feet, because the area of 4 feet cylinder is 12.5 feet, and 414 divided by 12.5 gives 33 nearly. — Answer, No. 13. Required, the number of tons of anthracite coal per year to heat a factory containing 9000 spindles — find 9000 in the column marked Spindles," (in Table No. 14, Manufactu- ring,) opposite to this number in the column marked " Tons," will be found 144 tons. — Answer, No. 14. The effective fall at the City of Columbus, Georgia, is 14 feet, the length of the dam is 500 feet, and the depth of the water on the dam at the usual low water mark is 16 inches ; required, the number of cubic feet of water passing over the dam per second — find ]6 in the column marked ''Depth," (in Table No. 2, Water Power,) opposite to this number in the column marked " No. Feet," will be found 5.24, which multiplied by 500 gives 2620 cubic feet of water passing over the dam per second. — Answer, No. 15. Required, the number of horse power that 2620 cubic feet of water per second will produce if applied to overshot PROBLEMS. 165 wheels — find 50 in the column marked " No. Feet/^ (in Table No. 3, Water Power,) opposite to this number in the table, and under 14 in the column marked " Diameter," will be found 53 horse power ; then, if 50 cubic feet will give 53 horse power, 2620 cubic feet will by simple propor- tion give 2777 horse power, — Answer. No. 16. Required, the number of overshot or breast wheels to transmit 2777 horse power, the wheels being 14 feet long — find 14 in the column marked ^' Diameter," (in Table No. 9, Water Power,) opposite to this number in the table, and under 14 in the column marked Length," will be found 38.2, the horse power of one v/heel 14 feet long; then, if 2777 is divided by 38.2 the result will give the number of wheels, which is 72, each 14 feet long. — Answer, No. 17. Required, the number of frame spindles with looms on No. 14 yarn, that 2777 horse power is capable of driving — find 142.5 in the column marked Actual Power," (in Table No. 3, Manufacturing,) opposite to this number in the column marked Frame Spindles," will be found 10,000 spindles; then, if 142.5 horse power will drive 10,000 frame spindles with looms, 2777 horse power will by simple pro- portion drive 194,877 frame spindles with looms on No. 14 yarn. — Answer. No. 18. Required, the number of pounds of cotton that 194,877 spindles on No. 14 yarn will manufacture per week — find 14 in the column marked "No. Yarn," (in Table No. 34, Manufacturing,) opposite to this number in the table, and under 4000 in the column marked " No. Spindles," will be found 1336 pounds, which multiplied by 6 gives 8016 pounds per week ; then, if 4000 frame spindles turn ofi* 8016 pounds 166 MECHANICAL PRINCIPIA. per week, 194,877 frame spindles will by simple proportion produce 390,534 per week, or about 48,800 bales per year; there is from 12 to 15 per cent waste in the cotton, which would increase the amount of cotton. — Answer. No. 19. Required, the number of operatives to operate 194,877 frame spindles with looms on No. 14 yarn — find 10,000 in the column marked ^' Spindles," (in Table No. 16, Manufac- turing,) opposite to this number in the table, and under 15 in the column marked No. Yarn," will be found 330 operatives ; then, if 1000 spindles require 330, 194,877 spin- dles will by simple proportion require 6431 operatives. — Answer, No. 20. Required, the amount paid per week to operate 194,877 frame spindles with looms on No. 14 yarn, (including all expenses except the cost of cotton,) — find 10,000 in the col- umn marked Spindles," (in Table No. 17, Manufacturing,) opposite to this number in the table, and under 15 in the column marked " No. Yarn," will be found 1600 dollars ; then, if 10,000 spindles require 1600 per week, 195,877 spin- dles will by simple proportion require 31,180 dollars per week . — Answer, No. 21. The length of a dam being 20 feet, and the depth of the water on the dam being 5 inches, required, the number of cubic feet of water passing over the dam per second — find 5 in the column marked Depth," opposite to this number in the column marked " No. Feet," (in Table No. 2, Water Power,) will be found 92, which multiplied by 20 gives 18.40, say 18 feet. — Answer, PROBLEMS. 167 No. 22. The constant supply of water on a sill being 18 cubic feet of water per second, and the effective fall being 30 feet, required, the number of mule spindles with looms on No. 36 yarn, that this power is capable of driving — find 18 in the column marked No. Feet," (in Table No. 3, Water Pow- er,) opposite to this number in the table, and under 30 in the column marked ^'Diameter," will be found 40.96 -horse power — find 40.96, or the nearest number to it which is 39, in the column marked Actual Power," (in Table No. 3, Manufacturing,) opposite to this number in the column marked " Mule Spindles," will be found 4000 spindles with looms on No. 36 yarn. — Answer, No. 23. The fall on a site is 16 feet, deduct from this three feet, when the effective fall will be 13 feet; required, the length of an overshot wheel to drive 4000 mule and frame spindles on No. 30 yarn with looms — find 13 in the column marked " Fall," opposite to this number in the table, (in Table No. 7, Manufacturing,) and under 4000 in the column marked " No. Spindles," will be found 24 feet, or two 12 foot wheels. — Ansioer. No. 24. A breast wheel is required to work its actual power on a fall of 14 feet, the length of the wheel being 12 feet, and the race being 4 feet wide ; required, the depth of the water in the wheel pit. The horse power of this wheel is 32.7, (found in Table No. 9, Water Power,) refer to Table No. 3, Water Power — find 14 in the column marked " Diam- eter," under this number in the table find 32.7, or the near- est number to it which is 32.86, opposite to this number in the column marked "No. Feet," will be found 31 cubic 168 MECHANICAL PRINCIPIA. feet discharged from the wheel per second — find 31 in the column marked ^'No. Feet," (in Table No. 5, Water Power,) opposite to this number in the table, and under 4 in the col- umn marked " Width," will be found 21 inches, the depth of the water in the wheel pit when the water is in motion. — Answer, No. 25. The effective fall on a site being 13 feet, and the number of cubic feet of water passing in the stream per second (four.d from a dam on the stream,) being 35, required, the horse power — find 35 in the column marked " No. Feet," (in Table No. 3, Water Power,) opposite to this number in the table, and under 13 in the column marked ^'Diameter," will be found 34.44 horse power. — Answer, No. 26. The effective head being 13 feet, required, the area of all the openings in an inward or centre discharging turbine water wheel, to transmit 34.44 horse power — find 13 in the column marked "Head," (in Table No. 12, Water Power,) opposite to this number in the column marked " Horse Power," will be found 88 horse power ; then, if 88 horse power require 100 inches area, 34.44 horse power will by simple proportion require 391 inches area. — Ansiver, No. 27. Required, the number of 4^ feet stones grinding wheat, with all the attendant machinery that this power is capable of driving — find 13 in the column marked " Head," (in Table No. 2, Flour and Corn Mills,) opposite to this number in the column marked " Area," will be found 135 ; then, if 135 inches area will drive one run of 4^ feet stones, 391 inches area will by simple proportion drive nearly 3 run of PROBLExMS. 