n Ma iAumuaig nfff'Jr' ''T raf5m*w ^M ^^fc WWt QJM «^^^^^^^^^ ^^^ IKj< Jk^^KX ^p g K i^^^ ^P^ ^Pl 1 ^^^^^ 8^1 ^1^ »E i' vS'aLfe THE J. PAUL GEITY MUSEUM LIBRARY THE TINMAN'S MANUAL AND BUILDER'S AND MECHANIC'S HANDBOOK, DESIGNED FOR Tinmen, Japanners, CopperBmitlis, Engineers, Mechanics, Builders, lilill- wriglits. Smiths, Masons, Carpenters, Joiners, Slaters, Plasterers, Painters, Glaziers, Pavers, Plumbers, Surveyors, Oraugers, &e., &c.; with Compositions and Receipts for other useful and important purposes in the Practical Arts. By I. R. BUTTS, Author of the " United States Bushiess Man's Law Cabinet," " Business Man's Law Library ;" " Merchant's and Shipmaster's Manual and Shipbuild- er's and Sailmaker's Assistant," &c., &c. SECOKTID I3r>ITI03Sr. BOSTON: PUBLISHED BY I. R. BUTTS & CO. CORNER OF SCHOOL AND WASHINGTON STREET, Over Ticliiior &; ^fields' Boolsstore. 1861. 7 Entered according to Act of Concpress, in the year 18C0, by I. R. Butts, in the Clerk's Office of the District Court of the District of Massachusetts. IHi J. PAUL GETTY ONTHR UBRAKY PREFACE The present work is offered to Tinmen, Builders, Mechanics, and Engineers, as a useful manual of reference, and information. The first part of the work containing Rules, Diageams and Tables, will be found very useful to Tinmen. Mr. Truesdell who has, for many years, used the Diagrams pre- pared by him for this work, now offers them to the public with every confidence. The Receipts for Japans, Varnishes, Cements, ^c., were taken from "Ure's Dictionary," " Cooley's Cyclopedia," " Muspratt's Chemisti'y," and other valuable publications. The sources from which most of the materials relating to Building, Mechanics, and Engineering have been derived, are " Grier's Mechanic's Calculator," "Templeton'a Workshop Companion," "The Engineer's and Contractor's Pocket-book," " Adcock's En- gineer," "Smeaton's Builder's Companion," and "Lowndes's Engineer's Handbook," which renders this portion of the work deserving of the utmost confidence. LETTER FROM L. W. TRUESDELL. Mr. Butts, — Dear Sir, — If I may be permitted to comment upon the first part of your book, I would like to point out to Tinmen the value of the Diagrams which, a few years ago, could not have been purchased at any price ; but as they are now to be published, and sold at a low price, I am confident they will be bought by every Tin- 4 PREFACE. man, for I know, by experience, the perplexities to which they are often subjected from the want of them. With these Directions and Diagrams, the Tinman will be enabled to cut a Right-Anglcd or Circular Elbow of any size, in a few min- utes, and produce as perfect a mitre joint as can be made ; also, patterns for Flaring vessels, of any size or flare. Envelopes for Cones, Pyramid Cakes, Covers for Oval Dishes and Boilers, Funnel-shaped Covers for Pails, Breasts for Cans, Lips for Measures of any size, &c.* When about to make a copy from these diagrams the person should proviile himself with a sheet of paper or tin-plate, and strictly follow the directions given. Suppose^ for example, that he is about to copy Fig. 1, the directions are, first, from the centre C describe a circle AB. Having described the circle AB, next, place the corner of the square on the centre C, and draw the lines CD and CE ; then draw the chord DE. When the Tinman has become familiar with the diagrams, he will find them simple and convenient, and be better qualified to undertake work of a difficult character. If an Elbow at right-angles, of ten or fifteen inches diameter, should be reiiuirod, with the directions and diagrams before him, he could cut it out in a few minutes ; and so with a curved elbow of any diameter, a semicircle, or an ellipses- shaped dish of any size. But without a rule or pattern it would be a difficult and troublesome undertaking. Having by experience proved the correctness and usefulness of these Diagrams, I can confidently recommend them to all persons engaged in the manufiicture of Tin Ware. L. W. TRUESDELL. OwEGO, N. Y. Sept. 23, 18G0. EXTRACT OF A LETTER FROM A TINMAN. Mr. Butts,— Dear Sib, — "Your • Tinman^ s ManuctV strikes me as being nearer what we want in our business, than anything I have ever seen, — and I have examined every thing of the kind I have been able to find. The best we have been able to do has been to jiick up what ideas we could from works on Geometry and Building, and work out what rules we could from them. I have often wondered why some person did not umlertake just what you have done. This work of yours supplies just the want that every thinking man who works at the business has felt, even from liis first start ; and the want is still more sensibly felt as he grows older, and finds how much there is to learu." ' In Tinman's Diagrams the allowance for locks is always omiiied. CONTENTS. RULES AND DIAGRAMS FOR WORKERS IN TIN, SHEET IRON AND COPPER. Page. Manufacture of Tin Plate 12 Quality of Tin Plate 14 CIRCLES. To find the Circumference 'of any Diameter 15 To find the Area of a Sector of a Circle 15 Proportion of Circles to enable ma- chinists to enlarge or reduce wheels without changing their motion 16 The Circle and its Sections 27 To find the centre of a Circle from a pan of the Circumference 33 Diameters, Circumferences, and Areas of Circles 41 CTUNDEKS. To find the Contents in Gallons of any Cylindrical Vessel 38 Tables giving the Content in Gal- lons of Cylinders from 1 inch to 30 feet Diameter 42 Table giving the Content in Gal- lons of Cans from 3 inches to 40 inches Diameter 45 BEVEL COVEES. To describe Bevel Covers for Ves- sels, or Breasts for Cans 25 To describe Bevel Covers for Ves- sels, or Breasts for Cans, {another mode) 32 To describe Covers for Pails 25 ELLIPSES OR OVALS. To describe an Ellipse 17 Definition of an Oval, — note 17 To describe an Ellipse {another mode) 18 To find the Circumference of an Ellipse 19 To find the Area of an Ellipse 19 To describe an Oval Boiler Cover 26 To draw an Ellipse, the transverse and conjugate Diameters being given, i. e. the length and width 116 To draw an Ellipse by means of two concentriccircles 117 1* Page- ELBOWS. To describe a Right Angled Elbow 20 To describe a Straight Elbow (old method) 21 To describe a Curved Elbow 22 To describe a Straight Elbow (another inode) 24 FLARING VESSELS. To describe a Flaring Vessel Pat- tern, a Set of Patterns for a Py- raimd Cake, or an Envelope for a Cone 28 To describe a Cone or Frustum.. . 29 To strike the Side of a Flaring Vessel 31 To construct the Frustum of a Cone 34 To strike out a Cone or Frustum. . 35 To find the content of a Cone . . 35 To find the Angles of a Frustum of an inverted Pyramid, such as a Mill Hopper, &c 36 To find the content of the Frustum of a Cone, such as a Coflee-pot, Bowl, &c .' 36 MISCELLANEOUS. To joint Lead Plates 23 Soldering for Lead, Zinc, Tin, and Pewter 23 To joint Lead Pipes, 24 Soldermg for Copper 160 To describe a Lip to a Mea.sure. . 27 To describe a Cycloid, or Curve. . 30 To describe a Heart 30 Tinning Iron 31 A good Solder 33 Sector, for obtaining Angles 34 Sector, definition of. 34 Rule to find the Content in Gallons of Frustums of Cones 37 Rule to find the Content in Gallons of any Cylindrical Vessel 38 Table to ascertain ithe weight of Pipes of various metals, and any Diameter required 38 Table of Tin Plates, size and weight per box 39 Table of Cans, quantity and qual- ity of Tin required for 2J to 125 gallons 39 CONTENTS. Page. Weight of a cylindrical and cubic inch, cubic foot and gallon ot AValer 40 Decimal Equivalents to the frac- tional parts of a Gallon or an Inch 40 Tables containing the Diamciers, Circumferences and Areas of Circles 42 Tables giving the Diameters and Circumferences of Circles 1~1 Tables to ascertain the weight of Lead Pipes 139 Capacity of Cans in Gallons from 3 inches to 40 inches in Diameter 45 New Tinning Process 40 rage. Crj'slallizing Tin Plate, how per- formed 46 Tinnir.g Vessels of Brass or Copper 46 Kustilien's .Metal for Tinning 46 Instruments used in Drawing. .. . 101 Composition of Britannia Metal for Spouts, Registers, Spoons, &c. . 91 Composition of Britannia Melal for Lamps, Pillars, Handles, and Castings 92 Solder for Britannia "Ware 91 Lacker for Tin Plate 73 & 94 Solder, Tinman's 96 Definitions of Arithmetical Signs used in this work 110 RECEIPTS FOR THE USE BUILDERS, JAPANNING AND VAUNISHINO. Directions for Jai)anning White Japan Grounds— Gum Copal Black Grounds— Black Japan Brunswick Black — Blue Japan Grounds — Scarlet Japan — Yel- low Grounds — Green Japan Grounds Orange Colored Grounds— Purple Japan Grounds — Black Japan- Japan Black for Leather — Trans- parent Japan — Japanners' Copal Varnish Tortoise Shell Japan— Painting Japan Work — Japanning Old Tea-trays— Japan Finishing. . . . TARNISHES — MISCELLANEOUS. Substances employed for making Varnishes Choice of Linseed Oil CIIIEF RESINS EMPLOYED IN MAKING VARNISH. Amber— Anime— Benzoin — Colo- phony — Copal Dammara— Llimi — Lac — Mastic — Saiidarach Turpenline — Alcoliol — Naphtlia anil Meihylated Spirit of Wine- Spirit Varnishes Essence Varnishes— Oil Varnialica — Lacker VARNISHES. Copnl Varnishes {six hinth) Copal Varnishes {three hhnts) Cab- inet Varniili— Table Varnish— Coiniiion Table Varnish — Copal Varnish for Inside Work Copal Polish— While Spirit Var- nisli— White Hard Spirit Var- oibhes —While Vurnish OP JAPANNERS, VARNISHERS, MECHANICS, &c. Soft Brilliant Varnish 62 Brown Hard Spirit Varnishes— To prepare a Varnish for Coating Metals — Varnish for Iron and Steel, for Iron Work, Black for Iron Work, Bronze for Statuary 63 Amber Varnishes, Black, Pale, Hard— Black Varnish 64 Varnish for certain parts of Car- riages, Coaches, Mahogany, for Cabinet IMakers— Cement Var- nish for water-tight Luting— The Varnish of Watin for GiUk-d Ar- ticles—Oak Varnish— Varnish for Wood-work— Dark Varnish for light AV^ood-work 65 Varnish for Instruments, for W'ood Toys of Spa, for Furniture— To French Polish 66 Furniture Polishes, Gloss, Cream, Oils, Pastes— Etching Varnishes 67 Varnish for Engraving, Maps, to fix Engravings or Lithographs on Wood, I for Oil Paintings and Lithograplis, lor Paintings and Pictures- Milk of AVax 68 Crj-stal Varnishes, Italian — AVater Varnish for Oil Paintings- Var- nish for Paper-hangings, Book- binders, Cordwork 69 Varnish for Printers — for Brick walls— Mastic Varnishes j^lndia Rublu-r Varnishes 70 Black Varnish for Harness— Boil- ed Oil or Linseed Oil Varnish— Dammar Varnish 71 Common Varnish — .Waterproof Varnishes — Varnishes for Bal- 49 50 51 52 53 54 60 01 62 loons. Gas Bags, ic— Gold Var- nisli — Wainscot Varnish for House Painting and Japanning LACKERS. Gold Lacker— Red Spirit Lacker- Pale Brass Lacker— Lacker for 72 CONTENTS. Page. Tin — Lacker Varnish — Deep Gold Colored Lacker — Lackers for Pictures, IMetal, Wood, or Leather 73 CEMENTS. Armenian, or Diamond Cement. . 74 Cements for mending- Glass Ware 74 Cement for Slone-vvare— Iron-Rust Cement — for making- Architectu- ral Ornaments — Varley's Mastic — Electrical and Chemical Appa- ratus Cement 75 Cements for Iron Tubes, Boilers, Ivory, Mother of Pearl, Holes in Castings, Coppersmiths and En- gineers, Plumbers, Bottle- corks, China and Leather 76 Cements for Marble, Marble--work- ers, Coppersmiths, Glass, mend- ing Iron Pots and Pans, Cisterns and Casks 77 Cements for mending Fractured Bodies of all kinds, for Cracks in "Wood, joining Metals and Wood, for fastening Brass to Glass Ves- sels, Blades, and Files — Gas-Fit- ter's Cement— Cement Paint. ... 78 builders' cemexts. Cements for Terraces, Roofs, Re- servoirs, Fronts of Houses, &c.. . 79 Cements for Brick Walls, Seams, and Tile roofs SO Coarse Sluff. SO Parker's Cement— Hamelein's Ce- ment — Plaster in imitation of Marble — Scagliola 81 Maliha, or Greek Mastic — Fine Stuff— Stucco for Inside Walls 82 Higgins's Stucco — Gauge Stuff- Page. Composition — Foundations of Buildings 83 Concrete Floors — Fite-proof Com- position 84 RECEIPTS. To Polish Wainscot and Mahoga- any — Imitation of Mahogany — Furniture Varnish — To make Glass and Stone Paper 85 Whitewash — Paint for Coating AVire "Work — To Bleach Sponge — Lac Varnish for Vines— Razor Paste — Leather Varnish — To keep Tires Tight on Wheels 86 To Cut Glass — Prepared Liquid Glue — Marine Glue — Paste for Envelopes — Dextrine, or British Gum — Gum Mucilage 87 Flour Paste — Sealing Wax for Fruit Cans— Fusible Metal— Me- tallic Cement 83 Artificial Gold — Or-mulo — Blanch- ed Copper — Browning Gun Bar- rels — Silvering Powder for Coat- ing Copper 89 Alloys for Journal Boxes — Bells of Clocks — Tools — Cymbals and Gongs — Solder for Steel Joints — Files — To prevent Tools from Rusting — Axle-Grease- to Gal- vanize—Soft Gold Solder 90 RECEIPTS AND COMPOSITIONS. Nearly 200 Compositions for Me- chanists, Iron and Brass Found- ers, Turners, Tinmen, Copper- smiths, Dentists, Finishers of Brass, German Silver, Britan- nia, and other useful purposes in the Practical Arts 91 MECHANICAL DEAWING. Instruments used in Drawing 101 I Mechanical Drawing and Perspec- The Sector' 103 live 105 PRACTICAL GEOMETRY. Definition of Arithmetical Signs. . 110 PROBLEMS. To find the Circumference of a Di- ameter 15 To find the area of a Sector 15 To find the Proportion of Circles by which to enlarge or reduce Wheels without changing their motion 16 To find the various and proper Di- mensions of Materials whereby to construct Hipped Roofs,&c.. . 36 To find the Centre of a Circle from a part of the Circumference 33 The Circle and its Sections 27 Sector, for obtaining Angles 34 To inscribe an Equilateral Trian- gle within a given Circle Ill Within a given Circle to inscribe a Square 112 Within a given Circle to inscribe a regular Pentagon 112 Within a given Circle to describe a regular Hexagon 113 To cut off the Corners of a given 8 CONTENTS. Page. Square, so as to form a regular Octagon 113 To divide a given Line into any Number of Parts, which Parts shall be in the same Proportion to each other as the Parts of some other given line, whether those parts are equal or unequal 114 On a given Line to draw a Poly- gon of any Number of Sides, so that that Line shall be one side of a Polygon 114 OF DRAWIXG CUEVED LINES. To draw an Ellipse with the Rule and Compasses, the transverse and conjugate Diameters being given ; i. c. the length and width IIG To draw an Ellipse by means of Page, two Concentric Circles - 116 To draw an Ellipse of any length and width ■ % 18 To find the Circumference &. Area of an Ellipse 19 Other methods for describing an Ellipse 117 To find the Centre and the two Axes of an Ellipse 118 To draw a flat Arch by the inter- section of Lines, liaving the Opening and Spring or Rise given 119 To find the Form or Curvature of a raking Moulding that shall unite correctly with a level one 119 To find the Form or Curvature of the Return in aji open or broken Pediment 120 EPITOME OF MENSURATION. Ofthe Circle, Cylinder, Sphere, Zone, &c Of the Square, Rectangle, Cube Surfaces and solidities of Bodies Of Triangles, Polygons, &c Of Ellipses, Cones, Frustums, &c. INSTKUMEJfTAL AEITHMETIC. Utility ofthe Slide Rule • Numeration 123 123 124 124 125 125 126 To Multiply Numbers by the Rule 126 To divide Numbers upon the Rule 126 Proporlion or Rule of Three Direct 127 Square &. Cube Roots of Numbers 127 Rule of Three Inverse 127 Mensuration of Surface 128 Mensuration of Solidity and Ca- pacity 129 Power of Steam Engines 130 OfEngme Boilers 130 RULES AND TABLES FOR ARTIFICERS AND ENGINEERS. Measurement of Bricklayer's work 132 Table to find the number of Bricks in any given Wall 133 Measurement of AVells 4. Cisterns 133 Measurement of Mason's AV'ork.. 133 Measurement of Carpenter's and Joiner's AVork 134 Table of different sized Nails to alb 135 Table of different sized Sashes, &c 13G Measurement of Slater's AVork.. . 136 Table of American Slates 136 Table of Imported Slates 137 Measurement of Plasterer's AVork 137 Measurement of Paver's AVork. . . . 137 Measurement of Painter's AVork... 137 Measurement of Glazier's AVork. . 138 Table of Size and Number of Lights to the 100 Square Feet... 138 Measurement of Plumber's AVork 138 Table ol Sizes and Weight of Pa- tent Lead Pipe 139 Table of Boston Lead Pipe 139 Table of Comparative Strength and Weight of Ropes and Chains... 139 8TUENGTU OF MATERIALS. Dcfinilinn* 140 Table of Tenacities, Resistance to Compression, &c,, of various Bodies 140 Resistance to Lateral Pressure. . . 140 Table of Practical Data 141 To find the dimensions of a beam of Timber to sustain a given AVeight 141 To determine the absolute strength of a Rectangular Beam of Tim- ber 141 To determine the dimensions of a Beam with a given degree of de- flection 142 Cast-iron Beams of strongest sec- lion 142 Of Wooden Beams, Trussed 142 Absolute Strength of Cast-iron Beams 142 Dimensions for Cast-iron Beams.. 143 To find the AVeight of a Cast-iron Beam- 143 Resistance to flexure by vertical pressure 143 To determine the dimensions for a Column of Timber 144 Resistance of Bodies to Twisting 144 Relative strength of Metals to re- sist Torsion 144 CONTENTS. Page. Breaking strength of a Bar of Wioughl Iron 145 Lateral strength of Wrought Iron as compared with Cast-iron 145 Load on Bridges, Floors, Roofs, and Beams 145 Strength of Beams, Bar of Wood, Stoiie, Metal, Ropes, Tubes, or Hollow Cylinders 146 Models proportioned to Machines 14G Metals arranged according to their Strength...". 147 Woods arranged according to do. 147 Strength of Cords, &c 147 Strength ofReclaugular and Round Timber 148 Table of the Cohesive Power of Bars of .Metal 148 Relative Strength of Cast and Mal- leable Iron 148 STRENGTH OF BEAMS. Solid, Rectangular, Rovnd, Hollow 149 To find the breaking Weight in lbs. 149 To find the proper Size for any giv- en purpose 150 Strength of Cast-iron with Feath- ers or Flanges 150 Wrought Iron Beams and Girders 151 Hollow Girders 152 To find the Strength of a Round Girder- 152 To find the Strength of any Beam 152 SOLID COLUMNS. To find the Strength of any Wro't Iron Column with Square ends 153 To find the Strength of Round Col- umns exceeding 25 diameters in Length 154 Tables of Powers for the Diame- ters and Lengths of Columns. . . 154 HOLLOW COLUMNS. Square Columns of Plate Iron riv- etted 155 To find the Strength of any Hol- low Wrought Iron Column .... 355 Round Columns of Plate Iron .... 156 CKANE. To find the Strain on the Post. . . 150 COLD WATER PUMP. To find tne proper Size, under any circumstances, capable of sup- plying t-\vice the quantity ordina- rily used in injection 156 FANS. Velocity of Fans 157 The best Velocity of Circumfer- ence for different Densities..,, 157 Page. To find the Horse Power required for any Fan 157 To find ihe Density to be attained with any given Fan 157 To find Ihe Quantity of Air that \vill be delivered by any Fan, the Density being known 158 FRICTION. From Mr. Rennie's Experiments.. 158 CENTRIFUGAIi FORCE In terms of Weight 158 PEDEST.'VI, AND BRACKET. Thickness of cover, diameter, dis- tance, solid metal, &c 159 TEMPERING. For Lancets, Razors, Penknives, Scissors, Hatchets, Saws, Chis- els, Springs, &c 159 CASE HARDENING Articles, how Case Hardened. . . . 159 To Case Harden Cast Iron 160 HEAT. Effects of Heat on Metals, &c., at certain Temperatures 160 SOLDERING. For Joints, Copper, Iron and Brass 160 BORING. The best speed for boring Iron, drilling, and turning 161 BRASS. Compositions of Brass 161 Brass Castings, mode of Casting.. 161 ROPE. To find the Breaking Weight of Tarred Hemp Rope 162 To find the AVeight per Fathom of Rope or Tarred Cordage 163 To find the "Weight per Fathom of Tarred Hawser or Manilla Rope 163 To find the AVeisht per Fathom of Hawser laid Manilla 163 WEIGHT OF CASTINGS. To find the Weight of any Casting 163 To find the AVeighl from the Areas 163 To find the AVeight in cwts 163 AVeight of Boiler Plates 163 To find the Weight of Boiler Plates 164 CONTINUOUS CIRCULAR MOTION. AVhen Time is not taken into Ac- count 164 10 CONTENTS. Page. To find the number of Revolutions of the lasl lo one of llie first, in a train of Wheels and Pinions. . . . 164 When Time must be regarded. . . . 165 The distance between the Centres and Velocities of two AVheels be- ing given, to find their Diameters 165 To determine the Proportion of Wheels for Screw-cutting by a Lathe 166 Table of Change AVheels for Screw cutting; the leading Screw be- ing half inch pitch, or contain- ing 2 threads in an inch 167 Table by which to determine the Number of Teeth, or Pitch of Small Wheels, or what is called the Manchester Principle 167 Strength of the Teeth of Cast Iron Wheels at a given Velocity 163 WHEELS A>T> GUDGEONS. To find size of Teeth necessary to transmit a given Horse Power. . 163 To find the Horse Power that any Wheel will transmit 169 Page. To find the multiplying Number for any Wheel 169 To find the Size of Teeth to carry a given Load in lbs 169 ■WATEE. To find the Quantity of Water that will be discharged through an Orifice, or Pipe, in the side or bottom of a Vessel 169 To find the size of Hole necessary lo discharge a given Quantity of Water under a given Head 170 To find the Height necessary to discharge a "fiven Quantity thro' a given Orifice 170 The Velocity of AVater issuing from an Orifice in the side or bot- tom of a Vessel ascertained.... 170 To find the Quantity of AVater that will run through any Orifice, the top of which IS level with the Surface of AA'ater, as over a Sluice or Dam 170 To find the Time in which a Vessel will empty itself through a given Orifice 170 MECHANICAL TABLES FOR THE USE OF OPERATIVE SmiHS, MILLWRIGHTS, AND ENGINEERS. Tables of the Diameters and Cir- cumferences of Circles 171 Observations on do 177 Circumferences of Angled Iron Hoops — outside 179 Circumferences of Angled Iron Hoops— inside 180 Observations on the above Tables 181 Tables of the AVeight of 100 lbs. of Ship Spikes, Hatch Nails, Hook Heads, Dock Nails, IJoat Spikes, Railroad Spikes &. Horse Shoes 182 Coppers, dimensions and weight of 183 Copper Tubing, weight of 183 Brass, Copper, Steel and Lead, weight of a Fool from .\ to 3 inch- es Round or Square Ift3 Flat Cast Iron, weight of a Fool.. . 181 Cast Iron, AVeight of a Superficial Foot, from | to 2 inches thick. . 181 Table giving the AVeight of Cast Iron, Copper, Brass, and Lead Balls, from 1 to 12 inch diameter 184 Cast Iron, weight of a Fool in lenglli of .'Square and Round. . . . 185 Rtcel, weight of a Foot of Flat. . . . lt-5 Parallel Angle Iron, of equal sides 180 Parallel Angle Iron, unequal sides 186 Taper Angle Iron, of equal sides. . 186 Parallel T Iron, unequal width and depth 187 Parallel T Iron, of equal depth and width 187 Taper T Iron 187 Tableof AA'cighlof Sash Iron 188 Table of AVeight of Rails, top and bottom Tables 188 Table of AA''eight of Temporary do. 188 Tables showing the AVeight of a lineal Foot of Malleable Reclan- pular, or Flat Iron, from ,V lo 3 mches in thickness 189 ELASTIC FORCE OF STEAM. Table of the Elastic Properties of Steam and corresponding tempe- rature of Water 194 Production it Properties of Steam 195 Table of the Elastic Force of Steam the Pressure of the Atinospherc not being included 195 Table of the Consumption of Coal per hour in Steamers 196 Evaporative Power of Coal 196 GAUGER'S RULES AND TABLES. To Gauge Conks, U. Stales Gallons 201 To Gauge Casks, Imperial Galloiiri 202 To Ullage, or fiiii: TO DESCRIBE A CURVED ELBOW. 23 Describe two circles TJX and V'S, the curves desired for the elbow, having the distance from U to V equal to the diameter ; then divide the circle V, W, R and S, into as many sections as desired ; then construct a rectangle, Fig. 8, ADEB, the width equal to the -width of one section V'W, Fig. 7, and the length equal to the circumference of the elbow ; then span the dividers from the point R to the point P at the dotted line. Fig. 7, and with the dividers thus spanned mark the points FF' Fig. 8, from points A and D, and draw the lines FG and F'G' ; from point I draw the two diagonal lines IF and IG, span the dividers so as to divide one of these diagonal lines into six equal parts, viz. I, L,/0, T, 0, V, G ; from the point L erect a perpendicular line produced until it intersects the line IH produced ; from the point of intersection M, as a centre, describe the arc NIO for the top of the elbow ; with the same sweep ol the dividers describe the arcs NO and NO ; then draw an indefinite straight line PQ tangent to the arcs NO and NI, having the points of contact at S and S ; on this tangent line erect a perpendicular line passing through the point N • (same as in Fig. 5), produced until it intersects the line BE pro- duced ; then place one foot of the dividers on the point of intersection and span them over the dotted line to the point T, (same as in Fig. 5), and with the dividers spanned describe the arcs TS, TS, TS, and TS ; these arcs and the arcs NO, NIO and ON, will be one side of the section, and by the same rule the other side of the section may be described at the same time, which will be a pattern to cut the other sections by. SOLDERING. ^ For Lead the solder is 1 part tin, 1 to 2 of lead; — for Tin 1 to 2 parts tin to 1 of lead ; — for Zinc 1 part tin to 1 to 2 of lead ; — for Pewter 1 part tm to 1 of lead, and 1 to 2 parts of bismuth. The surfaces to be joined are made perfectly clean and smooth, and then covered with sal-ammoniac, or resin, or both ; the solder is then applied, being melted in, and smoothed over by the soldering iron. To Joint Lead Plates. — The joints of lead plates for some purposes are made as follows : — The edges are brought together, hammered down into a sort of channel cut out of wood, and secured with a few tacks. The hollow is then scraped clean with a scraper, rubbed over with candle grease, and a stream of hot lead is poured into it, the surface being afterwards smoothed with a red-hot plumber's iron. 24 TO DESCRIBE A STRAIGHT ELBOW. TO DESCRIBE A STRAIGHT ELBOW. [Another Method for describing a Straight Elbow.] Figs. 9 & 10. Fig. 10. FiQ- 9- / ■^^ e. d r / \ C I / \ & a y N> a Fig. 9. — Draw a profile of half of the elbow -wanted, and mark a semicircle on the line representing the diameter, divide the Bemi, circle into six eqiial parts, draw perpendicular lines from each divi- sion on the circle to the angle line as on figure. Fig. 10. Draw the circumference and depth of elbow wanted, and divide into twelve equal parts, mark the height of perpendic- ular lines of Fig. 9 on Fig. 10 a 6 c &c. ; set your dividers the same as for the semicircle and sweep from e to e intersecting with f and the same from a to the corner, then set the dividers one-third the circumference and sweep from e to i each side, and from a to 6 each side at bottom ; then set your dividers three-fourths of the cir- cumference and sweep from c to d each side on top, and from c to b at bottom, and you obtain a more correct pattern than is gen- erally used. Allow for the lap or seam outside of your drawing, and lay out the elbow deep enough to put together by swedge or machine. Be careful in dividing and marking out, and the large end will be true without trimmiug. The seams must be added to drawing. To Joint Lead Pi/)es.— Widen out the end of one pipe with a taper ■wood drift, and scrape it clean inside ; scrape the end of the other pipe outside a little taijcrcd, and insert it in the former : then solder it with common lead solder as before described ; or if required to be strong, rub a little tallow over, and cover the joint with a ball of melted lead, liolding a cloth (2 or 3 plies of greased bed-tick) on the under side ; and smoothing over witli it and the plumber's iron. TO DESCRIBE BEVEL COVERS. 25 TO DESCRIBE BEVEL COVEES FOR VESSELS, OR BREASTS FOR CANS. [Dra\rn for this work by L. W. Truesdell, Tinman, Owcgo, N. T.] Fig. 11. From as a centre, describe a circle DE larger than the vessel ; and from C as a centre, describe a circle AB the size of the vessel, then with the dividers the same as you described the circle the size of the vessel, apply them six times on the circumference of the circle larger than the vessel ; for can-breasts describe the circle FG the size you wish for the opening of the breast. TO DESCRIBE PITCHED COVERS FOR PAILS, &c. Fig. 12. To cut for pitched covers, draw a circle one inch larger than the hoop is in diameter after burring, then draw a line from the centre to ^ 3 26 OVAL BOILER COVER. the circumference as in the figure, and one inch from the centre and connecting with this line draw two more lines the ends of which sh.all be one inch on either side of the line first drawn, and then cut out the piece. TO DESCRIBE AN OVAL BOILER COVER. [Drawn for this vork by L. W. Teuesdell, Tinman, Owcgo, N. Y.] Fig. 13. From C as a centre, descrihe a circle whose diameter will he equal to tlic width of the boiler outside of the wire, and draw the line AB perpendicular to the line EF, having it pass through the point D, which is one-half of the length of the boiler ; tlicn mark the point J one quarter of an inch or more as you wish, for the pitch of the cover, and apply tlie corner of the scjuare on tlie line AB, allowing the blade to fall on the circle at II, and the tongue at the point .T ; tlien draw the lines IIB, B.I, CA and AJ, which completes the description. TO DESCRIBE A LIP TO A MEASURE. 27 TO DESCRIBE A LIP TO A MEASURE. [Drawn for this work by L. "W. Telesdell, Tinman, Owego, N. Y.] Orig'liial. Fig. 14. Let the circle AB represent the size of the measure ; span the divi- ders from K to F three-quarters of the diameter ; describe the semi- circle DKE ; move the dividers to G the width of the lip required, and describe the semicircle KPJ, which will be the lip sought. THE CIRCLE AND ITS SECTIONS. 1. The Areas of Circles are to each other as the squares of their diameters ; any circle twice the diameter of another contains four times the area of the other. 2. The Radius of a circle is a straight line drawn from the centre to the circumference. 3. The Diameter of a circle is a straight line drawn through the centre, and terminated both ways at the circumference. 4. A Chord is a straight line joining any two points of the circum- ference. 5. An Arc is any part of the circumference. 6. A Semicircle is half the circumference cut off by a diameter. 7. A Segment is any portion of a circle cut off by a chord. 8. A Sector is a part of a circle cut off by two radii. 28 FLARING VESSEL. TO DESCRIBE A FLARING VESSEL PATTERN, A SET OF PATTERNS FOR A PYRAMID CAKE, OR AN ENVELOPE FOR A CONE. [Drawn for this work by L. W. Truesdell, Tinman, Owego, N. T.] Oi-igirxal. Fig. 15. s ^— f-^ n From a point G as a centre, describe a circle AB equal to the large circumference ; with the point F as a centre, the depth of the vessel, describe a circle DE equal to the small circumference ; then draw the lines Gil and KS tangent to the circles AB and DE ; from the point of intersection as a centre, describe the arcs ACB and DFE ; then ADKB will be the size of the vessel, and three such pieces will bo an envelope for it, and AJBTFU the altitude ; then by dividing the sector TO DESCRIBE THE FRUSTUM OF A CONE. 29 SOH into sections AB, DE, PQ, and WX, you will have a set of patterns for a pyramid cake ; and the sector AOB will be one-third of an envelope for a cone. In allowing for locks, you must draw the lines parallel to the radii, as represented in the diagram by dotted lines, which will bring the vessel true across the top and bottom. TO DESCRIBE A CONE OR FRUSTUM. Fig. 16. D c.''' \ / "N^ G / / / .A. First draw a side elevation of the desired vessel, DE, then from A as a centre describe the arcs CDC and GEG ; after finding the diam- eter of the top or large end, turn to the table of Diameters and Cir- cumferences, where you will find the true circumference, which you will proceed to lay out on the upper or larger arc CDC, making due allowance for the locks, wire and burr. This is for one piece ; if for two pieces you will lay out only one-half the circumference on the plate ; if for three pieces one-third ; if for four pieces one-fourth ; and so on for any number, remembering to make the allowance for locks, wire and burr on the piece you use for a pattern. 