1(39 4r> feet stones grinding wheat, with all the attendant ma- chinery. — Answej\ No. 28. Required, the depth of the water in the wheel pit, the width of the race being 6 feet, (35 feet per second is the number discharged from the wheel,) — find 35 in the column marked " No. Feet," (in Table No. 5, Water Power,) op- posite to this number in the table, and under 6 in the column marked " Width," wiW be found 17 inches, the depth of the water in the wheel pit when the wheel is in motion. — Answer, No. 29. Required, the length of an overshot water wheel, the di- ameter being 12 feet, to drive 2 run of 4^ feet stones grind- ing wheat, with all the attendant machinery — find 12 in the column marked "Fall," (in Table No. 5, Corn and Flour Mills,) opposite to this number in the table, and under 2 in the column marked "No. Run," will be found 11 ^ feet, the calculated length of the wheel. — Ansiver. No. 30. Required, the length of an overshot wheel, the diameter being 22 feet, to drive 3 run of 4|- feet stones grinding wheat, with all the attendant machinery — find 22 in the column marked " Fall," (in Table No. 5, Corn and Flour Mills,) opposite to this number in the table, and under 3 in the col- umn marked "No. Run," will be found 9^ feet, the calcu- lated length of the wheel. — Answer, No. 31. Required, the length of an overshot wheel, the diameter being 16 feet, to drive 2 run of 4^ feet stones grinding corn —find 16 in the column marked " Fall," (in Table No. 6, 170 MECHANICAL PKINCli'lA . Corn and Flour Mills,) opposite to this number in the table, and under 2 in the column marked " No. Run/' will be found 10 feet, the length of the wheel. — Answer. No. 32. The head being 16 feet, and the area of all the openings in an inward discharging turbine water wheel being 297 inches, required, the number of 4^ feet stones grinding wheat, with all the attendant machinery this wheel is capable of driving — find 16 in the column marked "Head," opposite to this number in the table find 297, over this number in the column marked " No. Run," will be found 3, the num- ber of run this wheel is capable of driving. — Answer, No. 33. The whole fall on a site being 32-J- feet, required, the per cent loss of an overshot wheel due to this fall, and the per cent loss of an overshot wheel due to half of this fall ; (in this problem it is necessary to suppose the statement in Note A to be correct ;) the diameter of an overshot wheel due to 32-J- feet fall is 30 feet, the diameter due to half of this fall is 13f feet — find 30 in the column marked Fall," (in Table No. 10, Water Power,) opposite to this number in the column marked " Per Cent," will be found 23 per cent — find 14 in the column marked " Fall," opposite to this num- ber in the column marked " Per Cent," will be found 38 per cent : the per cent loss due to 13f- feet is 39 per cent nearly ; the difference of 39 and 23 is 16 per cent ; allow 6 per cent for the difference in the inertia of the wheels when loaded, and also the difference in the power due to the water on the wheel when any part of the machinery is stopped, which is very small unless the power is lost when the wheel runs above its calculated velocity ; then the lost power by dividing the fall into two falls will be 10 per cent. — Answer. PROBLEMS. 171 No. 34. The effective fall being 5 feet, and the diameter of an outward discharging turbine water wheel being 72 inches, required, the number of revolutions of the wheel per minute — find 5 in the column marked " Head," opposite to this number in the table, and under 72 in the column marked Diameter," will be found 41 revolutions. — Answer, No. 35. The whole fall of a stream or site is 18 feet ; this site is subject to two feet back-water three months in the year ; but when there are two feet back-water the head is raised one foot ; the water on the dam being one foot deep then the whole fall is 17 feet ; allow two feet for the head being drawn down &c., then the effective fall will be 15 feet ; required, the area of all the openings in an inward discharging turbine water wheel, to drive one run of 4^ feet stones grinding wheat, with all the attendant machinery — find 15 in the column marked " Head," (in Table No. 2, Corn and Flour Mills,) opposite to this number in the table, and under 1 in the col- umn marked "No. Run," will be found 109 inches area. — > Answer. No. 36. The fall on a breast wheel being 18 feet; there are five gates to let the water on the wheel, the upper gate being under a head of 2 feet, and the lower gate under a head of 10 feet ; required, the per cent loss of the wheel when sup- plied with water from the upper gate under a head of 2 feet, and the per cent loss when supplied from the lower gate under a head of 2 feet, (according to the statement in Note A)~find 18 in the column marked "Fall," (in Table No. 10, Water Power,) opposite to this number in the column marked " Per Cent," will be found 33 per cent loss ; find 172 MECHANICAL PRINCIPIA. 10 in the column marked " Fall," (which is the fall from the lower gate,) opposite to this number in the column marked "Per Cent," will be found 49 per cent loss of power. — Answer. No. 37. Required, the area of all the openings in an outward dis- charging turbine water wheel, to drive 1 run of 4-^ feet stones grinding corn, the effective head when the reservoir is full being 16 feet; the reservoir is frequently drawn down 6 feet, as the constant supply of water is not sufficient to drive the wheel, hence the wheel must be calculated for 10 feet fall — find 10 in the column marked "Head," opposite to this number in the table, (in Table No. 3, Corn and Flour Mills,) and under 1 in the column marked " No. Run," will be found 137 inches area. — Answer. No. 38. The diameter of the wheel in No. 37 Problem, being 48 inches, required, the number of revolutions per minute ; take some number between 16 and 10 — as the average head will be nearer 16 than 10, choose 14 — find 14 in the column marked "Head," (in Table No. 13, Water Power,) oppo- site to this number in the table, and under 48 in the column marked " Diameter," will be found 102 revolutions. — Answer. No. 39. The effective fall being 16 feet, required, the area of all the openings in an inward discharging turbine water wheel, to drive two run of 4| feet stones grinding wheat, with all the attendant machinery — find 16 in the column marked " Head," (in Table No. 2, Corn and Flour Mills,) opposite to this number in the table, and under 2 in the column marked No. Run," will be found 198 inches; area.