3* 30 TO DESCRIBE A HEAPvT. CYCLOID. TO DESCRIBE A HEART. [Drawn for this work by L. W. Tkuesdell, Tinman, Owego, N. Y.] Fig. 17. Draw an indefinite line AB ; then span the dividers one-fourth the ■width you wish the heart, and describe two semicircumferences AC and CB ; span the dividers from A to B, the width of the heart, and desaribe the lines AD and BD, which completes the description. CYCLOID. Fig. 18. ABA Cjcloid, a curve much used in mechanics. It is thus formed : — If the circumference of a circle be rolled on a right lino, beginning at any point A, and continued till the same point A arrive at the line again, making just one revolution, and thereby measuring out a straight line ABA equal to the circumference of a circle, while the TO STRIKE THE SIDE OF A FLARING VESSEL. 31 point A in the circumference traces out a curve line ACAGxi : then this curve is called a cycloid ; and some of its properties are contained in the following lemma. If the generating or revolving circle be placed in the middle of the cycloid, its diameter coinciding with the axis AB, and from any point there be drawn the tangent CF, the ordinate CDE perpendicular to the axis, and the chord of the circle AD ; then the chief properties are these : The right line CD equal to the circular arc AD ; The cycloidal arc AC equal to double the chord AD ; The semi-cycloid ACA equal to double the diameter AB, and The tangent CF is parallel to the chord AD. This curve is the line of swiftest descent, and that best suited for the path of the ball of a pendulum. TO STRIKE THE SIDE OF A FLARING VESSEL. Fig. 19. To tind the radius of a circle for striking the side of a flaring ves- sel having the diameters and depth of side given. Rule. -^As the difference between the lai'ge and small diameter is to the depth of the side, so is the small diameter to the radius of the circle by which it is struck. Example. — Suppose ABCD to be the desired vessel, with a top diameter of 12 inches, bottom diameter 9 inches, depth of side 8 inches. Then as 12 — 9 = 3 : 8 : : 9 to the radius. • 8x 9 = 72 -7-3 = 24 inches, answer. TINNING IRON. Cleanse the metal to be tinned, and rub with a coarse cloth, previously dipped in hydrochloric acid, (muriatic acid) and then rub on French putty with the same clotB. French putty is made by mixing tin filings with mercury. 32 TO DESCRIBE BREASTS FOR CANS. TO DESCRIBE BEVEL COVERS FOR VESSELS, OR BREASTS FOR CANS. Fia. 20. Construct a right angle ADB, and from tlic point C, tlie altitude height you wish the breast, erect a perpendicular line F ; then on the line B, mark the point E one-half the diameter of the can ; and on the line F, mark the point G one-half the diameter of the opening in the top of breast ; draw a line N to pass through the points E and G pro- duced until it intersects the line A ; place one foot of the dividers at the point of intersection II, and place the other on the point E, and describe the circle EIK ; span the dividers from the point H to point G, and describe the circle GLM ; then span the dividers from the point D to E, and step them six times on the circle EIK, which gives the size of the breast. Remember to mark the lines for the locks parallel with the radii. A GOOD SOLDEK. Take 1 lb. of pure Banca tin, and melt it, then add half a pound of clean lead, an>£. 9_-. D xxxx 100 17 by 12.i 1 2 21 o _ o o D xxxxx 100 17 by 12^ 1 3 14 '^ .2 ^ !H D xxxxxx 100 17 by 12i 2 7 4J a.':^ m SDC 200 15 by 11 1 1 27 £ —Is SD X 200 15 bv 11 1 2 20 fe J =. 2 -3 SD XX 200 15 by 11 1 3 13 S D XXX S D xxxx 200 200 15 by 11 15 by 11 2 2 6 27 ition, ortec costi than •egu: S D xxxxx 200 15 by 11 2 1 20 •6 D. ■" S D xxxxxx 200 15 by 11 2 2 13 «.= = o o ^3 Qi -J « Qi ^H r: cfi o r^ about TTT Taggers, 225 14 by 10 1 c3 3 Cw IC 225 12 by 12 " 1 X 225 12 by 12 1 XI 225 12 by 12 1 XXX 225 12 by 12 About the same weight 1 xxxx 225 12 by 12 » >per Box, as the plates above of similar brand, 14 by 10. 1 c 112 14 by 20 1 X 112 14 by 20 1 XX 112 14 by 20 1 XXX 112 14 by 20 I xxxx 112 14 by 20 - Leaded or'il C Terms jl x 112 112 14 by 20 14 by 20 1 1 1 > For Roofing. OIL CANISTERS, (from2i to 125 ff alls.) WITH THE QUANTITY AND QUALITY OF TIN REQUIRED FOR CUSTOM WORK. Galls. Quantity and Quality. Galls. 33 Quantity and Quality. 2^ 2 Plates, I X in body. 13^ Plates, IX in body, "3 3i 2 « S DX breadths high. 5^ 2 " DX 45 13^ Plates, S D X in body. 8 4 « IX 60 13i " D X " 10 3^ « DX 90 154 " D X « * 15 4 " DX 125 20 " D X « • The boUom tier of plates to be placed lengthwise. 40 WEIGHT OF WATER AND DECIMAL EQUIVALENTS. WEIGHT OF WATER. 1 cubic inch is equal to .03617 pounds. 12 cubic inclies is equal to .434 pounds. 1 cubic foot is equal to 02. 5 pounds. 1 cubic foot is equal to 7.50 U. S. gallons. 1.8 cubic feet is equal to 112.00 pounds. 35.84 cubic feet is equal to 2240.00 pounds. 1 Cylindrical inch .. is equal to .02842 pounds. 12 Cylindrical inches . is equal to .341 pounds. 1 Cylindrical foot . . is equal to 49.10 pounds. 1 Cylindrical foot . . is equal to 6.00 U. S. Gallons. 2.282 Cylindrical feet .. is equal to 112.00 pounds. 45.64 Cylindrical feet . . is equal to 2240.00 pounds. 11.2 Imperial gallons . . is equal to 112.00 pounds. 224 Imperial gallons . . is equal to 2240.00 pounds. 13.44 United States galls, is C(iual to 112.00 pounds. 268.8 United States galls, is equal to 2240.00 pounds. Centre of pressure is at two-thirds depth from surface. DECIMAL EQUIVALENTS TO THE FRACTIONAL PARTS OF A GALLON, OR AN INCH. [The Inch, or Gallon, being divided into 32 parts.] [In multiplying decimals it is usual to drop aU but the two or tlirce first figures.] Deci- mals. Gallon. or Inch. 3 5 1 a ll Deci- mals. Gallon. or Inch. 12 p 3 1 Decimals. Gallon. . ^ Inch. 1 S i & .03123 1-32 i^ .375 3-8 H i .71875 23-32 23 55 .0625 1-16 2 ^ I .40625 13-32 13 H n'\ .75 3-4 24 6 3 .09375 3-32 3 i i .4375 7-16 14 U 13 .78125 25-32 25 6i 3i .125 1-8 4 1 i .46875 15-32 15 n IJ .8125 13-16 26 6i3i .15625 5-32 5 li SLS 1-2 16 4 2 .84375 27-32,27 63 33 .1875 .S-16 an ? .53125 17-32 17 ^ 21 .875 7-8 '28 7 34 .21875 7-32 7 13 I .5625 9-16 18 4i 2] .90625 29 32 29 7.i3| .25 1-4 8 12 1 1. 59375, 19-32 19 ■ii 2i .9375 13-16 30 74 n .28125 9-32 9 '2-1 14 .625 ! 5-8 20 5 2h .96875 31-32 31 73 H ,3125 1 5-16 10 2i H -65625 21-32 21 5\ 2^ 1.000 1 328 4 .34375 11-32 ,11 \2i ill .6873 ill-16,22 ,5i,2|,| 1 APPLIC.VTTON. Required tlie rrnllnns in any Cylindrical Vessel. Pup- pose a vessel 9 1-i inrlies deep, i^ inclics (liiimcttT, and contents 2G163, that is, 2 gallons and 61 hundrwllli parts o( a jL;allon,no\v to ascertain lliis de- cimal of jT gallon refer to llic al.ovc 'i'ablc, lor the decimal ihal is nearest, which is -620, op])ositc to which is 5-!!llis of a gallon, or 20 gills, or 5 pints, cr 2 1-2 quarts, consequently the vessel contains 2 gallons anil 5 pnits. INCHES. To find what part of an inch the decimal -708 is. Uefcr to the above Table for the decimal that is nearest, which is 71875, opi)osile to which is 23-32, or nearly 3-4ths of an inch. A. TA.BLE CONTAINING THE DIAMETERS, CIRCUMFERENCES, AND AREAS OF CIRCLES, AND THE CONTENT OF EACH IN GALLONS AT 1 FOOT IN DEPTH. XJXILIT'Z' OF THE T.A.BLE. EXAMPLES. 1. Required the circumference of a circle, tlie diameter being ^«;e inches ? In the column of circumferences opposite the given diameter, stands 15'708* inches, the cii'cumference required. 2. Required the capacity, in gallons, of a can the diameter being 6 feet and depth 10 feet ? In the fourth column from the given diameter stands 211.4472* being the content of a can 6 feet in diameter and 1 foot in depth, ■which being multipled by 10 gives the required content, two thou- sand one hundred fourteen and a half gallons. 3. Any of the areas in feet multiplied by .03704, the product equal the number of cubic yards at 1 foot in depth. 4. The area of a circle in inches multiplied by the length or thick- ness in inches, and by .263, the product equal the "weight in pounds of cast iron. * See opposite page (page 40) for Decimal Equivalents to the Fraciional parts of a Gallon, aud an Inch. 42 DIAMETERS AND CIRCUMFERENCES OF CIRCLES. DIAMETERS AND CIRCUMFERENCES OF CIRCLES, AND THE CONTENT IN GALLONS AT 1 FOOT IN DEPTH. [Jlrea in Inches.'] Diam. Circ. ia. 31416 3- 5343 39270 4-3197 4-7124 5-1051 5-4978 5-8905 6-2332 6 6759 7-0686 74613 7-S540 8-2467 8-6394 90321 9-4248 9-8175 0-210 0-602 0-995 1-38S 1-781 2 173 2-566 2959 3351 3-744 4-137 4-529 4-922 5-315 5-708 6-100 6-493 6-S86 7-278 7-671 8-064 8-457 8-849 9-242 9635 20027 Area. in. Gallons. •7854 -9940 1-2271 1-4848 1-7671 20739 2-4052 2-7611 3-1416 3-5465 3-9760 4-4302 4-9087 5-4119 5-9395 6-4918 7-0686 7-6699 8.2957 8-9462 9-6211 10-320 11-044 11 793 12-566 13-364 14-186 15-033 15-904 16-800 17-720 18-665 19-635 20-629 21-647 22-690 23-758 24-850 25-967 27-108 28-274 29-464 30-679 31-919 -04084 -05169 •063S0 •07717 -09188 •10784 •12506 -14357 -16333 -18439 •20675 •23036 •25522 •28142 •30S83 •33753 -36754 -39879 •43134 •46519 •50029 ■53664 •57429 -61324 -65343 •69493 •73767 •78172 '82701 •87360 -92144 -97058 •02102 -07271 -12564 •17988 •23542 -29220 -35028 -40962 -47025 •53213 •59531 -65979 Diam. h A 8 i 7. 8 in. i 8 J. 4 3 S h Circ. in. 20-420 20-813 21-205 21-598 21-991 22-383 22-776 23-169 2.3-562 23-954 24-347 24-740 25-132 25515 25-918 26-310 26-703 27-096 27-489 27-881 28-274 28-667 29-059 29-452 29-845 30-237 30 630 31-023 31-416 31 -.808 32-201 32 594 32-986 33379 33 772 34-164 34 557 34-950 35 343 35-735 .36-128 36.521 36-913 37-306 Area. in. Gallons. 33-183 34-471 35-7S4 37-122 38-484 39-871 41-282 42-718 44-178 45-663 47-173 48-707 50^265 51-848 53456 55-088 56-745 58 426 60-132 61-862 63617 65-396 67-200 69-029 70-882 72-759 74-662 76-588 78 540 80-515 82516 84-540 86-590 8S-664 90 762 92 885 95-033 97-205 99-402 101-623 103 S69 106- 139 108434 110-7.53 1-72552 1-79249 1>S6077 1-93)34 2-00117 2-07329 214666 2 221.34 2.29726 2-37448 2-45299 2 5.3276 2-61378 2-69609 2-77971 2-86458 2-95074 3-03815 3-12686 3-21682 3-30808 3-40059 3-49440 3-58951 3-6S586 378.347 388242 3-98258 4-0S40S 4^1 8678 4-29083 4-39608 4-50268 4-61053 4-71962 4-S-2S46 4-94172 5-05466 5- 16890 5 28439 5-40119 5-51923 5-63857 5-75916 DIABIETERS AND CIRCUBIFEEENCES OF CIRCLES. 43 DIAMETERS AND CIRCUMFERENCES OF CIRCLES, AND THE CONTENT IN GALLONS AT 1 FOOT IN DEPTH. [Area in Feet."] Diam. Circ. Area in ft. Gallons. Diatn. Circ. Area in ft. Gallons. Ft In. Ft. In. 1ft. in depth' Ft. In. Ft. In. 1 ft. in deplli 3 If •7854 5-8735 i 4 6 14 If 15-9043 118-9386 1 3 4f .9217 6-8928 4 7 14 4f 14 71 16-4986 123-3830 2 3 8 1-0690 7-9944 4 8 171041 127-9112 3 3 11 1 2271 9-1766 4 9 14 ll' 17-7205 132-5209 4 4 2i 1-3962 10-4413 ' 4 10 15 21 183476 137-2105 5 4 5| 1 5761 11-7666 4 11 15 5^ 18-9858 142-0582 6 4 8| 1-7671 13 2150 1 7 4 llf 1-9689 14 7241 5 15 8h 19-6350 146-8384 8 5 2i 21816 16-3148 5 1 15 11| 16 23 20-2947 151-7718 9 5 5| 2-4052 17-9870 5 2 20-96.56 156-7891 10 5 9 2 6398 19-7414 5 3 16 5i 21-6475 161-88S6 11 6 H 2S852 21-4830 5 5 4 5 16 9 17 01 22-3400 23-0437 167-0674 172-3300 2 6 3| 3 1416 23-4940 5 6 17 H 237583 177-6740 2 1 6 H 3-4087 25-4916 5 7 17 6| 24-4835 183-0973 2 2 6 9| 3-6869 275720 5 8 17 9f 25-2199 188-6045 2 3 7 03 3-9760 297340 5 9 18 0| 25-9672 1941930 2 4 7 n 4-2760 32-6976 o 10 18 31 26-7251 199-8610 2 5 7 7 4-5869 34-3027 5 11 18 71 27-4943 205-6133 2 6 7 lOi 4-9087 36-7092 8 2 7 8 1§ 5-2413 39-1964 2 8 8 "^8 7| 5-5850 41 7668 6 18 101 19 n 28-2744 211-4472 2 9 8 5-9395 44-4179 6 3 30-6796 229-4342 2 10 8 log 6-3049 471505 6 6 20 41 21 2| 33-1831 248-1564 2 11 9 «-"iiiac,2ozs.; Alum, 1 oz.; Salt, 2 ozs.; Water, 2 galls. Alii the Suit after builiug the other ingredients, and u(C it hot. BRONZES, SILVERING, AND VARNISHES. 95 No. 82. Olive Hronze Dip, for 7?rnss.— Nitric Acid, 3 czs ; Muri atic Acid, 2 ozs.; add Titanium or Palladium ; when the metal is dissolveo add 2 galls, pure soft water to each pint of the solution. No. 83. Bkown Bronze Paint, /or Copper Vessels. — Tincture ol Steel, 4 ozs. ; Spirits of Nitre, 4 ozs. ; Essence of Uendi, 4 ozs. ; Blue Vitriol, 1 oz.; Water, A pint. Mix in a bottle. Apply it with a fine brush, the ressel being lull of boiling water Varnish after the application of the bronze. No. 84. Bron/k, for all kinds of Metal. — Muriate of Ammonia 'Sal Ammoni.ir), 4 drs.; Oxalic Acid, I dr.; Vinegar, 1 pint. Dissolve the Oxalic Acid first. Let the work be clean. Tut on the 'bronze with a brush, repeating; the operation as many times as may be necessary. No. 85 Bronze Paint, for Iron or Brass — Chrome Green, 2 Ihs.; Ivory Black, I oz. ; Chrome Yellow, 1 oz. 3 Good Japan, 1 gill ; grind all togelhcr and mi.x with Linseed Oil. No. 86. To Bronze Gun Barrels.— Dilute Nitric Acid v.ith Water and rul> the gun barrels with it ; lay them by for a few days, then rub them with Oil and polish them with bees-wax. No. 87. For Tinning Brass. — Water, 2 pails full} Cream of Tar- tar, 1-2 lb.; Salt, 1-2 pint. Shaved or Grained Tin. — Boil the work in the mixture, keeping it in motion during the time of boiling. No. 88. Silvering by Heat. — Dissolve 1 oz. of Silver in Nitric Acid ; add a small quantity of Salt ; then wash it and add Sal Ammoniac, or 6 ozs. of Salt and White Vitriol ; also \ oz. of Corrosive Sublimate, rub them together till they form a paste, rub the piece which is to be Silvered with the paste, heat it till the Silver runs, after which dip it in a weak vitriol pickle to clean it. No. 89. Mixture for Silvering. — Dissolve 2 ozs. of Silver with 3 grains of Corrosive Sublimate; add Tartaric Acid, 4 lbs.; Salt, 8 qts. No. 90. Separate Silver from Copper. — Mix Sulphuric Acid, 1 part; Nitric Acid, 1 part; Water, 1 part; boil the metal in the niixture till it is dissolved, and throw in a little Salt to cause the Silver to subside. No. 91. Solvent for Gold. — Mix equal quantities of Kitric and Muriatic Acids. No. 92. Varnish, ybr Smooth Moulding Patterns. — Alcoho., 1 gall.; Shell Lac, 1 lb.; Lamp or Ivory Black, sufficient to color it. No 93. Fine Black Varnish, /or Coaches. — Melt in an Iron pot, Amber, 32 ozs.; Resin, 6 ozs.; Asphaltum, 6 ozs.; Drying Linseed Oil, I pt.j when partly cooled add Oil of Turpentine, wormed, 1 pt. No. 94. Chinese White Copper. — Copper, 40.4; Nickel. 31.6; Zinc, 25.4; and Iron, 2.6 parts. No. 95. Manheim Gold. — Copper, 3; Zinc, 1 part; and a small quantity of Tin. No. 96. Alloy of the Standard Measures used by tub British Government. — Copper, 576 ; Tin. 59 ; and Brass, 48 parts. No. 97. Bath Metal. — Brass, 32 ; and Zinc, 9 parts. No. 98. Speculum Metal. — Copper, 6 ; Tin, 2 ; and Arsenic, I pari Or, Copper, 7 ; Zinc, 3 ; and Tin, 4 parts. No. 99. Hard Solder. — Copper, 2; Zinc, I part. No. 100. Blanched Copper. — Copper,8; and Arsenic, ^ part. No. 101. BitiTANNiA Metal. — Brass, 4 ; Tin, 4 parts ; when fused, add Bismuth. 4 ; and Antimony, 4 parts. This composition is added at discretion to melted Tin. 96 SOLDERS AND CEMENTS. No. 102. Plumber's Solder. — Lead, 2; Tin, I part. No. 103. Tinman's Solder. — Lead, i ; Tin, 1 part. No. lOi. Pewterer's SoLDEii. — Tin, 2; Lead, 1 part. No. 105. Common Pewter. — Tin, 4; Lead, 1 part. No. 106. Best Pewter. — Tin, IOO5 Antimony, 17 parts. No. 107. A Metal that Expands in Cooling. — Lead, 9 j Anil- men)-, 2 ; Bismuth, 1 pari. This Jletal is very useful in filling Email defects in Iron castings, &c. No. 108. Queer's Metal. — Tin, 9; Antimony, 1} Bismuth, 1 ; Lead, 1 part. No. 109. Mock Platinum. — Brass, 8; Zinc, 5 parts. No. 110. Silver Coin of the United States. — Pure Silver, 9; Alloy, 1 part; the alloy of silver is fine copper. No. 111. Gold Coin of the United States. — Pure Gold, 9 ; Alloy. 1 part ; the alloy of gold is ^ silver and | copper, (not to exceed J^ silver). No. 112. Silver Coin of Great Britain. — Pure Silver, 11.1 5 Copper, 9.9 parts. No. 113. Gold Coin of Great Britain. — Pure Gold, 11 ; Copper, 1 part. Previons to 1826 Silver formed part of the alloy of Gold coin ; hence the difitrent color of English Gold money. No. 114. Ring Gold. — Pure Copper, 6^ pwts.; Fine Silver, 31 pwts.j Pure Gold, 1 oz. and 5 pwts. No. 115. Mock Gold. — Fuse together Copper, 16; Platinum,7j Zinc, 1 part. When Steel is a'loyed with 1-500 part of Platinum, or with 1-JCO part of Silver, it 1( rendered much harder, more malleable, and better adapted for every kind of cutting Instrument. Note. — Tn making alloys, care must be taken to have the more infusible metals melted fir.-t, and afterwards add the otliers. No. 116. Compo-^ition Used in Welding Cast Steel. — Borax, 10; Sal .Ammoniac, 1 part ; grind or pound thorn roughly together ; then fuse them in a metal pot over a clear fire, taking care to contiinip the heat until all spume has disappeared from the surface. \\'hen ilic liquid appears clear, ih<' composition is ready to be poured out to cool and concrete J afterwards being pround to a fine powder, it is ready for use. To use tliis roinpositinn, the Steel to be welded is raised to a heat which may be expressed by " bright yellow;" it is then dipped among the welding powder, and again placed in the fire until it attains the same degree of heat 03 before, it is then r,;ady to l>a placed under the hammer. No. 117. Cast Ikon Cement. — Clean borings, or turnin^is, of Cast Iron. 16; Sal Ammoniac, 2 ; Flour of Sulphur, 1 part; mix thorn well to- gether in a mortar and keep them dry. W'lien rcquircil for u>p, take of ihe mixture, 1 ; clean borings, 20 parts; mix thoroughly, and add a sufficient quantity of water. A little grindstone dust added improves the cement. No. 118. Booth's Patent Grease, /or /JaiVicai/ j4t/m. — Water, 1 pall.; Clean Tallow. 3 lbs.; Palm Oil, 6 lbs.; Common Soda, ^ lb. Or, Tallow, 8 lbs.; Palm Oil. 10. The mixture ti> be healed to about 210° F., and well stirred till it cools down to about 70", wheu it is ready for use. No. 119. Cement, for Sleam-pipe Joints, S,'C., with Faced Flan)e is equal to the square of the h^'potcnusc. 7. The difference between the squares of the hypotenuse and given side of a righl-ajigled triangle is equal to the .square of the reiiuircd side. 8. The area of a triangle equals half the product of the base multiplied by the perpendicular height ; or, 9. The area of a triangle equals half the productof tiie two sides and the natural sine of the contained angle. 10. The side of any regular polygon multiplied by its npoihcm or perpen- dicular^ and by the uumbcr of its sides, e(juals twice the area. EPITOME OF MENSITKATION. 12d TABLE OF THE ARE^iS OF REGULAR POLYGONS EACH OF WHOSE SIDES IS UNITY. Name of No ofi Apotheni or Area when Interior Central Polygon. Sides Perpend'lar. Side IS Limy Angle. Angle. Triangle 3 0.2887 0.4330 60° 0' 120° 0' Square 4 0.5 1, 90. 90 Pentagon 5 0.6882 1.7205 108 72 Hexagon 6 0.8660 2.5981 120 60 Heptagon 7 1.0386 3.6339 128 34f 51 25^ Octagon 8 1.2071 4.8284 135 45 Nonagon 9 ].3737 6.1818 140 40 Decagon 10 1.5388 7.6942 144 36 Undecagon 11 1.7028 9.3656 147 16^4^ 32 43/t Dodecagon 12 1.8660 11.1962 150 30 The tabular area of the corresponding polygon multiplied by the square of the side of the given polygon equals the area of the given polygon. OF ELLIPSES, CONES, FRUSTUMS, &C. 1. The square root of half the sum of the squares of the two diameters of an ellipse multiplied by 3.1-116 equals its circumference. 2. The product of the two axes of an ellipse multiplied by .7854 equals its area. 3. The curve surface of a cone is equal to half the product of the circum- ference of its base multiplied by its slant side, to which, if the area of the base be added, the sum is the whole surface. 4. The solidity of a cone equals one third of the product of its base mul- tiplied by its altitude or height. 5. The squares of the diameters of the two ends of the frustum of a cone added to the product of the two diameters, and that sum multiplied by its height and by .2618, equals its solidity. INSTRUMENTAL ARITHMETIC, OR UTILITY OF THE SLIDE RULE. The slide rule is an instrument by which the greater portion of operations in arithmetic and mensuration may be advantageously performed, provided the lines of division and gauge- points be made properly correct, and their several values familiarly understood. The lines of division are distinguished by the letters a B c D j A b and c being each divided alike, and containing what is termed a double radius, 11* 126 UTILITY OF THE SLIDE RULE. or double series of logarilhmic numbers, each scries being supposed to be divided into 1000 equal parts, and distributed along the radius in the fol- lowing manner : From 1 to 2 contains 301 of those parts, being the log. of 2. „ 3_ n 3 477 it 4 602 it 5 699 u 6 778 tt 7 845 t( 8 003 ti 9 934 il II /I It 4. 5. 6. 7. 8. 9. 1000 being the whole number. The line D on the improved rules consists of only a single radius ; and although of larger radius, the logarilhmic series is the same, and disposed of along the line in a similar proportion, form.ing exactlj' a line of square roots to the numbers on the lines b c. NUMERATION. Numeration teaches us to estimate or propCrly value the numbers and divisions on the rule in an arithmetical form. Their values are all entirely governed by the value set upon the first figure, and being decimally reckoned, advance tenfold from the commence- ment to the termination of each radius : thus, suppose 1 at the joint be one, the 1 in the middle of the rule is ten, and 1 at the end, one hundred : again, suppose 1 at the joint ten, 1 in the middle is 100, and 1 or 10 al the end is 1000, &.C., the intermediate divisions on which complete the whole system ofits notation. TO MULTIPLY NUMBERS BY THE RULE. Set 1 on B opposite to the multiplier on A ; and against the number to be multiplied on b is the product on a. Multiply by 4. Set 1 on B to 4 on A ; and against 6 on B is 24 on A. The slide thus set, against 7 on b is 28 on a. &c. TO DIVIDE NUMBERS UPON TIIE RULE. Set the divisor on b to 1 on a ; and against the number to be divided on B is the quotient on A. Divide 63 by 3. Set 3 on B to 1 on A 3 and against 63 on b is 21 on a. 8 32 9 36 10 40 12 48 15 60 23 100 UTILITY OF THE SLIDE RULE. 127 PROPORTION, OR RULE OF TUREE DIRECT Rule. — Set the first term on b to the second on a 5 and against the third upon B is the fourth upon a. 1. If 4 yards of cloth cost 38 cents, what will 30 yards cost at the same rate? Set 4 on B to 38 on A ; and against 30 on B is 285 cents on A. 2. Suppose I pay 31 dollars 50 cents for 3 cwt, of copper, at what rate is that per ton ? I ton == 20 cwt. Set 3 upon b to 31.5 upon a ; and against 20 upon b is 210 upon A. • RULE OF THREE INVERSE. Rule. — Invert the slide, and the operation is the same as direct proper- tion. 1. I know that six men are capable of performing a certain given por- tion of work in eight days, but I want the same performed in three j how many men must there be employed ? Set 6 upon c to 8 upon a ; and against 3 upon c is 16 upon a. 2. The lever of a safety-valve is 20 inches in length, and 5 inches between the fixed end and centre of the valve; what weight must there be placed on the end of the lever to equipoise a force or pressure of 40 lbs. tending to raise the valve ? Set 5 upon c to 40 upon a ; and against 20 upon c is 10 upon A. 3. If 8| yards of cloth, 1.^ yard in width, be a sufficient quantity, how much will be required of that which is only 7-8ths in width, to effect the same purpose ? Set 1.5 upon c to 8.75 upon a ; and against .875 upon c is 15 yards upon a. SQUARE AND CUBE ROOTS OF NUMBERS. On the engineer's rule, when the lines c and d are equal at both ends, c is a table of squares, and D a table of roots, as Squares 1 4 9 16 25 36 49 64 81 on c. Roots 12 3 4 ar 6 7 8 9 on d. To find the geometrical mean proportion between two numbers. Set one of the numbers upon c to the same number upon D ; and against the other number upon c is the mean number or side of an equal square upon D. Required the mean proportion between 20 and 45. Set 20 upon c to 20 upon d ; and against 45 upon c is 30 upon D. To cube any number, set the number upon c to 1 or 10 upon D ; and against the same number up mi d is the cube number upon c. 128 TTTIXITY OF THE SLIDE RULE. Required the cube of 4. Set 4 upon c to 1 or 10 upon D ; and against 4 upon D is 64 upon c. To extract the cube root of any number, invert the slide, aud set the number upon b to 1 or 10 upon d ; and where two numbers of equal value coincide on the lines B D, is the root of the given number. Required the cube root of 64. Set 64 upon b to 1 or 10 upon D ; and against 4 upon B is 4 upon D, or root of the given number. On *hc common rule, when 1 in the middle of the line c is set opposite to 10 on D, then c is a table of squares, and d a table of roots. To cube any number by this rule, set the number upon c to 10 upon D- and agamst the same number upon d is the cube upon c. MENSURATION OF SUEFACE. 1. Squares, Rectangles, ^c. Rur.E. — When the length is given in feet and the breadth in inches, set tlie breadth on B to 12 on a ; and against the length on A is the content in square feet on B. If the dimensions are all inches, set the breadth on B to 144 upon A 5 and against the length upon A is the number of square feet on B. Re()uircd the content of a board 15 inches broad and 14 feet long. Set 15 upon b to 12 ujjon a ; and against 14 upon a is 17.5 square feet on B. 2. Circles, Polygons, S(c. Rule. — Set .7854 upon c to 1 or 10 upon d ; then will the lines c and D be a table of areas and diameters. Areas 3.14 7.06 12.5G 19.63 28.27 38.48 50.26 63.61 upon c; Diam. 2345678 9 upon d. In the common rule, set .7854 on c to 10 on D j then c is a line or table of areas, and D of diameters, as before. Sol 7 upon li to 22 upon A ; then B and a form or become a table of di- ameters and circumferences of circles. Cir. 3.14 6 28 9.42 12.56 15.7 18.85 22 25.13 28.27 upon a. Dia. 123 4 56 78 9 upon b. Poti/gons from 3 to 12 sides. — Set the gauge-point upon c to 1 or 10 upon u ; and against the length of one side upon d is the area uponc. Sides 3 5 6 7 8 9 10 II 12 Gauge-points .433 1.7 2.G 3.G3 4.82 6.18 7.69 9.37 11.17 Required the area of an equilateral triangle, each side 12 inches in length. Scri .433 upon c to 1 upon D 3 and against 12 upon D arc 62.5 square Inches upon c. UTILITY OF THE SLIDE RULE. 129 TABLE OF GAUGE-POINTS FOR THE ENGINEER'S RULE. Names Cubic inches Cubic feet Imp. Gallons Water in lbs. Gold Silver Mercury Brass " Copper " Lead " Wrot iron " Cast iron ♦' Tin " Steel " Coal " Marble " Freestone " F, F,V. I F, 1,1. I 1,1, I. i! F, I I, I. I. 578 1 163 16 814 15 118 193 18 141 207 222 219 202 127 591 632 83 144 231 23 1175 216 169 177 26 203 297 32 315 292 183 85 915 728 ! 106 1273 1 1833 22 277 ! 294 353 276 . 293 352 141 1 149 178 261 1 276 334 203 216 258 333 354 424 319 331 397 243 258 31 357 338 453 384 407 489 378 i 401 481 352 i 372 448 22 i 33 23 102 : 116 13 11 1162 14 105 121 306 305 155 286 225 369 345 27 394 I 424 419 385 242 113 141 121 33 529 528 269 5 389 637 596 465 682 733 728 671 42 195 21 FOR THE COMMON SLIDE RULE. Names. F, F, F. F, I, I. 1.1,1. i F,I. 1,1. F. r Cubic inches 36 518 624 660 799 i 625 113 Cubic feel 625 9 108 114 138 119 206 Water in lbs. 10 144 174 184 22 191 329 Gold 507 735 88 96 118 939 ISO Silver " 938 136 157 173 208 173 354 Mercury " 738 122 127 [ 132 162 141 242 Brass " 12 174 207 ; 221 265 23 397 Copper " 112 163 196 ' 207 247 214 371 Lead 880 126 152 ! 162 194 169 289 Wrot iron " 129 186 222 235 283 247 423 Cast iron " 139 2 241 254 3*4 , 265 458 Tin 137 135 235 25 300 i 261 454 Steel " 1.36 183 22 233 278 239 418 Coal " 795 114 1.38 146 176 ! 151 252 Marble " 370 53 637 ' 725 81 72 121 Freestone " 394 57 69 ! 728 873 755 132 JIENSURATION OF SOLIDITY AND CAPACITY. General Rule. — Set the length upon u to the gauge point upon a ; and against the side of the square, or diameter on D, are the cubic contents, or weight in lbs. on c. 1. Required the cubic contents of a tree 30 feet in length, and 10 inches quarter girt. Set 30 upon b to 144 (the gauge-point) upon a ; and against 10 upon u is 20.75 feet upon c. 130 UTILITY OF THE SLIDE RULE. 2. In a cylinder 9 inches in length, and 7 inches diameter, liow many cubic inches ? Set 9 upon B to 1273 (the gauge-point) upon a ; and against 7 on d is 346 inclies on c. 3. What is the weight of a bar of cast iron 3 in. scjuare, and 6 ft. long? Set 6 upon B to 32 (the gauge-point) upon a ; and against 3 upon D is 168 pounds upon Ci By the common nde. 4. Required the weight of a cylinder of wrought iron 10 inches long, and 5J diameter. Set 10 upon B to 283 (the gau2;-e-poinl) upon a; and against 5^ upon D is 66.65 pounds on c. 5. ^V^lat is the weight of a dry rope 23 yards long, and 4 inches circum- ference 1 Set 25 upon e to 47 (the gauge-point) upon a j and against 4 on d is 53 16 pounds on c. 6. What is tlie weight of a short-linked chain 30 yards in length, and 6-16ths of an inch in diameter? Set 30 upon b to 52 (the gauge-point) upon A ; and against 6 on D is 129.5 pounds on c. POWER OF STEAM EXGIXES. Condensing Engines. — Rule. Set 3.5 on c to 10 on D ; then D is a line of diameters for cylinders, and c the corresponding number of horses' power ; thus, H. Pr. 3iJ 4 5 G 8 10 12 IG 20 25 30 40 50 on c. C. D. 10 in. 10| 12 13.i 15^ 17 18| 21^ 24 2G| 29^ 33| 37| on D. The same is effected on the common rule by setting 5 on c to 12 on d. Non-condensing Engines. — Rule. Set the pres.>-ure of steam in pounds per square inch on B to 4 upon a ; and against the cylinder's diameter on D is the number of horses' power upon c. Required the power of an engine, when the cylinder is 20 inches diameter and steam 30 pounds per square inch. Set 30 on B to 4 on A ; and against 20 on D is 30 horses' power on c. The same is effected on the common rule by setting the force of the steam on B to 250 on a. OF ENGINE BOIIERS. IIow many .superficial feet arc contained in a boiler 23 feet in length and 6^ feet in width ? Set 1 on B to 23 on A ; and against 5.5 upon B is 126.5 square feet upon A. If 5 square feet of boiler surface be sufficient for each horse-power, how many horses' power of engine is the boiler equal to ? Set 5 upon B to 12G.ti upon A ; and against 1 upon fi is Z5.5 upon A. RULES AND TABLES FOE AETIFICERS AND ENGINEERS, 132 MEASUREMENT OF BRICKLAYERS* WORK. ARTIFICERS' RULES AND TABLES For Computing the Work of Bricklayers, Well Dig- gers, Masons, Carpenters and Joiners, Slaters, Plas- terers, Painters, Glaziers, Pavers, and Plumbers. MEASUREMENT OF BRICKLAYERS' WORK. Brickwork is estimated at the rate of a number of bricks in thickness, estimat- ing a brick at 4 inches thick. The dimensions of a building are usually taken by measuring half round on the outside, and half round on the inside ; the sum of these two gives the compass of the wall, — to be multiplied by the height, for the content of the materials. Chimneys are by some measured as if they were solid, deducting only the vacuity from the hearth to the mantel, on account of the trouble of them. And by others they are girt or measured round for their breadth, and the height of the story is their height, taking the depth of the jambs for their thickness. And in this case, no deduction is made for the vacuity from the floor to tlie mantel- tree, because of the gathering of the breast and wings, to make room for the hearth in the next story. To measure the chimney shafts, which appear above the building, gird them about with aline for the breadth, to multiply by their height. Anil account their thickness half a brick more than it really is, in consideration of the plastering and scaflolding. All windows, doors, &c., are to be deducted out of the contents of the walls in which they are placed. But tliis deduction is made only with regard to materials ; for the whole measure is taken for workmanship, and that all outside measure too, namely, measuring quite round the outside of the building, being in consideration of the trouble of the returns or angles. There are also some other allowances, such as double meas- ure for feathered gable ends, &c. Example. — The end wall of a house is 28 feet long, and 37 feet high to the eaves : 15 feel high is four bricks or 16 inches thick, oilier 13 feel is three bricks or 12 inches thick, and the remaining 11) feet is two bricks or 8 inches thick; above which is a triangular gable 12 feet high and one brick or 4 inches in thickness. What number of bricks are there in the said wall? A>is. 25,620. tliiclincss. 28 X 15 = 420 X '1 = Ifisn contents of Isl story. 28 X 12 = 3.30 X 3 = 1003 " " 2d " 23X10 = 260x2= 5G0 " " 3d " 12 -T- 2= 6X28 = 108X1= 1(53 " "gable. 34 10 square feet area of whole wall. 7^ bricks to square foot. 23,912 By the table 1,708 3000 suprfi. ft. = 22,500 bricks, 400 " " = 3,000 " Answer,— 25,620 bricks. 