-^r Ansiver, \^ ; U- No. 40. Required, the horse power of the wheel in No. 89 Prob- lem, the effective fall being 16 feet — find 16 in the column marked Head," (in Table No. 12, Water Power,) oppo- site to this number in the column marked ^' Florse Power," will be found 12.1 horse power ; then, if 100 inches area gives 12.1 horse power, 198 inches area will by simple proportion give 24 horse power nearly. — Answer. No. 41. Required, the number of cubic feet of water discharged from the wheel in No. 39 Problem per second, (supposing this wheel to produce the same effect as the overshot or breast wheel on the same fall,) — find 16 in the column marked " Diameter," (in Table No. 3, Water Power,) below this number in the table, find 24 horse power, or the nearest number to it, which is 24.24, opposite to this number in the column marked " No. Feet," will be found 20 cubic feet of water ; in this case 2-J feet of the fall should be allowed for head and clearance, same as allowed to the overshot wheel, then the whole fall will be 18^ feet. — Answer, No. 42. Required, the depth of the water in the wheel pit in No. 39 Problem, the width of the race being 6 feet — find 20 (cubic feet, the number discharged from the wheel per second) in the column marked " No. Feet," (in Table No. 5, Water Power,) opposite to this number in the table, and under 6 in the column marked Width," v/ill be found 12 inches, the depth of the water in the wheel pit when the wheel is running, — Answer. 174 MECHANICAL PRINCIPIA. No. 43. Required, the depth of the water in the wheel pit in No. 39 Problem, the width of the race being 12 feet — find 20 in the column marked No. Feet," (in Table No. 5, Water Power,) opposite to this number in the table, and under 12 in the column marked " Width," will be found 7 inches, the depth of the water. — Answer, No. 44. Required, the length of an overshot water wheel, the fall being 16 feet, to drive the blast, &c., to a furnace which turns off 6 tons of No. 1 Iron per day — find 16 in the col- umn marked Fall," (in Table No. 1, Furnace,) opposite to this number in the table, and under 6 in the column mark- ed No. Tons," will be found 13 feet, the length of the wheel. — Answer. No. 45. For each ton of No. 1 Iron per day it requires aboyt 7 calculated horse power, the effective fall being 18 feet ; re- quired, the area of all the openings in an outward discharg- ing turbine water wheel, to drive the blast, &c., to a furnace which makes 6 tons of No. 1 Iron per day, which requires 42 horse power — find 18 in the column marked Head," (in Table No. 12, Water Power,) opposite to this number in the column marked Horse Power," will be found 25.2 horse power ; then, if 25.2 horse power require 100 inches area, 42 horse power will by simple proportion require 166 inches area. — Ansioer. No. 46. Required, the width of the canal to convey the water from the dam to the wheel in No. 45 Problem, the depth of the canal being 4 feet — find 18 (the effective fall in No. 45 PROBLEMS. 175 Problem,) in the column marked ^'Diameter," (in Table No. 9, Water Power,) opposite to this number in the table, find 42, (horse power of the wheel in No. 45 Problem,) over this number in the column marked Length," will be found 12 feet, the length of an overshot wheel on the same fall of 42 horse power- — find 12 in the column marked " Length," (in Table No. 4, Water Power,) opposite to this number in the column marked " Area," will be found 20, which divided by 4 gives 5 feet, the width of the canal. — - Answer, No. 47. Required, the area of all the openings in an inward dis- charging turbine water wheel to drive a furnace blast, &;c., which makes 3 tons of No. 1 Iron per day, which requires 21 calculated horse power, the effective fall being 12 feet — find 12 in the column marked " Head," (in Table No. 12, Water Power,) opposite to this number in the column mark- ed "Horse Power," will be found 7.8 horse power; then, if 7.8 horse power require 100 inches area, 21 horse power will by simple proportion require 269 inches area. — Answer. No. 48. The actual power required in No. 47 Problem is about 16 horse power ; required, the width of the belt to transmit 16 horse power, the diameter of the smallest drum being 4 feet — find 16 in the column marked Plorse Power," (in Table No. 2, Belting,) opposite to this number in the table, and under 4 in the column marked " Diameter," will be found 14.4, say 14 inches, the width of the belt. — Answer, No. 49. The average depth of the water on a dam which is 40 feet long during the summer months is 3 inches ; required, the number of cubic feet of water passing over the dam per 176 MECHANICAL PRINCIPIA. second — find 3 in the column marked " Depth," (in Table No. 2, Water Power,) opposite to this number in the column marked "No. Feet," will be found .42, which multiplied by 40 gives 16.8, say 17 cubic feet per second. — Answer, No. 50. Required the horse power of 17 cubic feet of water per second, the effective fall being 18 feet — find 17 in the column marked " No. Feet," (in Table No. 3, Water Power,) op- posite to this number in the table, and under 18 in the column marked " Diameter," will be found 23.18 horsepower. — Answer, No. 51. Required, the length of an overshot wheel 18 feet in di- ameter, to transmit 23.18 horse power — find 18 in the col- umn marked Diameter," (in Table No. 9, Water Power,) opposite to this number in the table find 23.18, or the near- est number to it which is 24.6, over this number in the col- umn marked " Length," will be found 7 feet, the length of the wheel. — Answer, No. 52. Required, the number of tons of No. 1 Iron that a fur- nace will make per day, being supplied with the power of an overshot wheel 18 feet in diameter and 7 feet in length — find 18 in the column marked " Fall," (in Table No. 1, Furnace,) opposite to this number in the table find 7, or the nearest number which is 6 or 8, over 6 in the column mark- ed No. Tons," will be found 3 tons, over 8 will be found 4 tons, hence 3-^ tons is due to 7 feet : there is about 25 per cent surplus power in this wheel, hence the actual produc- tion is about 4f tons per day. — Answer. PROBLEMS. 177 No. 53. Required, the number of horse power to drive 2 large size circular saws, and two of Woodworth's large size board- planing machines — find 2 in the column marked " Large Size Circular Saws," (in Table No. 1, Miscellaneous Machi- nery,) opposite to this number in the column marked Horse Power," will be found 10 horse power: — find 2 in the column marked Woodworth's Planing Machines," (in Table No. 3, Miscellaneous Machinery,) opposite to this number in the column marked " Horse Power," will be found 12 horse power, which added to 10, makes 22 horsepower. — Answer, No. 54. The efiective fall being 12 feet, required, the area of all the openings in an inward discharging turbine wheel to drive 2 large size circular saws, and 2 large size planing ma- chines, which require 22 horse power — find 12 in the col- umn marked Head," (in Table No. 12, Water Power,) opposite to this number in the column marked " Horse Pow- er," will be found 7.8 ; then, if 7.8 horse power require 100 inches area, 22 horse power will by simple proportion, re- quire 282 inches area. — Answer, No. 55. Required, the number of horse power to drive 2 large size upright saws, (for sawing logs,) and 1 large size cir- cular saw, and 1 large size planing machine — find 2 in the col- umn marked Upright Saws," (in Table No. 2, Miscellaneous Machinery,) opposite to this number in the column marked "Horse Power," will be found 14 horse power : find 1 in the column marked " Circular Saws," opposite to this number in iho ctolumn marked " Horse Power," will be found 5 horse power : find l in the column marked " Planing Machines," opposite to this number in the column marked Horse 9 178 MECHANICAL PRINCIPIA. Power," will be found 6 horse power; then 14, 5 and 6 added together, makes 25 horse power. — Answer, No. 56. Required, the length of an overshot wheel, the diameter being 12 feet, to produce 25 horse power — find 12 in the col- umn marked " Diameter," (in Table No. 9, Water Power,) opposite to this number in the table find 25, or the nearest number to it, which is 25.8, over this number in the column marked "Length," will be found 11 feet, the length of the wheel. — Answer, No. 57. Required, the area of the canal to convey the water from the reservoir to the wheel in No. 56 Problem — find 11 in the column marked " Length," (in Table No. 4, Water Power,) opposite to this number in the column marked " Area," will be found 19 feet area ; if the canal is 3 feet deep it will be nearly 6 feet wide, because 6 multiplied by 3 gives 19 nearly, or it is 6^ by 3 feet. — Answer, No. 58. Required, the number of cubic feet of water discharged from the wheel in 56 Problem per second, the wheel is 25 horse power and 12 feet in diameter — find 12 in the column marked " Diameter," (in Table No. 3, Water Power,) under this number in the table find 25, or the nearest num- ber to it, which is 25.45 ; opposite to this number in the column marked "No. Feet," will be found 28 feet. — Answer, No. 59. , Required, the depth of the water in the wheel pit in No. 66 Problem, the width of the race beinjj 8 feet— find 28 in PROBLEMS. 179 the column marked " No. Feet," (in Table No. 5, Water Power,) opposite to this number in the table, and under 8 in the column marked " Width," will be found 12 inches, the depth of the water in tlie wheel pit. — Answer, No. 60. Required, the area of all the openings in an outward dis- charging turbine water wheel, to drive the machinery in 55 Problem, the power to drive which is 25 horse, the effective head being 20 feet — find 20 in the column marked " Head," (in Table No. 12, Water Power,) opposite to this number in the column marked " Horse Power," will be found 29.5 horse power ; then, if 29.5 horse power require 100 inches area, 25 horse power will by simple proportion require 84 inches area nearly. — Answer* No. 61. Required, the area of all the openings (to drive one large size upright saw, which requires 7 horse power) in the out- ward discharging turbine water wheel, the head being 5 feet — find 5 in the column marked Head," (in Table No. 12, Water Power,) opposite to this number in the column mark- ed " Horse Power," will be found 8.8 horse power ; then, if 3.8 require 100 inches area, 7 will by simple proportion require 189 inches area. — Answer, No. 62. Required, the number of revolutions per minute of the wheel in No. 61 Problem, the diameter being 48 inches — find 5 in the column marked " Head," (in Table No. 13, Water Power,) opposite to this number in the table, and un- der 48 in the column marked Diameter," will be found 61 revolutions. — Answer, 180 MECHANICAL PRINCIPIA. No. 63. The effective fall being 12 feet, required, the length of a breast wheel to drive 18 different size cut-nail machines, with the attendant machinery — -find 12 in the column mark- ed " Fall," (in Table No. 1, Nail Machines,) opposite to this number in the table, and under 18 in the column mark- ed " No. Machines," will be found 14;^ feet, the length of the wheel. — Answer. No. 64. Required, the area of all the openings in an inward dis- charging turbine water wheel, the effective head being 16 feet, to drive 16 nail machines of different size, with the at- tendant machinery ; the calculated power is 2 horse power to each machine ; then the horse power required to drive 16 machines is 32 — find 16 in the column marked " Head," (in Table No. 12, Water Power,) opposite to this number in the column marked "Horse Power," will be found 12.1 horse power, then if 12.1 horse power require 100 inches area, 32 will by simple proportion require 264 inches area. — Answer. No. 65. Required, the area of all the openings in an outward dis- charging turbine water wheel, the head being 6 feet, to drive 8 different size cut-nail machines, which requires 16 horse power — find 6 in the column marked Head," (in Table No. 12, Water Power,) opposite to this number in the column marked " Horse Power," will be found 4.6 horse power; then, if 4.6 horse power require 100 inches area, 16 horse power will by simple proportion require 347 inches area. — Aoswer. PROBLEMS. 