10 " " = 75 " 6 " " = 45 " 3416 " " = 25,620 bricks ^ Table by ii'hich to ascertain the number of Bricks necessary to construct any Piece of Building, from afour-inch Wall to ttvoity-four inches in Thickness. The utility of the Table (on next page) can be seen by the following Ex- ample. Required the number of bricks to build a wall of 12 inches thickness, nnu containing an area of 0,437 square feci. Square feet 1000 22,.'')00 bricks— See table. X 6 6000 = 135 000 NoTK. — 7J bricks. 400 = 9,000 equal one superficial loot. 30 = 075 7= 158 6,437= 144,833 bricks. MEASUREMENT OF BRICKWORK, WELLS t CISTERNS. 133 Superficial Numtel- of B>-icks lo Thickness of Wall. 4-inch 8inch. 12-inch. 16-lnch- 20-inch. 1 24-inch. 1 8 15 23 30 38 45 2 15 30 45 60 75 90 3 23 45 68 90 113 135 4 30 60 90 120 150 J 80 5 38 75 113 150 188 225 6 45 90 135 180 225 270 7 53 105 156 210 263 315 8 60 120 180 240 300 3(10 9 68 135 203 270 338 405 10 75 150 225 300 375 450 20 150 300 450 600 750 900 30 225 450 675 900 1125 1.330 40 300 600 900 J 200 1500 ISdO 50 375 750 1125 1500 1875 2250 60 450 900 1350 1801) 2250 2700 70 525 1050 1575 2100 2625 3150 SO 600 1200 ie-00 2400 3000 3600 90 675 1350 2025 2700 a375 4050 100 750 1500 2250 3000 3750 4500 200 1500 3000 4500 6000 7500 9000 300 2250 4500 6750 9000 11250 13500 400 3000 6000 9000 12000 15000 160(10 5(10 3750 7500 11250 15000 18750 22500 600 4500 9000 13500 l&OOO 22500 27000 700 5250 10500 15750 21000 26250 31500 800 6000 12000 18000 24000 30000 36000 900 6750 13500 20250 27000 33750 40500 1000 7500 15000 22500 30000 37500 45000 MEASUREMENT OF WELLS AND CISTERNS. There are two methods of estimating the value of excavating. It may bo done by allowing so much a day for every man's work, or so much per cubic foot, or yard, for all that is excavated. Well Di§^ng. — Suppose a Well is 40 feet deep, and 5 feet in diameter,, required the number of cubic feet, or yards? 5 X 5 = 25 X .7354 = 19.635 X 40 = 785.4 cubic feet. Suppose a well .o be 4 feet 9 inches diameter, and ]6i feet from the bottom to the surface of the water ; how many gallons are therein coniained ? 4-752 X 16.5 X 5.875 = 2187.152 gallons. Again, suppose the well's diameter the same, and its entire depth 35 feet; re- quired the quantity in cubic yards of material excavated in its formation. 4.752 X 35 X -02909 = 22.9?2 cubic yards. A cylindrical piece of lead is required 7^ inches diameter, and 1G8 lbs. ia weight ; what must be its length in inches ? 7.52 X .3223 = 18, and 163 -^ 18 = 9.3 inches. Digging for Foundations, If c. — To find the cubical quantity in a trench, or an excavated area, the lengih, width, and depth must be multiplied togellier. These are usually given in feet, and therefore, to reduce the amount into cubic yards it must be divided by 27. Suppose a trench is 40 feet long, 3 feet wide, and 3 feet deep, required the number of cubic feet, or yards? 40 X3 = 120x3=360feet^27 = 13j yards. 24 cubic feet of sand, 17 ditto clay, 18 ditto earth, equal one ton. 1 cubic yard of earth or gravel, before digging, will occupy about IJ cubio yards when dug. 31EASUREMENT OF MASONS' WORK. To masonry belong all sorts of stone-^vork ; and the measure made use of is a foot, either superficial or solid. Walls, columns, blocks of stone or marble, &c., are measured by the cubio 12 134 MEASUREMEXT OF MASONS' & CARPENTEES' WORK. foot; and pavements, slabs, chimney-pieces, &c., by the superficial or square foot. Cubic or solid measure is used lor ihe materials, and square measure for the workmanship. In the solid measure, the true lenglli, breadih and liuckness, are taken, and multiplied continually together. In the superficial, there must be taken the leiigih and breadih ol every part of the projection, which is seen with- out the general upright face of the building. E.XAMPLE. — In a chimney-piece, suppose the length of the mantel and slab each 4 feet 6 inches ; breadth of both together 3 feel 2 inches ; lenijlh of each jamb 4 feet 4 inches ; breadth of both together 1 fool 9 inches. Required ihe superficial content. — Ans. 21 feel 10 inches. 4 ft. 6 in. X 3 ft. 2 in. = 34 ft. 3 in. ) „, .^, ,„ . . , 4" 4 " xl"!)" =7" 7 >' {21 feet 10 inches. Rubble Walls (unhewn stone) are commonly measured by the perch, which is 16J feel long, 1 loot deep, and IJ fool thick, equivalent to 'ii^ cubic feet. 25 cu- bic feel is sometimes allowed to ihe perch, in measuring stone before it is laid, and 22 after it is laid in the wall. This species of work is of two kinds, coursed and uncoursed ; in the former the stones are gauged and dressed by the hammer, and the masonry laid in horizontal courses, but not necessarily confined to the same height. The uncoursed rubble wall is formed by laying the stones in the wall as they come to hand, without any previous gauging or working. 27 cubic feet of mortar require for its preparation, 9 bushels of lime and 1 cubic foot of sand. Lime and sand lessen about one-third in bulk when made into mortar ; like- wise cement and sand. Lime, or cement and sand, to make moriar, require as much water as is equal to one-third ot their bulk. All sandstones ought to be placed on their natural beds ; from inattention to this circuinsiance, the slones often split off at the joints, and the position of the lamina much sooner admits of ihe destructive action of air and water. The heaviest slones are most suited for docks and harbors, breakwaters to bridges, &c. Granite is the most durable species of stone yet known for the purposes of building. It varies in weight according to quality ; the heaviest is the most durable. MEASUREMENT OF CARPENTERS' AND JOINERS' WORK. To this branch belongs all the wood work of a house, such as flooring, parli- lioning, roofing, &c. Large and plain articles are usually measured by the square foot or yard, &.C., but enriched mouldings, and some other articles, are oltcn esti- mated by running or lineal measures, and some things are rated by the piece, All joints, girders, and in fact all the pans of naked flooring, are measured by the cube, and their quantities are found by multiplying the length by ilie breadth, and the product by the depth. The same rule appplies to the measurement of all the timbers of a roof, and also the framed limbers used in the construction of partitions. Flooring, that is to say, the boards which cover the naked flooring, is meas- ured l)y the square. Tlie dimensions are taken from wall to wall, and the pro- duct IS divided by 100, which gives the number of squares ; but deductions must be made for staircases and chimneys. In measuring of joists, it is to be observed, that only one of their dimensions IS the same willi that of ihe floor ; fo the other exceeds the length of il e nmin by the thickness of the wall, and oiie-il ird of the same, because each enc is let iiilu the wall about two-thirds of its thickness. No deductions are made for hearths, on account of the additional trouble and waste of materials. Partitions are measured from wall to wall for one dimension, and from floor to floor, as far as they extend, forihe other. No deduction is made lor door- ways, on account of the trouble of frnming Ihem. In mi-.isuiinp ol" joiners' work, the string is made to ply close to every part of the Work over which it pusses. The measure for centtrine for CKi.t.Ans is fcaind by iniiking a string puss over ttie surface of the arch for the breadth, and taking ihe length of the cellar fof MEASUEEMENT OF CARPENTERS* & JOINERS' WORK. 135 the length ; but in groin centering, it is usual to allow double measure, on ac- count of their extraordinary trouble. In roofing, the length of the house in the inside, together with two-thirds of the thickness of one gable, is to be considered as the length , and the breadth is equal to double the length of a string which is stretched from the ridge down the rafter, and along the eaves-board, till it meets with the top of the wall. For staircases, take the breadth of all the steps, by making a line ply close overihem, from the top to the bottom, and multiply the length of this line by the length of a step, for the whole area.— By the length of a step is meant the length of the front and the returns at the two ends ; and by the breadth, is to be under- stood the girth of its two outer surfaces, or the tread and riser. For the baliisirade^ take \he whole length of the upper part of the handrail, and girt over its end till it meet the top of the newel post, lor the length ; and twice the length ot the baluster upon the landing, with the girth of the hand- rail for the breadth. For wainscoiing, tnke the compass of the room for the length ; and the height from the floor to the ceiling, making the string ply close into all the mouldings fcr the breadth. Out of this must be made deductions for windows, doors, and chimneys, &:c., but workmanship is counted for the whole, on acco'unt of the extraordinary trouble. For doors, it is usual to allow for their thickness, by adding it to both dimen- sions of length and breadth, and then to multiply them together for the area. If the door be paneled on both sides, take double its measure for the workman- ship ; but if the one side only be paneled, take the area and its half for the Workmanship. — For the surrounding architrave, gird it about the outermost parts for its leiiirth ; and measure over it, as far as it can be seen when the door is open, for the breadth. Window-shutters, bases, ^c, are measured in the same manner. In the measuring of roofing for workmanship alone, holes for chimney-shafts and sky-lights are generally deducted. But in measuring for work and mate- rials, they commonly measure in all sky-lights, lutheranlights, and holes for the chimney-shafts, on account of their trouble and waste of materials. The diiors and shutters, being worked on both sides, are reckoned work and half work. Hemlock and Pine Shingles are generally 18 inches long, and of the average width of 4 inches. A%Tien nailed to the roof 6 inches are generally left cut to the weather, and 6 shingles are therefore required to a square foot. Cedar and Cypress Shingles are generally 20 inches long, and 6 inches wide, and therefore a less number are required for a "square." On account of waste and delects, 1000 shingles should be allowed to a square. Two 4penny nails are allowed to each shingle, equal to 1200 to a square. The weight of a square of partitioning may be estimated at from 1500 to 2000 lbs.; a square of single-joisted flooring, at from 1200 to 2000 lbs.; a square of framed flooring, at from 2700 to 45(XI lbs; asquareof deafening, at about 1-500 lbs. 100 superficial feet make one square of boarding, flooring, &c. In selecling Timber, avoid spongy heart, porous grain, and dead knots; choose the brightest in color, and where the strong red grain appears to rise on the surface. The Carpenter will find in the " Business Man's Assistant " Tables giving the solidcontentsot Timber and Logs ; the square feet in Scantling from 2.2 to 15.16 in- ches ; the square feet in Boards and Planks; the contents of Logs in standard Board measure; the strength and weight of Iron Cylinders, Trusses, Plates, Cast Iron for Beams, and Hoop Iron. Number of Americcin Iron Machine Cut Nails, in a pound, (by count.) Size. Number. Size. Number. Size. Number. 3 penny . . 408 4 " ... 275 5 " ... 227 6 penny . . 156 8 " . . . lUO 10 " ... 66 12 penny ... 52 20 " .... 32 30 " .... 25 136 MEASUKE3IENT OF SLATERS' WORK. SASH TABLE.— Size and Prices of Sashes, Shutters, Ifc. Cincinnati, Ohio. 1 Size of Sash "S S £ ■-■ o ej J? '3 I Price of Window Size of Lights. for 12 light 'Windows. Price Sash Light Price Vcnit Shutt per p Frames. Width. ' Length. Box. Common. IneliLS. In. feet. in. feet. in. cts. $ cts. $ cts. $ CIS. 8 by 10 li 2 4 3 10 4 1 37i 2 00 1 20 8 by 10 n 2 4 3 10 5 1 62^ 2 00 1 20 9 by 12 li 2 74 4 6i 5 1 62i 2 50 1 30 9 by 12 u 2 7| 4 6i 6 1 75 2 50 1 30 10 by 12 ij 2 10^ 4 6i 5 1 62h 2 50 1 30 10 by 12 n 2 m 4 6^ 6 1 75 2 50 1 30 10 by 14 n 2 lOi 5 2i 7 2 12i 2 75 1 40 10 by 15 If 2 104 5 6i 74 2 25 2 75 1 40 10 by 16 n 2 lOi 5 lO.i 8 2 374 3 20 1 50 11. by 15 n 3 2 5 6i 8 2 374 3 20 1 50" 11 by 16 n 3 2 5 lOi 84 2 50 3 35 1 60 11 by 17 n 3 2 6 2i 84 2 62.i 3 50 1 70 12 by 16 n 3 5 5 104 8* 2 62i 3 75 1 80 12 by 18 n 3 5 6 6i 9 2 874 4 00 1 90 12 by 20 n 3 5 7 2i 10 3 124 4 25 2 12i 12 by 22 n 3 5 7 10;^ 11 3 37i 4 50 2 30 12 by 24 n 3 5 8 6i 12 3 624 4 75 2 50 Sasli 1 1-2 or 1 ."i-t inches thick, add 11-2 cents per light, to 1 3-8 inch prices ; for Plough- ing and Boring sasli, add 1-2 cent i>er light ; all 1 3-8 sash arc made with hook rails. Vcnitian Shutters, 1 1-2 or 1 3-4 inches thick, add 50 cents per pnir to 1 3-8 inch prices. Shutters arc made 1 1-t inches longer than sash. Pivot or Rolling Shutters, extra price. MEASUREMENT OF SLATERS' WORK. In these article.s, the content of a roof is found by multiplying the length of the riilge by the girth over from cave? to eaves ; msiking allowance in this girth for the double row of slates at the bottom, or for how much one row of slates is laid over another. When the roof is ot » true pilcli, that is, forming a right angle at lop, llien the breadth of the building with its half added, is the girlh over both sides. In angles formed in a roof, running from ilic ridge to the eaves, when the angle bends inwards, it is called a valley ; but when oul\rards, it is called a hip.- It is not usual to make deductions for cliiinney-shafis, sky-lights or other openings. SLATES. [From the Quarries of Rutland County, VermoTit.} 3 inch Cover. No. of Slates 2 inch Cover. No. of slates 3 inch Cover. 2 inch Cover. No. of Slates No. of slates Sizes of Slates. to the Siiiiarc to the square Sizes of Slates. to the Square to the square or 100 Feet. or 100 Feet. or 100 Feet. or 100 Feet. 24 l)y 16 86 84 18 by 11 174.i 163.i 24 Ijy 14 98 93i 18 by 10 192 180 24 by 12 114 109 18 by 9 213 200 22 by 14 108 W)2.i 16 by 12 184 171i 22 by 12 126 120 16 by 10 2214 205.1 22 by 10 152 144 16 by 9 246 228i 20 by 14 129 114 i 16 by 8 277 257 20 by 12 143 133i 14 by 10 262 240 20 by 11 146 1154 14 by 9 293 266i 20 by 10 169i 160 14 by 8 327 son 18 by 12 160 150 14 by 7 374 343 " Earh Slate i«3 inches iii)M> or rovKii. The rule for nii'iiniirini; Slatinft Is, to add one fiixit for all hipn and vnll<-y<*. No deduction U niudo for I.uthcnii) windows, skyligbtJ or chimneys, cxce[it they are of nuuiual size i then one half is deducted," plasterers', pavers', and painters' work. 137 IMPORTED SLATES. Names of Slates. Duchesses, .... Marchionesses, . . Countesses, .... Viscountesses, . . Ladies, do do ' do Plantations, .... do do. .... Doubles, do. small, . . School Slates for Blackboards, . . . Sizes. laches. Inches. 24 by 12 22 20 18 16 16 14 12 14 13 12 13 11 12 10 10 10 8 8 8 12 10 10 7 7 5 ft. by 2 1-2 ft 5 feet by 3 feet. Number of Super- ficial Feet each M of 1200 will cover. 1100 1000 750 666 583 466 400 333 600 458 1-3 1-3 416 2-3 320 5-6 262 1-2 Weight of each M of 1200 Slates. 60 55 40 36 31 25 22 18 1-2 33 25 23 17 1-2 14 1-2 cwt. (( (( it (( (( (( (( (( (( (< MEASUREMENT OF PLASTERERS' WORK. Plasterers' work is of two kinds, namely, ceiling — which is plastering upon laths — and rendering, winch is plastering upon walls, which are measured separately. The comenls are eslimaied eiiher by ihe fool or yard, or square of ICO feet. Enriched mouldings, &c., are rated by runningor lineal measure. One foot extra is allowed for each mitre. One half of the openings, windows, doors, &c., allowed to compensaie for trouble of finishing returns at top and sides. Cornices and mouldings, if 12 inches or more in girt, are sometimes estimated by the sq ft. ; if less than 12 inches ihey are usually measured by the lineal foot. 1 bushel of cement will cover 1 1-7 square yards at 1 inch in thickness, do. do. do. li do. do. | do. do. do. do. do. 2} do. do. J do. do. 1 bushel of cement and 1 of gand will caver 2^ sq. yds. at 1 inch in thickness. do. do. do. do. 3 do. f (jo. (jo. do. do. do. do. 4J do. | do. do. 1 bushel of cement and 2 of sand will cover 3| square yds. at 1 inch in thickness, do. do. do. do. 4i do. | do. do. do. do. do. do. 63 do. do. do. 1 cwt. of mastic and 1 gallon of oil will cover IJ yards at |, or 2J at J inch, 1 cubic yard of lime, 2 yards of road or drift sand, and 3 bushels of hair, will cover T5 yards of render and set on brick, and 70 yards on lath, or 65 yards plaster, or reyider, 2 coats and set on brick, and 60 yards on lath j floated work will require about the same as 2 coats and set. Laths are i} to It inches by 4 feet in length, and are usually set ^th of an inch apart. A bundle contains 100. 