181 No. 66. The smallest drum being 6 feet, required, the width of a belt to transmit 16 horse power — find 16 in the column marked " Horse Power," (in Table No. 2, Belting,) oppo- site to this number in the table, and under 6 in the column marked " Diameter," will be found 9.6, say 10 inches, the width of the belt to transmit 16 horse power. — Answer, No. 67. Required, the number of dead spindles on No. 25 yarn, to manufacture 3,000,000 pounds of cotton per day; this will give 900,000,000 pounds of cotton per year, the estimated production of the United States — find 25 in the column marked "No. Yarn," (in Table No. 35, Manufacturing,) opposite to this number in the table, and under 4000 in the column marked " No. Spindles," will be found 704 pounds; then, if 704 pounds require 4000 spindles with looms, 3,000,000 pounds will by simple proportion require 17,045, 454 spindles with looms, on No. 25 yarn. — Answer, No. 25 Yarn is probably near the mean or average number, therefore the number of spindles required for this number would probably be nearly equal to the whole num- ber of spindles now spinning the above amount of cotton. No. 68. Required, the number of horse power to drive 17,045,454 frame spindles with looms, on No. 25 yarn — find 10,000 in the column marked " Frame Spindles," (in Table No. 3, Manufacturing,) opposite to this number in the column marked " Actual Power," will be found 127.5 horse power ; then, if 10,000 spindles require 127.5 horse power, 17,045,454 spindles will by simple proportion require 217,329 horse power. — Answer. 182 MECHANICAL PRINCIPIA. No. 69. Required, the number of cubic feet of water per second, the effective fall being 16 feet, to drive 17,045,454 frame spindles with looms, on No. 25 yarn — find 50 in the column marked " No. Feet," (in Table No. 3, Water Power,) op- posite to this number in the table, and under 16 in the col- umn marked ^'Diameter," will be found 60.6 horse power ; then, if 60.6 horse power require 50 cubic feet per second, 217,329 horse power will by simple proportion require 179,314 cubic feet per second. — Answer. No. 70. Required, the length of a dam, over which 179,314 cubic feet of water will pass per second, the depth of the water on the dam being 60 inches, or 5 feet — -find 60 in the column marked " Depth," (in Table No. 2, Water Power,) opposite to this number in the column marked No. Feet," will be found 37.8 cubic feet; then, if 37.8 cubic feet require a dam 1 foot long, 179,314 cubic feet will by simple propor- tion require a dam 4743 feet long, or about f of a mile. — Answer, No. 71. Required, the amount paid for labor per week, to operate 17,045,454 spindles with looms, on No. 25 yarn — find 10,000 in the column marked " Spindles," (in Table No. 17, Man- ufacturing,) opposite to this number in the table, and under ' "No. 25," will be found 1080 dollars ; then, if 10,000 spindles require 1080 dollars per week to operate them, 17,045,454 spindles will by simple proportion require 1,840,909 dollars per week, or 92,045,450 dollars per year, nearly. — Answer, PROBLEMS. 183 No. 72. Required, the amount paid per week, including all ex- penses except the cost of cotton, to operate 17,045,454 spin- dles with looms, on No. 25 yarn — find 10,000 in the column marked Spindles," (in table No. 17, Manufacturing,) opposite to this number in the table, and under " No. 25," will be found 1460 dollars ; then, if 10,000 spindles require 1460 dollars per week, 17,045,454 spindles will by simple proportion require 2,488,636 dollars per week, or 124,431, 814 dollars per year, nearly. — Answer, No. 73. Required, the number of operatives to operate^7,045,454 spindles with looms, on No. 25 yarn — find 10,000 in the col- umn marked " Spindles," (in Table No. 16, Mdnufacturfng,) opposite to this number in the table, and under No. 25," will be found 300 operatives ; then, if 10,000 spindles require 300 operatives, 17,045,454 spindles will by simple propor- tion require 511,363 operatives. — Answer, The usual capital employed in manufacturing establish- ments (including the factory, houses, land, &;c.,) is about 25 dollars per spindle, hence the capital employed to operate 17,045,454 spindles with looms, is about 426,136,350 dollars. No. 74, Required, the cost per yard for manufacturing f sheet- ings, No. 14 yarn, and 2.9 or nearly 3 yards per pound, when cotton is worth 6 cents per pound — find 14 in the col- umn marked "No. Yarn," (in Table No. 19, Manufactur- ing,) opposite to this number in the table, and under 6 in the column marked " Price of Cotton," will be found 5.95 cents, the cost per yard. — Answer, 184 MECHANICAL PRINCIPIA, No. 75. Required, the cost per yard for manufacturing f shirt- ings, No. 36 yarn, and 5 yards per pound, when cotton is worth 8 cents per pound — find 36 in the column marked No. Yarn," opposite to this number in the table, and under 8 in the column marked " Price of Cotton," will be found 6.42 cents per yard. — Answer, No. 76. Required, the cost per yard for manufacturing f print- ing goods. No. 31 yarn, and 5.8 yards per pound, when cot- ton is worth 6 cents per pound — find 31 in the column marked No. Yarn," opposite to this number in the table, and under 6 in the column marked " Price of Cotton," will be found 4.24 cents per yard. — Answer, No. 77. A factory containing 50 \ looms, and on No. 14 yarn, will turn off about 9900 yards per week ; when cotton is worth 7 cents per pound, and the cash price of the goods is 7 cents per yard, required, the profits per week — the cost per yard for making the goods is 6.45 cents, which taken from 7, gives .55 profit per yard, which multiplied by 9900, gives 54.45 dollars per week, or 2722 dollars .per year. — Answer, The factory in No. 77 Problem, will contain about 2000 mule and frame spindles, which multiplied by 25 dollars, the usual cost per spindle, gives 50,000 dollars capital. The per cent interest on the capital is nearly No. 78. A factory containing 100 f looms on No. 31 yarn, will turn off about 18,000 yards per week ; if cotton is worth 7 PROBLEMS. 185 cents per pound, and the cash price of the printing goods is 5 cents per yard, required, the profits per week — the cost per yard for making this style is 4.46, which taken from 5, gives .54 profit per yard, which muhiplied by 18,000, gives 97.20 dollars per week, or 4,860 dollars per year. — Answer, No. 79. Required, the capital and per cent interest of the factory in No. 78 Problem, for 100 f looms on No. 31 yarn— 4,000 mule and frame spindles are usually allowed, which multi- plied by 25, gives 100,000 dollars capital ; 4,860 divided by 100,000, gives 4 per cent interest. — Answer. No. 80. A factory containing 64 f looms, on No. 33 yarn, will turn ofi" about 10,000 yards per week ; if cotton is worth 8 cents per pound, and the cash price of the goods being 7^ cents, required, the profits per week — the cost per yard for making this style of goods is 6.31, which taken from 7^, gives 1.19 profit per yard, which multiplied by 10,000, gives 119 dollars per week, or 5950 dollars per year. — Answer, No. 81. Required, the