1 bundle of laths and 500 nails cover about 4J yds. MEASUREMENT OF PAVERS' WORK. Pavers' work is done by the square yard. And the content is found by multi- plying the length by the breadih. Grading for paving is charged by the day. MEASUREMENT OF PAINTERS' WORK. Painters' work is computed in square yards. Every part is measured where the color lies ; the measuring line is forced into all the mouldings and corners. 12* 138 painters', glaziers', and fLUMEERS' WORK. Cornices, mouldings, narrow skirlings, reveals to doors and windows, and generally all work not more than nine inclies wide, are valued by ilieir length. Sasli-franies are charged so much each according to their size, and the squares so much a dozen. Mouldings, cut in, are charged by ihe foot run, and the work- man always receives an extra price for pnriy-colors. Writing is charged by the inch, and the price given is regulated by ihe skill and manner in which the work ' is executed : the same is true ot" imitations and marbling. The price ol'paiaiiii"- varies exceedingly, some colors being more expensive and requiring much more labor thiin others. In measuring open railing, it is customary lo tiiUe it as (lat work, which pays for the extra labor ; and as the rails are painted on all sides, the two surfaces are taken. It is customary to allow all edges and sinking?. MEASUREMENT OF GLAZIERS' WORK. Glaziers' work is sometimes measured by the sq. ft., sometimes by the piece, oral so much per light ; except wlierc the glass is set in metallic iVanies, when the charge is by the foot In estimating by the sq. ft., it is customary lo include the whole sash. Circular or oval windows are measured as if ihey were square. TABLE SHOWING THE SIZE AND NUMBER OF LIGHTS TO THE 100 SQUARE FEET. Size. Lights. Size. Lights. 1 Size. 1 Lights. ! Size. Lights 6 by S 3U0 12 by 14 86 14 by 22 47 20 by 20 36 7 by 9 229 12 by 15 80 14 by 24 43 20 by 22 33 8 by 10 180 12 by 16 75 15 by 15 64 20 by 24 30 8 by 11 164 12 by 17 71 15 by 16 60 20 by 25 29 8 by 12 1.50 12 by 18 67 15 by 18 53 20 Iiy 26 28 9 by 10 160 12 by 19 63 15 by 20 48 20 by 28 26 9 by 11 146 12 by 20 60 15 by 21 46 21 by 27 25 9 by 12 133 12 by 21 57 15 by 22 44 22 by 24 27 9 by 13 123 12 by 22 55 15 by 24 40 22 by 26 25 9 by 14 114 12 by 23 52 16 by 16 56 22 by 2S 23 9 by 16 100 12 by 24 50 16 by 17 53 24 by 28 21 10 by 10 144 13 by 14 79 16 by 18 50 24 by 30 20 10 by 12 120 13 by 15 74 16 by 20 45 24 by 32 19 10 by 13 111 13 by 16 69 16 by 21 43 25 by 30 19 10 by 14 103 13 by 17 65 16 by 22 41 26 by 36 15 10 by 15 96 13 by 18 61 16 by 24 38 2S by 34 15 10 by 16 90 13 by 19 58 17 by 17 50 30 by 40 12 10 by 17 85 13 by 20 55 17 by 18 47 31 by 36 13 10 by IS 80 13 by 21 53 17 by 20 42 31 by 40 12 11 by 11 119 13 by 22 50 17 by 22 38 31 by 42 12 11 by 12 109 13 by 24 46 17 by 24 35 32 by 42 10 11 by 13 101 14 bv 14 73 18 by 18 44 32 by 44 10 1 1 by 1 4 P4 14 by 15 68 18 by 20 40 33 by 45 10 11 by 1.5 87 14 by 16 64 18 by 22 36 34 by 46 9 11 by IG 82 14 by 17 60 18 by 24 33 30 l)y 52 9 11 by 17 77 14 by 18 57 19 by 19 40 32 by 56 8 11 by IS 73 14 by 19 54 19 by 20 38 33 by 56 8 12 by 12 100 14 by 20 61 19 by 22 34 36 by 58 7 12 by 13 92 14 by 21 49 19 by 24 32 38 by 58 7 MEASUREMENT OF PLUMBERS' WORK. Plumbers' work is rated at 30 much a pound, or else by the hundred weight, of 11-.' pounds. Sheet lead, used in roofing, pullering, &c., is from 7 to 12 lbs. to the Hi|uiire foot. And u pipe of iin inch bore is cuiniiionly frcnii to 13 lbs. lo ihe yard in length. — [Sec Table," Weij;hC of Lead Pipe per Fool'' J SIZE & WEIGHT OF LEAD PIPES, EOPES & CHAINS. 139 PATENT IMPROVED LEAD PIPE, SIZES AND WEIGHT PER FOOT. Calibre. Weight Calibre Weight Calibre AVeight Calibre Weight Calibre. Weight per foot. lbs. ozs. per foot, lbs. ozs. per foot, lbs. ozs.' per foot, lbs. ozs. Inches. per foot. Inches. Inches. Inches. Inches. lbs. ozs. % ^ 1 4 X 1 4 1 4 ij 5 8 K 1 8 ih 2 tt 6 A 4 10 u 2 u 2 4 1>^ 2 8 2 5 12 (C 3 u 2 8 u 3 cc G 1 % 13 IC 3 cc 3 8 !C 7 1 8 u 1 11 4 cc 4 2^1 ■S 11 y^ 8 Cf 1 8 1 1 8 (i 5 3 3 13 10 ec 2 IC 1 12 IK 3 3n^ 15 12 (C 2 12 (C 2 (( 3 8 1 4 -2 18 14 K 12 tc 2 8 IC 4 [ 4UI 20 _, 1 t( 14 <( 3 IC 4 8 : 5 22 Sheet Lead.— Weight of a Square Foot, 2\, 3, 3^, 4, 4^, 5, 6, 7, 8^, 9, 10 lbs. and upwards. BOSTON LEAD PIPE SIZES AND WEIGHT PER FOOT. 1-2 Inch. 5-8 Inch. 13-4 Inch. 1 Inch. 11-4 Inch. 11-2 Inch. 13-4 Inch. 2 Inch. Ibi. oz. lbs. cz. lbs. oz. lb$. oz. lbs. oz. lbs. oz. lbs. oz. lbs. oz. 10 2 12 1 1 1 8 2 4 3 ^ 3 10 4 12 12 3 1 6 1 12 2 8 3 12 4 3 ^ 8 IG 1 12 2 2 13 4 4 5 2 7 12 1 4 2 4 o 6 3 3 4 10 1 S 3 2 2 14 3 13 6 1 11 3 14 3 13 1 14 5 2 4 1 6 4 COMPARATIVE STRENGTH AND WEIGHT OF ROPES AND CHAINS. li ^1 si 1.2 5 a S| -1 ^1 roof Strength in ns and cwt. 3.3 Weight per athom in lbs. Diameter of iain in inches. li oof strength in ns and cwt. O Ph (h CU S- o Ui O b S B 3^ 2| 5|^ 1 5i 10 23 i 43 10 4^ 4-^ f 8 1 16f lOf 28 \^ 49 11 11 5 5f 7 10^ 2 10 lU 301 lin. 56 13 8 5f 7 ^ 14 3 5i m 36 Wr 63 14 18 6^ Of 9 TIT 18 4 3J. 13 39 n 71 16 14 7 IH * 22 5 2 I3f 45 ifV 79 18 11 8 15 4^ 27 6 4J. 144 48J- u 87 20 8 H 19 .3 32 7 7 15i 56 ItV 96 22 13 n 21 1 3 37 8 131 16 60 If 106 24 18 Note. — It must bn understood and also borne in mind, that, in eslimatins: the amount oflen^iile strain lo wliich a body is subjected, the weight of tlie body itself must also be taken in"lo account: for according to its position so may it approximate to us whole wcia-ht in lending lo produce extension within itself; as in the almost consiaiu application of ropes and chains to great depths, con- siderable heights, &c. 140 STRENGTH OF MATERIALS. STRENGTH OF MATERIALS OF CONSTRUCTION. IFrom Templeton's Workshop Companion.l Materials of construction are liable to four different kinds of strain ; viz., strelcliing, crushing, transverse action, and torsion or twisting : tlie first of wliich depends upon the body's tenacity alone ; the second, on its resistance to compression ; the third, «n its tenacity and compression com- bined ; and the fourth, on that property by which it opposes any acting force tending to ciiange from a straight line, to that of a spiral direction, the fibres of which the body is composed. In bodies, the power of tenacity and resistance to compression, in the di- rection of their length, is as the cross section of their area multiplied by the results of experiments on similar bodies, as exhibited in the following tables. Table shoicing the Tenacities, Resistances to Compression, and other Prop- erties of the common Materials of Construction. Absolute. Corapa red with Cast Iron. Kames of Bodies. Tenacity Resistance to compres- sion iu lbs. Its Its ex- Its in lbs. per strength tensibility stitfnesg sq. inch. per sq. inch. is is is Ash, 14130 0.23 2.6 0.089 Beech, . 12225 8548 0.15 2.1 0.073 Brass, 17968 10.304 0.435 0.9 0.49 Brick, . 275 562 Cast Iron, 13434 86397 1.000 1.0 1.000 Copper (wrought), . 33000 Elm, 9720 1033 0.21 2.9 0.073 Fir, or Pine, white, 12.346 2028 0.23 2.4 0.1 " " Red, . 11800 5375 0.3 2.4 0.1 «' " Yellow, 11835 5445 0.25 2.9 0.087 Granite (^Aberdeen), 10910 Gun-metal (copper 8, and tin 1). . 35838 0.65 1.23 0.535 Malleable Iron, 56000 1.12 0.86 1.3 Larch, 12240 5568 0.136 2.3 0.0585 Lead, 1S24 0.096 25 0.038 Mahogany, Honduras, 11475 8000 024 2.9 0.487 Marble, . 551 6060 Oak, 11880 9504 0.25 2.8 0.093 Rope (1 in. in circum.) 200 Steel, 128000 Stone, Bath, . 478 " Craigleith, , 772 5490 " Dundee, 2661 6630 " Portland, 857 3729 Tin (ca-t) 4736 182 0.75 25 Zinc (sheet) . 9120 365 05 0.76 RESISTANCE TO LATERAL PRESSORE, OR TRANSVERSE ACTION. The Strength of a square or rectangular beam to rcHist iaterni pressure, acliiig in a perpendicular chrcrtioii lo ils length, is as the breadth and scpiare of the depth; and inversely as the length j— thus, a beam twice the breadth ELASTICITY AND STRENGTH OF TIMBEE. 141 of another, all other circumstances being alike, equal twice the strength of the other J or twice the depth, equal four times the strength, and twice the length, equal only half the strength, &c., according to the rule. Table of Data, containing the Results of Experiments on the Elasticity and Strength of various Species of Timber, by Mr. Barlow. Snecies of Value of Value of Species of Timber. E. S. 1 Timber. Teak, 174.7 2462 1 Elm, . Poena, 122.26 2221 ' Pitch pine, English Oak, 105. 1672 j Red pine, . Canadian do. 155.5 1766 i New England Fir. Dantzic do. S6.2 1457 Riga Fir, . Adriatic do. 70.5 13S3 Mar Forest do. Ash, . 119. 2026 Larch, Beech, 98. 1556 j Norway Spruce. Value of Value of E. S. 50.64 1013 88.68 1632 133. 1341 158.5 1102 90. 1100 63. 1200 76. 900 105.47 1474 To find the dimensions of a beam capable of .lustainin^ a given iceight, with a giv- en degree of deflection, when sttpported at both ends. Rule. — iMuhiply tlie wei,!,'ht to be supported in lbs. by the cube of the length in fee! ; divide the product by 3"2 times the tabular value of E, multiplied into ihe given elefleciiun in inches ; and the quotient is tlie breadth multiplied by the cube of the depth in inches. Note 1 .—"When the beam is intended to be square, then the fourth root of the quotient is the breadth and depth required. Note 2.— If the beam is to be cylindrical, multiply the quotient by 1.", and the fourth root of the product is the diameter. Ex. The distance between the supports of a beam of Riga fir is 16 feet, and the weight n must be capable of sustaining in the middle of iis length is S00() lbs, with a deflection of pot more than 3 of an inch ; what must be the depth of the beam, supposing the breadth 8 inches? 16 X 8000 „ -— — ^^ = 15175 -^ 8 = V1897 = 12.35 in., the depth. 90 X 32 X .75 1 I' To determine the absolute strength of a rectangular beam of timber, lehen supported at both ends, and loaded in the middle of its length, as beams in general ought to be calcidatfd to, so that they may be rendered capable of withstanding all accident- al cases of emergency. Rule. — IMuhiply the tabular value of S by four times the depth of the beam in inches, and by the area of the cross section in inches ; divide the product by the distance between the supports in inches, and the quotient will be the absolute strength of the beam in lbs. Note ].— If the beam be not laid horizontally, the distance between the supports.fot calculation, must be the horizontal distance. Note 2.— One fourth of the weight obtained by the rule, is the greatest weight that ought to be applied in practice as permanent load. Note 3.— If the load is to be applied at any other point than themiddle, then the strength will be as the product of the two distances is to the square of half the length of the beam between the supports ;— or, twice the distance from one end, multiplied by twice from the other, and divided by the whole length, equal the effective length of the beam. Ex. In a building IS feet in width, an engine boiler of 5} tons (dS-lO lbs. to a ton) is to be fixed, the center of which to be 7 feet from the wall, and having two pieces of red pine, 10 inches by 6, which I can lay across the two walls for the purpose of slinging ii at each end,— may I with sufficient confidence apply them, 60 as to efl'ect this object ? •2210X5.5 -=- 2 = 6160 lbs. to carry at each end. And IS feet — 7 = 11, double each, or 14 and 22, then I-IX-^ -=- 18 = 17 feet, or 2(W inches, efTective length of beam. Tabular value of S, red pine, =1341X'lXlP.Xf'0 -r- 201 = 15776 lbs. the abso- lute strength of each piece of timber at that point. 112 STRENGTH OF RECTANGULAR BEAMS. To determine tht dimensions of a rectangular beam capable of supporting a rsquired weight, with a given degree of deflection, when fixed at one end. Rci.E. — Divide the weight to be supported, in lbs., by the tabular value of E, mulllplied by the breadth and deflection, both in inches ; and the cube root of the quotient, muUiplied by the length in feet, equal the depth required m inches. Ex. A beam of ash is intended to bear a load of 7U0 lbs. at its extremity ; its length being 5 feet, breadth 4 inches, and the defleclion not to exceed J an inch. Tabular value of E = 119X4X-5 = 23S the divisor ; then 700 -^ 238 = V2.94 X 5 = 7.25 inches, depth of the beam. To find the a'jsolute strength of arectangular beam, when fixed at one end, and load- ed at the other RcLE — Multiply the value of S by the depth of the beam, and by the area of its section, both in inches ; divide the product by the leverage in inches, and the quotient equal the absolute strength ol the beam in llis. Ex. A beam of Riga fir, 12 inches by 4i, and projecting 6J feet from the wall; what is the greatest weight it will support at the extremity of its length ? Tabular value of S = 1100. 12X4.5 = 54 sectional area. Then, 1100X12X54 -h 7S = 913S.4 lbs. When fracture of a beam is produced by vertical pressure, the fibres of the lower section of fracture are separated by extension, whilst at the same lime those of the upper portion are destroyed by compression ; hence exists a point in section where neither the one nor the other takes place, and which is distinguished as the point of neutral axis. Therefore, by the law of fracture thus established, and proper data of tenacity and compression given, as in the preceding table, we are enabled to form metal beams of strongest section with tlie least possible material. Thus, in cast iron, the resistance to compression is nearly as (ij to 1 of tenacity, consequently a beam of cast iron, to be of sirontjest section, must be of the following form, and a parabola in the direction of its length, the quantity of material in the bottom flange being al-.out G.J times that of the upper. But such is not the case with beams of lim- ber ; for although the tenacity of timber be on an average twice that of its resistance to compression, its flexibility is so great, that any considerable length of beam, where columns cannot be situated to its support, requires to be strengthened or trussed by iron rods, as in the following manner. T And these applications of principle not only tend to diminish deflection, but the required purpose is also more eflcctivcly attained, and that by lighter pieces of timber. To ascertain the absolute strength of a cast iron beam of the preceding form, or that of strongest section. RiT.K.— Multiply the sectional area of the bottom flanse in inches by the depth of the beam in niches, and divide the product by the distance between the sup- ports, aUo in inches; and 514 limes the quotient equal the absolute strength of the beam in cwts. . The strongest form in which any given quantity of matter can be disposed is that of a hollow cylinder; and it ha oiie-flrih of the cylinder's exicrnal dinineter; the relative strength of a Kollil to that of a hollow cylinder being us the diameters of tiieir sections. ( Set Tables.) "WEIGHT CAST IRON BEAMS WILL SUSTAIN. 143 A Table showing the Weight or Pressure a beam of Cast Iron, 1 inch in breadth, iviil sustain, without destroijitig its elasiicjurce. whe7i it is sup- ported at each end, and loaded in the middle of its length, and also the deflection in the middle which that weight will produce. By Mr. Hodgkinson, Manchester. Length. 6 feet. 7 feet. 8 feet. 9 feet. * 10 feet. Depth Weight Defl. Weight i Defl. Weight Defl. Weight Defl. Weiglit Defl. in in. in lbs. 1278 in m- in lbs. in in. in lbs. in in. in lbs. in in. in lbs. in in 3 .21 1089 .33 954 .426 855 .54 765 .66 3* 1739 .205 1482 .28 1298 .365 1164 .46 1041 !..57 4 2272 .18 1936 .245 1700 .32 1520 .405 1360 .5 4* 2S75 .16 2450 .217 2146 .284 1924 36 1721 .443 5 3560 .144 3050 .196 2650 .256 2375 .32 2125 .4 6 5112 .12 4356 .163 3816 .213 3420 .27 3060 .33 7 6958 .103 5929 .14 5194 .183 4655 .23 4165 .29 8 9088 .09 7744 .123 6784 .16 6080 203 5440 .25 9 9801 .109 8586 .142 7695 .18 6885 .22 10 12100 .098 10600 .128 9500 .162 8500 .2 11 12826 .117 11495 .15 102S5 .182 12 15264 .107 13680 .135 12240 .17 13 16100 .125 14400 .154 14 18600 .115 16700 .143 12 feet. 14 feet. 16 feet. 18 fe et. 20 feet. 6 2548 ■48 2184 .65 1912 .85 1699 1.08 1530 1.34 7 3471 .41 2975 .58 2603 .73 2314 .93 2082 1.14 8 4532 .36 3884 .49 3396 .64 3020 .81 2720 1.00 9 5733 .32 4914 .44 4302 .57 .3825 .72 3438 .89 10 7083 .28 6071 .39 5312 .51 4722 .64 42.50 .8 11 8570 .26 7346 .36 6428 .47 5714 .59 5142 .73 12 10192 .24 8736 .33 7648 .43 6796 ..54 6120 .67 13 11971 .22 10260 .31 8978 .39 7980 .49 7182 .61 14 13883 .21 11900 .28 10412 .36 9255 .46 8330 .57 15 15937 .19 13660 .26 11952 .34 10624 .43 9562 .53 16 18128 .18 15536 .24 13584 .32 12080 .40 10880 .5 17 20500 .17 17500 .23 15353 .30 13647 .38 12282 .47 18 22932 .16 19656 .21 17208 .28 15700 .36 13752 .44 Note. — This Table shows ihe greatest weight that ever ought lo be laid upon abeam for permanent load ; and, if there be any liability to jerks, &e., ample allowance must be made ; also, the weight of the beam itself must be included. (See Tables of Cast Iron.) To find the weight of a east iron beam of given dimensions. Rule. — Multiply the sectional area in inches by the length in feet, and by 3.2, the product equal the weight in lbs. Ex. Required the weight of a uniform rectangular beam of cast iron, 16 feet in length, 11 inches in breadth^and }^ inch in thickness. 11 X 1-5 X 16 X 3.2 = 844.8 lbs. RESISTANCE OF BODIES TO FLEXURE BY VERTICAL PRESSURE. When a piece of timber is employed as a column or support, its tendency to yielding by compression is diflerent according to the proportion between its length and area of its cross seciion ; and supposing the form that of a cylinder ■whose length is less than seven or eight times its diameier, it is impossible to bend it by any force applied longitudinally, as it will be destroyed by splitting before that bending can lake place ; but when the length exceeds this, the col- umn will bend under a certain load, and be ultimately destroyed by a similar 144 ELASTICITY OF TORSION. kind of action to ihat wliieh lias place in the transverse strain. Columns of cast iron and of oilier bodies are aUo similarly circumsianced. When llie length of a cast iron column wiih flat ends equals about thirty times its diameter, fracture will be produced wholly by bending olihe material. When of less length, fracture takes place partly by crushing and partly by bending. But, when the column is enlarged in the middle of its length trom one and a half to twice its diameter at the ends, by being cast hollow, the strength is greater by one-seventh than in a solid column containing the same quantity of material. To determine the dimensions of a support or column to bear, without se7liiiile curva- ture, a given pressure in the direction of its axis. Rule. — Multiply the pressure to be supported in lbs. by the square of the col- umirs length in feet, aiKl divide the product by twenty times the tabular value of E ; and the quotient will be equal to the breadth multiplied by the cube of th© least thickness, both being expressed in inches. Note 1. — When the pillar or support is a square, its side will be the fourth root of the quotient. Note 2.- If (he pillar or column be a cylinder, multiply the tabular value of E bj 12, and the fourth root of the quotient equal the diameter. Ex. 1. What should be the least dimensions of an oak support, to bear a weight of 2240 lbs, without sensible flexure, its breadth being 3 inches, and its lengths feet? Tabular value of E = 105, 2240 X 52 Ex. 2 Required the side of a square piece of Riga fir, 9 feet in length, to bear a permanent weight of GOOD lbs. Tabular value of E = 96, ^ GOOO X 9* . ::Tr , . ,, and V - fifi~ ~ '•^^-33 = 4 inches nearly. ELASTICITY OF TORSION, OR RESISTANCE OF 3B0DIES TO TWISTING, The angle of flexure by torsion is as the length and extensibility of the body directly and inversely as the diameter ; hence, the length of a bar or shaft being given, the power, and the leverage the power acts with, being known, and also the number of degrees of torsion that %vill not affect the action of the machine, to determine the diameter in cast iron with a given angle of flexure. Rule. — Multiply the power in lbs. by the length of the shaft in feet, and by the leverage in I'eet ; divide the product by fifty-five limes the number of decrees in the angle of torsion ; and the fourth root of the quotient equal the shaft's diame- ter in inches. Ex. Required the diameters for a series of shafts 35 feet in lengih, and to transmit a power equal to 1-J45 lbs., acting at the circumference ol a wheel 2J feet radius, so that the twist of the sliaAs on the application of the power may not exceed one degree. r^l5 X 35 X 2 5 — — Trv^TT^—- =<.v/1981 = 6.67 inches in diameter. 55 X 1 To determine the side of a square shaft to resist torsion with a ^iven flexure. Rui.E. — M'llliply the power in pounds by the leverage it acts with in feel, and also by the lengih ol the shuft in feel ; divide this product by 02.5 times the angle of flexure in degrees, and the square root of the quotient equals the area of the shaft in inches. Ex. Suppose the lengih of a shaft to be 12 feet, and to be driven by a power equal to 700 lbs., nz-iing at 1 foot from the centre of the shaft — required the area oictoii section, no that it may not exceed 1 degree of flexure. -j^^^j— =«.vA)0.8 ^ 0.53 inches. Relative strength of Bodies to resist Torsion, I^ad heinei 1- Tin 1.4 Copper 4..'! Yellow Uruss 4.0 Gun Melnl ."j.n Cast Iron il.O Swedish Iron 9.5 English Iron 10.1 Illisterid Steel 10 Shear Steel 17.0 STRENGTH OF MATERIALS — GRIER, AND OTHERS. 145 STRENGTH OF MATERIALS. iFrom Griefs Mechanic's Calculator, SfC.'\ Bar of Iiion. — The average breaking weight of a Bar of Wrouglit Iron, 1 inch square, is 2o tons; its elasticity is destroyed, however, by aljout two- fifths of ihnt weight, or 10 tons. It is e.^tendcd, within the limits oi its elas- ticity, .000096, or one-tenthousandih part of an inch for every Ion of str.iin per square inch of sectional area. Hence, the greatest constant load should never exceed one-fifth of its breaking weight, or 5 tons for every square inch of sectional area. The lateral strength of wrought iron, as compared with cast iron, is as 14 to 9. Mr. Barlow finds that wrought iron bars, 3 inches deep, 1 1-2 inches thick, and 33 inches between the supports, will carry 4 1-2 tons. Bridges. — The greatest extraneous load on a square foot is about 120 pounds. Floors. — The. least load on a square fool is about 160 pounds. Roofs. — Covered with slate, on a square foot, 51 1-2 pounds. Bf.ams. — When a beam Is supported in the middle and loaded at each end, it will bear the same weight as when supported at bnih ends and load- ed in the middle ; that is, each end will bear half the weight. Cast Iron Beams should not be loaded to more than one-fifth of their ultimate strength. The strength of similar beams varies inverselj' as their lengths ; that is, if a berfm 10 feet long- will support 1000 pounds, a similar beam 20 feet long would support only 500 pounds. A beam supported at one end will sustain only one-fourth part the weight which it would if supported at both ends. When a beam is fixetl at both ends, and loaded in the middle, it will bear one-half more than it will when loose at both ends. When the beam is load- ed uniformi}' throughout it will bear double. Whe.n the beam is fixed at both ends, and loaded uniformly, it will bear triple the weight. In any beam standing obliquely, or in a sloping direction, its strength or strain will be equal to that of a beam of the same breadth, thickness, and material, but only of the length of the horizontal distance between the points of support. In the construction of beams, it is necessary that their form should be such that they will be equally strong throughout. If a beam be fixed at one end, and loaded at the other, and the breadth uniform throughout its length, then, that the beam may be equally- strong throughout, its form must be that of a parabola. This form is generally used in the beams of steam engines. When a beam is regularly diminished towards the points that are least strained, so that all the sections are similar figures, whether it be supported at each end and loaded in the middle, or supported in the middle and load- ed at each end, the outline should be a cubic parabola. When a beam is supported at both ends, and is of the same breadth throughout, then, i/the load be uniformly distributed throughout the length of the beam, the line bounding the compressed side should be a semi-ellipse. The same form should be made use of for the rails of a wagon-way, where they have to resist the pressure of a load rolling over them. Similar p/a?es of the same thickness, either supported at the ends or all round, will carry the same weight either uniformly distributed or laid on similar points, whatever be their extent. 13 146 STRENGTH OF MATERIALS GRIER. The lateral strength of any beam, or bar of wood, stone, metal, &c., is hi proportion to its breadth multiplied b}' its depth^. In square beams the lateral strengths are in proporlion to tlie cubes of the sides, and in general of like-sided beams as the cubes of the similar sides of the section. The lateral strength of any beam or bar, one end being fixed in the wall and the other projecting, is inversely as the distance of the weight from the section acted upon ; and the strain upon any section is directly as the dis- tance of the weight from that section. The absolute strength of ropes or bars, pulled lengthwise, is in proportion to the squares of their diameters. All cylindrical or prismatic rods are equally strong in every part, if they are equally thick, but if not they will break where the thickness is least. The strength of a tube, or hollow cylinder, is to the strength of a solid one as the difference between the fourth powers of the exterior and interior diameters of the tube, divided by the exterior diameter, is to the cube of the diameter ol a solid cylinder, — the quantity of matter in each being the same. Hence, from this it will be found, that a hollow cylinder is one-half Stronger than a solid one having the same weight of material. The strength of a column to resist being crushed is directly as the square of the diameter, provided it is not so long as to have a chance of bending. This is true in metals or stone, but in timber the proporlion is rather greater Ihan the square. MODELS PROPORTIONED TO MACHINES. The relation of models to inachines, as to strength, deserves the particu jar attention of the mechanic. A model may be perfectly proportioned in all its parts as a model, yet the machine, if constructed in the same propor- tion, will not be sufficiently strong in every part; hence, particular attention should be paid to the kind of strain the different parts are exposed to; and from the statements which follow, the proper dimensions ol the structure may be determined. If the strain to draw asunder in the model be 1, and if the structure is 8 times larger than the model, then the stress in the structure will be 8'' equa' 612. If the structure is G times as large as the model, then the stress oi. the structure will be 6-' equal 216, and so on ; therefore, the structure will be much less firm than the model ; and this the more, as the structure is cube times greater than the model. If we wish to determine the greatest size we ean make a machine of which w'c have a model, we have, The greatest weight which the beam of the model can hear, divided by the weight which it actually sustains equal a quotient which, when multi- plied by the size of the beam in the model, will give the greatest possible size ol the same beam in the structure. Ex. — If a beam in the modfl be 7 inches long, and bear a weight of 4 lbs. but is capable of bearing a weight of 2G lbs. ; what is the greatest length which we can make the corresponding beam in the structure ? Here 2G -f- 4 = C-5, therefore, 6-5x7= 45 5 inches. The strength to resist crushing, increases from a model to a structure in proporlion to their size, but, as above, the strain increases as the cubes; wherefore, in this rase, also, the model will be stronger than the machine, and the greatest size of the structure will be found by employing the square root ol the quotient in the last rule, instead of the quotient itself; thus, If the greatest weight which the column in a model can bear is 3 cwt., and if it actually bears 28 lbs., then, if the column be 18 inches high, we have V/( -^ ) = 3-401 ; wherefore 3-4G4 X 18 = 62-352 iochcs, the length of the column in the structure. STRENGTH OF MATERIALS — ADCOCK. 147 STRENGTH OF MATERIALS. [From Adcock's Engineer.] List of metals, arranged according to their strength. — Steel, wrought- iron, cast-iron, platinum, silver, copper, brass, gold, tin, bismuth, zinc, anti- mony, lead. According to Tredgold's and Duleau's experiments, a piece of the best bar-iron 1 square inch across the end would bear a weight of about 77,373 lbs., while a similar piece of cast-iron would be torn asunder by a weight of from 16,243 to 19,464 lbs. Thin iron wires, arranged parallel to each other, and presenting a surface at their extremity of 1 square inch, will carry a mean weight of 126,340 lbs. List of woods, arranged according to their strength. — Oak, alder, lime, box, pine (s?//r.), ash, elm, yellow pine, fir. A piece of well-dried pine wood, presenting a section of 1 square inch, is able, according to Eytclwein, to support a weight of from 15,646 lbs. to 20.408 lbs., whilst a similar piece of oak will carry as much as 25,850 lbs. Hempen cords, twisted, will support the following weights to the square inch of their section i i-inch to 1 inch thick, 8,746 lbs.; 1 to 3 inches thick, 6,800 lbs.; 3 to 5 inches thick, 5,345 lbs.; 5 to 7 inches thick, 4,860 lbs. Tredgold gives the (bllowing rule for finding the weight in lbs. which a hempen rope will be capable of supporting : ftlultiply the square of the circumference in inches by 200, and the product will be the quantity sought. In the practical application of these measures of absolute strength, that of metals should be reckoned at one-half, and that of woods and cords at one-third of their estimated value. In a parallelopipedon of uniform thickness, supported on two points and loaded in the middle, the lateral strength is directly as the product of the breadth into the square of the depth, and inversely as the length. Let W represent the lateral strength of any material, estimated by the weight, b the breadth, and d the depth of its end, and I the distance between the points of support ; then W = fd-b -h I. If the parallelopipedon be fastened only at one end in a horizontal posi- tion, and the load be applied at the opposite end, W = fd-b -h 4/. It is to be observed that the three dimensions, 6, d, and /, are to be taken in the same measure, and that b be so great that no lateral curvature arise from the weight ;/in each formula represents the lateral strength, which varies in different materials, and which must be learnt experimentally. A beam having a rectangular end, whose breadth is two or three times greater than the breadth of another beam, has a power of suspension re- spectively- two or three times greater than it ; if the end be two or three times deeper than the end of the other, the suspension power of that which has the greater depth exceeds the suspension power of the other, four or nine times ; if its length be two or three limes greater than the length of another beam, its power of suspension will be ^ or 1-3 respectively that of the other ; provided that in each case the mode of suspension, the position of the weight, and other circumstances be similar. Hence it follows that a beam, one of whose sides tapers, has a greater power of suspension if placed on the slant than on die broad side, and that the powers of suspen- sion in both cases are in the ratio of their sides ; so, for instance, a beam, one of whose sides is double the width of the other, will carr^' twice as much if placed on the narrow side, as it would if laid on the wide one. In a piece of round timber (a cylinder) the power of suspension is in proportion to the diameters cubed, and inversel}' as the length; thus a beam with a diameter two or tliree times longer than that of another, will carry a weight 8 or 27 times heavier respectively than that whose diameter is unity, the niode of fastening and loading it being similar in both cases. 