capital and the per cent interest of the fac- tory in No. 80 Problem, for 64 f looms on No. 33 yarn — - 2,500 mule and frame spindles are usually allowed, which multiplied by 25, gives 62,500 dollars capital ; 5,950 divi- ded by 62,500, gives 9^ per cent nearly. — Answer, No. 82. Required, the horse power of an engine, the diameter of the cylinder being 18 inches, the effective pressure being 50 pounds per inch, and the velocity of the piston 300 feet per 9* 186 MECHANICAL PRINCIPIA. minute — find 50 in the colunan marked "Pressure/' (in Table No. 6, Steam Power,) under this number in the table, and opposite to 18 in the column marked Diameter," will be found 38.55, which multiplied by 3.00, gives 115.65 horse power ; this being an ordinarily finished high pressure engine, deduct 20 per cent, which gives 92.52 effective horse power. — Answer. •V No. 83. Required, the diameter of the cylinder of an ordinarily finished high pressure engine, the effective pressure being 55 pounds per inch, and the velocity of the piston being 250 feet per minute, to drive 2000 mule spindles with looms, on No. 30 yarn ; the calculated power required is 28 horse power; (see Notes A, B, and C ;) 25 per cent of 28 is 7, which added to 28 gives 35, (which is the theoretical power of the engine;) divide 35 by 2.50, which gives 14, (the theo- retical power due to 100 feet velocity of the piston per mi- nute,) — find 55 in the column marked Pressure," (in Table No. 6, Steam Power,) under this number in the table find 14, or the nearest number to it, which is 13.09 or 15.84, say 15.84, opposite to this number in the column marked " Di- ameter," will be found 11 inches, the diameter of the cylinder. — Answer, No. 84. Suppose the calculated power in No. 83 Problem was 36 horse power, required, the diameter of the cylinder ; 25 per cent of 36 is 9, which added to 36 gives 45, which divi- ded by 2.50 gives 18 — find 55 in the column marked " Pressure," under this number in the table find 18, or the nearest number to it, which is 18.84, opposite to this number in the column marked Diameter," will be found 12 inches, the diameter of the cylinder. — Answer, PROBLEMS. 187 No. 85. Required, the diameter of the cylinder of an ordinarily- finished high pressure engine, the effective pressure being 60 pounds per inch, and the velocity of the piston being 225 feet per minute, to drive 6000 mule and frame spindles with looms, on No. 30 yarn ; the calculated power required is 90 horse power ; 25 per cent of 90 is 22.5, which added to 90 gives 112.5, which divided by 2.25 gives 50 — find 60 in the column marked Pressure," (in Table No. 6, Steam Power,) below this number in the table, find 50, or the nearest num- ber to it, which is 51,54, opposite to this number in the column marked Diameter," will be found 19 inches, the diameter of the cylinder. — Answer, No. 86, Suppose the velocity of the piston in No. 85 Problem was 275 feet per minute, required, the diameter of the cylin- der ; then 1125 divided by 275 gives 40.91 — find 60 in the column marked Pressure," below this number in the table find 40.91, or the nearest number to it, which is 41.26, opposite to this number in the column marked Diameter," will be found 17 inches, the diameter of the cylinder. — Answer, No. 87, Required, the efiective pressure per inch of an ordinarily finished high pressure engine, the diameter of the cylinder being 10 inches, and the velocity of the piston being 250 feet per minute, to drive 3000 frame spindles with looms on No. 25 yarn ; the calculated power required is 51 horse power ; 25 per cent of 51 is 12.75, which added to 51, gives 63.75, which divided by 2.50, gives 25.5 — find 10 in the column marked ^' Diameter," (in Table No. 6, Steam Power,) oppo- 188 MECHANICAL PEINCIPIA. site to this number in the table find 25.5, or the nearest number to it, which is 25.46, over this number in the col- umn marked Pressure," will be found 107 pounds, effec- tive pressure per inch. — Answer. No. 88. Required, the velocity of the piston per minute of an or- dinarily finished high pressure engine, the diameter of the cylinder being 12 inches, and the effective pressure being 60 pounds per inch, to drive 8000 frame spindles with looms on No. 40 yarn ; the calculated power required is 48 horse power; 25 per cent of 48 is 12, which added to 48 gives 60 — find 12 in the column marked ^' Diameter," (in Table No. 6, Steam Power,) opposite to this number in the table, and under 60 in the column marked Pressure," will be found 20.56 ; now if 20.56 horse power require 100 feet per minute, 60 horse power will by simple proportion require 291 feet, the velocity of the piston per minute. — Answer, No. 89. Required, the diameter of the cylinder of an ordinarily finished high pressure engine, the effective pressure being 50 pounds per inch, and the velocity of the piston being 250 feet per minute, to drive 24 cut-nail machines ; the calcula- ted power required is 48 horse power ; 25 per cent of 48 is 12, which added to 48 gives 60, which divided by 2.50 gives 24 — find 50 in the column marked Pressure," (in Table No. 6, Steam Power,) under this number in the table find 24, or the nearest number to it, which is 23.32, opposite to this number in the column marked Diameter," will be found 14 inches, the diameter of the cylinder. — Answer, No. 90. Required, the diameter of the cylinder of an accurately finished condensing engine, the effective pressure being 30 PROBLEMS. 189 pounds per inch, and the velocity of the piston being 300 feet per minute, to drive 12 cut-nail machines ; the calculated power required is 24 horse power; 33.33 per cent of 24 is 8, which added to 24 gives 32, which divided by 3.00 gives 10.66 — find 30 in the column marked " Pressure," below this number in the table find 10.66, or the nearest number to it, which is 10.28, opposite to this number in the column marked Diameter," will be found 12 inches, the diameter of the cylinder. — Answer. No. 91. Required, the efiective pressure per inch of an accurately finished high pressure engine, the diameter of the cylinder being 10 inches, and the velocity of the piston being 300 feet per minute, to drive 18 cut-nail machines; the calcula- ted power required is 36 horse power; 17.65 per cent of 36 is 6.35, which added to 36 gives 42.35, which divided by 3.00 gives 14.12 — find 10 in the column marked Diam- eter," (in Table No. 6, Steam Power,) opposite to this number in the table find 14.12, or the nearest number to it, which is 14.04, above this number in the column marked Pressure," will be found 59 pounds, effective pressure. — Answer, No. 92. Required, the diameter of the cylinder of an ordinarily finished condensing engine, the effective pressure being 36 pounds per square inch, and the velocity of the piston being 300 feet per minute, to drive the blast, &;c., to a furnace which makes 7 tons of No. 1 Iron per day; the calculated power required is 49 horse power ; 42.86 per cent of 49 is 21, which added to 49 gives 70, which divided by 3.00 gives 23.33 — find 36 in the column marked Pressure," below this number in the table find 23.33, or the nearest number to itj which is 24.76, opposite to this number in the column 190 MECHANICAL PRINCIPIA. marked "Diameter," will be found 17 inches, the diameter of the cylinder. — Ansioer. No. 93. Required, the number of pounds of coarse anthracite coal per day, to drive 6000 mule spindles with looms, on No. 36 yarn; the actual power required is 58.5 horse power — find 58.5, say 58, in the column marked " Horse Power," (in Table No. 2, Steam Power,) opposite to this number in the column marked " Pounds," will be found 2436 pounds of coal. — Ansiver, No. 94. Required, the number of pounds of coarse anthracite coal per day, to drive 2000 mule and frame spindles with looms, on No. 30 yarn ; the actual power required is 22.5 horse power, say 22 — find 22 in the column marked " Horse Power," opposite to this number in the column marked " Pounds," will be found 924 pounds. — Answer, No. 95. Required, the number of pounds of coarse anthracite coal per day, to drive two run of 4^ feet stones, grinding corn ; the actual power required is 28 horse power — find 28 in the column marked " Horse Power," (in Table No. 2, Steam Power,) opposite to this number in the column marked "Pounds," will be found 1176 pounds. — Answer. No. 96. Required, the number of pounds of coarse anthracite coal per day, to drive 17,045,454 frame spindles with looms, on No. 25 yarn ; the actual power required is 217,329 horse power — find 100 in the column marked " Horse Power," opposite to this number in the column marked " Pounds," will be found 4200 pounds ; then, if 100 horse power re- PROBLEMS. 191 quire 4200 pounds per day, 217,329 horse power will require by simple proportion 9,127,818 pounds per day, or 1,369,170 tons per year (300 working days). No. 97. Required, the number of cords of southern pine wood per day, to drive 2000 frame spindles with looms, on No. 14 yarn; the actual power required is 28.5, say 28 horse power — find 28 in the column marked Horse Power," (in Table No. 3, Steam Power,) as 28 is between 25 and 30, the num- ber of cords of wood required will be between 3 and 3-^, say 3| cords. — Ansioer, No. 98. Required, the number of cords of southern pine wood per day, to drive 1 run of 4^ feet stones grinding corn, and 1 run of 4-J feet stones grinding wheat, with all the attendant machinery ; the actual power required is 26 horse power — find 26, or the nearest number to it, which is 25, in the col- umn marked " Horse Power," (in Table No. 3, Steam Pow- er,) opposite to 25 in the column marked Cords," will be found 3 cords. — Answer, No. 99. Required, the length of a boiler which is 48 inches in diameter, to drive 1000 frame spindles with looms, on No. 14 yarn ; the calculated power required is 19 horse power —find 48 in the column marked Diameter," (in Table No. 1, Steam Power,) below this number in the table find 19, or the nearest number to it, which is 18.8, opposite to this number in the column marked " Length," will be found 18 feet, the length of the boiler. — Answer. 192 MECHANICAL PRINCIPIA. No. 100. A boiler is 26 feet long, and 36 inches in diameter ; re- quired, the number of mule spindles with looms, on No. 30 yarn, this boiler is capable of driving ; the calculated power of the boiler is 15 horse power ; to drive 1000 mule spindles with looms, on No. 30 yarn, it requires 14 horse power ; hence, the boiler is capable of driving 1000 spindles. — Answer, No. 101. Required, the diameter of a boiler, the length being 30 feet, to drive one run of 4-J- feet stones grinding corn ; the calculated power required is 16 horse power — find 30 in the column marked Length," (in Table No. 1, Steam Power,) opposite to this number in the table find 16, or the nearest number to it, which is 17.6, over this number in the column marked " Diameter," will be found 36 inches, the diameter of the boiler. — Answer. No. 102. There are two boilers, each 40 feet long ; required, their diameters to drive three board planing machines, and three circular saws ; the calculated power required, is 33 horse power — find 40 in the column marked Length," (in Table No. 1, Steam Power,) opposite to this number in the table, find half of 33, which is 16.6 nearly, over this number in the column marked Diameter," will be found 30 inches, the diameter of the boilers. — Answer. No. 103. Required, the number of cubic feet of water per day (12 hours) to supply an engine to drive two circular saws, and two planing machines ; the calculated power required is 22 horse power — find 22 in the column marked Horse PROBLEMS. 193 Power,'^ (in Table No. 4, Steam PoAver,) opposite to this number in the table, and under 12 in the column marked " Hours/' will be found 290.4 cubic feet of water. — Answer, No. 104. Required, the number of cubic feet of water per day (12 hours) to supply an engine to drive two run of 4^ feet stones grinding corn ; the calculated power required is 28 horse power — find 28 in the column marked ^' Horse Power," (in Table No. 4, Steam Power,) opposite to this number in the table, and under 12 in the column marked " Hours," will be found 369.6 cubic feet of water. — Answer, No. 105. Required, the number of cubic feet of water per day (12 hours) to supply engines to drive 17,045,454 frame spindles with looms, on No. 25 yarn ; the calculated power required is 289,772 horse power — find 100 in the column marked Horse Power," (in Table No. 4, Steam Power,) opposite to this number in the table, and under 12 in the column marked Hours," will be found 1320 cubic feet; then, if 100 horse power require 1320 cubic feet, 289,772 horse power will by simple proportion require 3,824,990 cubic feet per day. — Answer, ■ No. 106. Divide 3,824,990 cubic feet by 43,200, the number of seconds in 12 hours, gives 88.5 cubic feet- per second ; required, the length of a dam over which 88.5 cubic feet of water will pass per second, the depth of the water on the dam being 6 inches — find 6 in the column marked "Depth," (in Table No. 2, Water Power,) opposite to this number in the column marked ''No. of Feet," will be found 1.2; then, if 1.2 cubic feet of water require a dam one foot long, 88,5 194 MECHANICAL PRINCIPIA. cubic feet will by simple proportion require a dam 74 feet long, nearly. — Answer, No. 107. Required, the diameter of an overshot water wheel, to drive 17,045,454 frame spindles with looms, on No. 25 yarn, the constant supply of water being 88.5 cubic feet per second ; the actual power required is 217,329 horse power — find 30 in the column marked No. Feet," (in Table No. 3, Water Power,) opposite to this number in the table, and under 10 in the column marked Diameter,' ' will be found 22,65 horse power ; then, if 30 cubic feet will give 22.65 horse power, 88.5 will by simple proportion give 64.17 horse power; now, if 64.17 horse power require a wheel 10 feet in diameter, 217,329 horse power will by sim- ple proportion require an overshot wheel 33,866 feet, or 6.4 miles in diameter. — Answer, No. 108. A belt is running 1500 feet per minute ; required, the number of square inches in contact with the drum to trans- mit 1 horse power — find 1 in the column marked " Horse Power," (in Table No. 2, Belting,) opposite to this number in the table, and under 2 in the column marked Diameter," will be found 1.8 inches, the width of the belt; the diameter of the drum is 2 feet, and the belt is in contact with nearly half the circumference of the drum, which is about 37 inches, which multiplied by 1.8, (the width of the belt,) gives 66.6, say 66 inches, for each horse power. — Answer, No. 109. A belt is running 1500 feet per minute ; required, the weight which each square inch of the belt is constantly raising ; 33,000 pounds raised one foot high per minute is equal to one horse power, 22 pounds raised 1500 feet high PROBLEMS. 195 per minute, is also equal to one horse power ; hence, 66 square inches in contact with the drum, raises 22 pounds 1500 feet per minute, but if 66 square inches raise 22 pounds, one square inch will raise of a pound, or -J- of a pound. — Answer, No. 110. The diameter of the smallest drum being 10 feet, and the power to be transmitted being 1 horse power, required, the width of the belt — find 1 in the column marked " Horse Power," opposite to thin number in the table, and under 10 in the column marked Diameter," will be found .36, or about one third of an inch in width : it will be noticed that the strength of the belt is not taken into consideration. — — Answer, No. 111. The distance between New-York city and Albany being 160 miles, and the running time of a steamboat in making a trip being 10 hours, which gives 16 miles per hour; and the diameter of the wheels being 30 feet ; required, the num- ber of revolutions of the wheels per minute, (presuming that the water does not yield,) — find 30 in the column marked '"Diameter," (in Table No. 1, Paddle Wheels,) below this number in the table, find 16 miles per hour, or the nearest number to it, which is 16.06, opposite to this number in the column marked ^' Revolutions," will be found 15, the num- ber of revolutions per minute. — Answer, No. 112. In No. Ill Problem, the whole number of revolutions of the paddle wheels during the trip, was 12,000 (found by the indicator on the engine,) required, the per cent slip of the wheel (or water) ; divide 12,000 by the number of minutes occupied in making the trip, which is 600, which gives 20 196 MECHANICAL PRINCIPIA. revolutions per minute — find 20 in the column marked Revolutions," (in Table No. 2, Paddle Wheels,) below this number in the table find 16, (miles speed of the boat in No. Ill Problem,) opposite to this number in the column marked Per Cent," will be found 18 per cent, the slip of the wheel (or water). — Answer. No. 113. It is estimated that the United States will manufacture 400,000 bales of cotton this year, (1848,) or about 180,000, 000 pounds, which divided by 300, ^the number of working days in a year,) gives 600,000 pounds per day; required, the number of dead spindles on No. 20 yarn, to manufacture 600,000 pounds of cotton per day — find 20 in the column marked " No. Yarn," (in Table No. 35, Manufacturing,) opposite to this number in the table, and under 4000 in the column marked No. Spindles," will be found 896 pounds; then, if 896 pounds require 4000 spindles, 600,000 pounds will by simple proportion require 2,678,571 spindles. — Answer, These goods will average about 4 yards to each pound of cotton, then 180,000,000 pounds of cotton will give 720,000, 000 yards. Suppose the population of the United States were 20,000,000 ; required, the number of yards to each person ; divide 720,000,000 by 20,000,000, which gives 36 yards to each person. No. 114. Required, the amount of capital to operate 2,678,571 spindles with looms — the usual amount invested per spindle, is 25 dollars, which multiplied by 2,678,571 gives 66,964, 275 dollars, the present capital employed in cotton manufac- turing in the States. — Answer. PROBLEMS. 197 No. 115. Required, the number of operatives to operate 2,678,571 spindles with looms, on No. 20 yarn — find 20 in the column marked ''No. Yarn,'' (in Table No. 16, Manufacturing,) below this number in the table, and opposite to 10,000 in the column marked ''Spindles," will be found. 315; then, if 10,000 spindles require 315 operatives, 2,678,571 spindles • will by simple proportion require 84,375 operatives. — Answer. No. 116. Required, the amount paid for labor per week, to ope- rate 2,678,571 spindles with looms, on No. 20 yarn — find 10,000 in the column marked " Spindles," (in Table No. 17, Manufacturing,) opposite to this number in the table, and under 20 in the column marked " No. Yarn," will be found 1130 dollars; then, if 10,000 spindles require 1130 dollars per week to operate them, 2,678,571 spindles will by simple proportion require 302,678 dollars per week, or 15,133,900 dollars per year. — Answer, No. 117. Required, the amount paid per week, including all ex- penses except the cost of cotton, to operate 2,678,571 spin- dles with looms, on No. 20 yarn — find 10,000 in the column marked "Spindles," (in Table No. 17, Manufacturing,) opposite to this number in the table, and under 20 in the column marked " No. Yarn," will be found 1530 dollars ; then, if 10,000 spindles require 1530 dollars, 2,678,571 spindles will by simple proportion require 409,821 dollars per week, or 20,491,050 per year. — Answer, Books sold at the very lowest prices. LEAYITT, TROW & CO/S CATALOGUE OP MISCELLANEOUS, THEOLOGICAL, CLASSICAL, AND gSEI(D)(DIL ]B(D)®Ego liEATITT, TROW & CO., BOOKSELLERS, 191 Broadway, corner of Dey-street. LEAVITT, TROW & CO/S PUBLICATIONS. EDWARDS' WORKS. Fifth edition. The complete works of President Jonathan Edwards. A reprint of the Worcester edition, without alteration or mutilation. With a copious General Index. 4 vols. 8vo. Library sheep. 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