148 STRENGTH OF MATERIALS ADCOCK. The lateral streng-th of square timber is to that of a tree whence it is hewn as 10 : 17 nearly. A considerable advantasje is frequently secured by using hollow cylinders instead of solid ones, vvhicli, with an e(|ual expenditure of materials, have far greater strength, provided only that the solid part of the cylinder be of a suflicicnt thickness, and that the workmanship be good ; especially that in cast metal beams the thickness be uniform, and the metal free from flaws. According to Eytelwein, such hollow cylinders are to solid ones of equal weight of metal as 1.212:1, when the inner somi-diametcr is to the outer as 1 : 2 ; according to Tredgold as 17 : 10, when the two semi-diame- ters are to each oUier as 15 : 25, and as 2 : 1, when they are to each other as 7 : 10. A method of increasing the suspensive power of timber supported at both ends, is, to saw down from i^ to h of its depth, and forcibly drive in a wedge of metal or hard wood, until the timber is slightly raised at the mid- dle out of the horizontal line, liy experiment it was found that the suspen- sive power of a beam thus cut 1-3 of its depth was increased l-19th, when cut 4 it was increased l-29th, and when cut 3-4th through it was increased l-87th. The force required to crush a body increases as the section of the body increases ; and this quantity being constant, the resistance of the body diminishes as the height increases. According to Eytelwein's experiments, the strength of columns or tim- bers of rectangular form in resisting compression is, as 1. The cube of their thickness (the lesser dimension of their section). 2. As the breadth (the greater dimension of their section). 3. inversely as the square of their length. Cohesive power of Bars of Metal one inch square, in Tons. Copper, wrought . . . 15.08 Gun metal 16.23 Copper, cast 8.51 Iron, Swedish bar 29.20 Do., Russian bar 20.70 Do., Englsh bar .... . 25.00 Steel, cast 59.93 Do., blistered 59.43 Do., sheer 56.97 Brass, cast, yellow . . . 8.01 Iron, cast 7-87 Tin, cast 2.11 RELATIVE STRENGTH OF CAST AND MALLEABLE IRON. It has been found, in the course of the experiments made by Mr. Iloilg- kinsoii ami Mr. Fairbiirn, that the average strain that cast iron will bear in the waj' of tension, before breaking, is about seven Ions and a half per square inch ; the weakest, in the course of IG trials on various descriptions, bearing 6 tons, and the strongest 9 3-I' tons. The ex])erimcnts of Telford and i'rown show that malleable iron will bear, on an average, 27 tons ; the weakest bearing 21-, and the strongest 29 tons. On ap])roarhing the break- ing point, cast iron may snap in an instant, without any previous symptom, while wrought iron begins to stretch, with half its breaking weight, and so conlimies to stretch till it breaks. The experiments of Ilodgkinson and Fairbairn show also that cast iron is capable of sustaining compression to the extent of nearly 50 tons on the s(iuare mrli ; the weakest bearing 36iJ tons, and the strongest 60 tons. In this respect, malleable iron is nmch in- ferior to cast iron. With 12 tons on the S(|uare inch it yields, eontracis in length, and expands laterally; tlmugh it will bear 27 tons, or more, without actual fracture. ■ Rcnnie stalos that cast iron may be crushed with a weight of 93,000 lbs., and brick with one of 5G2 lbs. on ilic square inch. STRENGTH OF BEAMS. 149 STRENGTH OF BEAMS. [From Lowndes' Engineer's Hand-book, — Liverpool, I860.] SOLID, KECTANGULAR, AND ROUND : TO FIND THEIR STRENGTH Square and rectangular. (Depth ins.)2 x Thickness ins Length, ft. - X Tabular No. = Breaking weight, tons. Round. (Diameter ins.)3 „, . . »t ^ , . -^f nr^ — TT-^ X 1 abuiar No. = Breaking weiffht, tons. Length in ft. s> b > Hollow. (Outside dia. ins.)^ — (Inside dia. ins.) tons. Length, ft. X Tabular No. = Breaking weight Thickness not exceeding ( ^ .^"'=''/°^ 'f""- 2 ins. for iron 3 ins. for iron. ° ( 3 ins. for wood. 6 ins. for wood. 12 ms. for wood Square and Rectangular. Cast and Wrought Iron 1 •85 •7 Teak and greenheart •36 •32 •26 Pitch pine, and Cana^ dian oak .... •25 •22 •18 Fir, red pine, and Eng- lish oak .... •18 •16 •13 Round. Cast and Wrought Iron Teak and greenheart . Fir and English oak . •8 •28 •14 •68 •25 •125 ■56 •2 •1 To find the Breaking Weight in lbs. use the Tabular No. below. Thickness not exceeding | 1 inch for iron. 3 ins. for wood. 2 ins. for iron. | 3 ins. for iron. 6 ins. for wood. 12 ins. for wood. Square and Rectangular. Iron . . Teak . . Fir and oak 2240 1900 1570 800 710 570 400 355 285 13* 150 BEAMS — CAST IRON FLANGED. Round. Iron 1800 1570 1260 Teak 640 570 460 Fir and oak .... 320 285 230 Though wrought and cast iron are represented in these rules as of equal strength, it sliould he observed tiiat while a cast iron bar 1 inch X 1 inch X 1 foot inch long, of average quahty, will break with one ton, a similar bar of wrought iron only loses its elasticity, and deflects 1-lGth of an inch, yet as it can only carry a further weight by destroying its shape and increasing the deflection, it is best to calculate on the above basis : — y 1-lG with 1 ton. A wrought iron bar 1 in. xl in. X 1 ft. in. long C deflects 1-8 " I J " > 2 1-2 " 2i " The above rule gives the weight that will break the beam if put on the middle. If the weight is laid equally all over, it would require double the weight to break it. A beam should not be loaded with more than 1-3 of the breaking weight in any case, anil as a general rule not with more than 1-4, for purposes of machinery not with more than 1-C to I -10 depending oa circumstances. Tojind the proper size for any given purpose. Rectangular. Weight X Length ft. _ „ . _ . i- , ■ ■ ^. T — ^1 — jvj^' X o or 4 or 6, dec. accordmg to circumstances = Tabular No. ' " B v^ ins. Round. ^i/Weight X Length, ft, ^ „ '. 7~^ ~. ' '. ' V f„-r— I — 1VI X 3 or 4 or 6, &.C. accordmg to circumstances 1 abular J\o. ' ° = diam. ins. CAST lEON WITH FE.1THEI19 OR FL.\NGES : TO FIND THEIR STRENGTH. Sec. area, bottom flanse ins. X depth ins. „ r. . ■ • > , — — 5 i -7 X 2 = Breaking weight, tons. Length in feel. " " ' If the metal exceeds 1 inch in thickness deduct l-8th. If above 2 inches deduct I-4th. This description of beam is of the strongest form, when the sectional area of the bottom flange is six limes that of the top flange. In designing this description of beam, the bdttoni flange may be from 1-2 to 1 1-2 the depth of beam; the top flange from I-l to l-;{ the width of ihc bottom one, and 2-3 lo 1-2 the thickness of it ; the feather being made al the top a little thicker than the top (lange, increasing to the bottom to nearly the thickness of the bottom flange ; in this way avoiding any sud- den vari.'itiou in the ihirkiiess and saving weight ; many cngiiw^ers, however, prefer keeping tlic same tliickn(?ss throughout in cverv part. The verti- cal brackets for slilfening the girilor shouhl not be ma Saws. Purple - - - 530 •^ 5 All kinds of percussive tools. Dark purple - - 550'^ > g; Blue - - - 570"5''P""°- Dark blue - - 600° Soft for saws. To Temper by the Thermometer. Put the articles to be tempered into a vessel containing a sufficient quantity to cover them, of Oil or Tallow; Sand; or a mixture of 8 parts bismuth, 5 of lead, and 3 of tin, the whole to be brought up to, and kept up at the heat corresponding to the hardness required, by means of a suitable thermometer, till heated equally throughout; the articles are then withdrawn and plunged into cold water. If no thermometer is available, it may be observed that oil cr tallow begins to smoke at 43C or straw color, and that it takes lire on a light being presented, and goes out when the light is withdrawn, at 570'* or blue. CASE HARDENING. Put the articles requiring to be hardened, after being finished but not polished, into an iron box in layers with animal carbon, that is, 160 HEAT. SOLDERING. BORING AND TURNING. horns, hoofs, skins, or leather, partly burned so as to be capable of being reduced to powder, taking care that every part of the iron is coinpletcly surrounded ; make the box tight with a lute of sand and clay in equal parts, put the wbole into the fire, and keep it at a light red heat for half an hour to two hours, according to the depth of har- dened surface required, then empty the contents of the box inio water, care being taken that any articles liable to buckle be put in separately and carefully, end in first. Cast iron may be case hardened as follows: — Bring to a red heat, and roll it in a mixture of powdered ])russiate of potash, saltpetre and sal-anuuoniac in equal parts, then plunge it into a bath containing 2 oz. prussiate of potash, and 4 oz. sal-ammo- niac per gallon of water. HEAT. EFFECTS OF HEAT 'AT CERT.AIN TEMPERATURES. — GrIER. Tin and Bismuth, equal parts, melt at 283 degrees, Fahrenheit ; tin melts at 442 ; polished steel acquires straw color at 460 ; bismuth melts at 476 ; sulphur burns at 560; oil of tuipentine boils at 560; polished steel acquires deep blue color at 580 ; lead melts at 594 ; lin- seed oil boils at GOO; (luicksilvcr boils at 660 ; zinc melts at 700; iron, bright red in the dark at 752 ; iron, red-hot in twilight at 8S4 ; led heat fully visible in daylight at 1077 ; brass melts at 3807 ; copper melts at 4587; silver melts at 4717; gold melts at 5237; welding heat of iron, from 12777; welding heat of iron, to 13427; greatest heat of smith's foige 17327; cast iron begins to molt at 17977; cast iron thoroughly melted at 20577. SOLDERING. The solder for joints requires to be of some metal more fusible than that of the substances to be jointul. For Copper, usual solder 6 to 8 parts brass to 1 of zinc ; 1 of tin sometimes added. A slill stronger solder, 3 parts brass, 1 of x.inc. To prepare this solder. — Melt the brass in a crucible, when melteil add in the zinc, and cover over for 2 ot 3 minules (ill the combination is ctrected, tlien pour il out, over a bundle of Iwigs, into a vessel of water, or into a mould composed of a number of little cliatinels, so that the sohler may be in long strips convenient for use. Brass tilings alone will answer very well. To braze with this xoliler. — Sci-.\\)c. the suil'accs perfectly clean, and secure the flange or joint carefully ; cover the surfaces to be brazed with borax powder moistened ; apply the solihu-, and melt it in with the llanie of a clear coki; fire from a snuth's hearth ; partic- ular care being taken not to burn the cuiqier. BORING AND TURNING. BRASS CASTINGS. IGl Iron and brass are soldered with spelter, which is brass and zinc in equal parts; the process being performed in a manner similar to the above. For ironwork, however, sometimes rather differently ; the articles aie fixed in their position, and the solder applied, a covering ot'loam is then put over all to exclude the air, the work thus prepared is then put into the fire a sufficient time to melt the solder in. BORING AND TURNING. The best speed for boring cast iron is about 7.^ feet per minute. For drilling about 10 or 11 feet per minute is a good speed for the circumference of the tool. For a 1 inch drill 40 revolutions = 11 feet per minute, other sizes in proportion For turning, the proper speed for the circumference is about 15 feet per minute. BRASS. COMPOSITIONS OF BRASS. Copper. Tin. Zinc. Watch-makers brass 1 part — 2 parts German brass 1 « 1 " Yellow brass 2 «' __ 1 " Speculum meta! 2 " 1 part Bell metal 3 " , Light castings and small bearings . . . 4 " i " Ditto a little harder .... 4 " h " Heavy castings 6 to 7 1 " Gun met.il 9 « The addition of a little lead makes the metal more easily wrought, and is advantageous when the work is not intended for exposure to heat. BEASS CASTING. As it is often useful to engineers, especially abroad, to be able to cast brass, a slight description of the process may not be out of place. The ordinary furnace used is of very simple construction. After lighUng the fire, put the pot intended for use bottom upwards over it, so as to warm gradually through. As soon as the fire is burned well through, put the pot into its place, resting the bottom on a fire brick to keep it off the bars, and filling round with lumps of coke to steady it; then put in the copper, either blocks cut up into pieces of convenient size, or if this is not to be had, shest copper doubled up ; as the metal sinks down add more copper or old brass till the pot is nearly full of melted metal ; now add the tin, and when this is melted and mixed, put in a piece or two of zinc ; if this begins to flare add the rest of the zinc in, stir it well in, lift the pot off at 14* 162 BRASS CASTINGS. WEIGHT OF ROPE. once, skim the rubbish off the top, and pour into the mould. If, however, it does not tlare up, put a little coal on to excite the fire, and cover over till it comes to a proper heat. As soon as the zinc begins to flare, add in the rest, and take the pot off the fire. If old brass alone is melted down no tin is required, Lnt a small quantity of zinc. If part copper and part brass, add tin and zinc in proportion to the new copper, with a little extra zinc for the biass. As soon as the boxes are run, it is tbe usual custom to open them at once, and to sprinkle the castings with water from tlie rose of a watering can, this has the effect of making them softer than they would otherwise be ; the boxes are then emptied, and fresh moulds made while fresh metal is being melted. When the casting is completed, draw the bearer forward, and let the bars all drop, so that the furnace can be eflectuallj- cleared from the clinkers, and put the pot among the ashes to cool gradually. The moulding boxes may be of hard wood, well secured at the corners, either bj- dovetailing or by strong nails and iron corner plates, with guides to keep the boxes fair with one another. A few cross bars in the top box help to carry the sand. Fresh green sand, the same as used for iron founding, mixed with a small ijuantity of coal dust, about one-twelfth part, should be sifted over tlie patterns on all sides to the thickness of about an inch, the box then tilled up with old sand, and properly rammed up, and well pricked to let the air and gas escape, then remove the patterns, and dust over the mould with a little charcoal powder from a bag, or with a little flour, cover over the box again, and the mould is ready for pouring. For long articles, spindles, bars, &c., make a good airhole at the opposite end from where the metal is poured, incline the box slightly, and pour the metal at the lower end; for flat, thin and sti-aggling ar- ticles it is necessary to have two or more pouring lioles, and to till them all at the same time. The pots generally used arc the Stourbridge clay pots, and black lead pots, both kinds being made of various sizes up (o 60 lbs. ; the former are less durable, but much cliea|)er than the latter, they re- quire to be carefully hardened by gradual exi)Osure to the fire. Clay pots are made of 2 parts raw Stourbridge clay to 1 of gas coke pulverized ; well mixed up together with water, drieii gently, and slightly baked in a kiln. Hlack load pots of 2 parts graphite, and 1 of fireclay, mixc the sjjindle and screw-wheels to be those fixed upon, also any one of the stud-wheels, to find the number of teeth in the other. GO X 12 5 „^, , GO X 12.5 X 20 ,,_^ ,-60-^oa = 2« ^-"'' '^^ m = ''' ''-'■''■ CONTINUOUS CIRCULAR MOTION. 167 Table of Change Wheels for Screw-cutting ; the leading Screw being ^ inch pitch, or containing 2 threads in an inch. Numb, of Number of Number of a teeth in a w ■a teeth in ■a teeth in s » 1 ■^ 1) ■Si >. to -3 O o fcc an c ■3. ll to 1 si si .= 2 t-i m bo (U<« w . o^ CO _ a "^ aji- OD — c - Cj r^r . XI O ^.5 31 *-9 ^ SI ^1 ^J ll ^ •2 ° Z.H 31 1 so 40 8i 40 55 20 60 19 50 95 20 100 li so 50 8^ 90 85 20 90 194 SO 120 20 130 u 80 60 83 60 70 20 75 20 60 100 20 120 ll 80 70 9h 90 90 20 95 20^ 40 90 20 90 2 SO 90 9| 40 60 20 65 21 80 120 20 140 2i SO 90 10 60 75 20 SO 22 60 110 20 120 2^ 80 100 10-^ 50 70 20 75 22.i 80 120 20 150 2| SO 110 11 60 53 20 120 22| 80 130 20 140 3 SO 120 12 90 90 20 120 232 40 95 20 100 H SO 130 12:1 60 85 20 90 24 65 120 20 130 H 80 140 13 90 90 20 130 25 60 100 20 150 n 80 150 13i 60 90 20 90 251 30 85 20 j 90 4 40 80 133 80 100 20 110 26 70 130 20 140 4i 40 S5 14 90 90 20 140 27 40 90 20 120 4i 40 90 Hi 60 90 20 95 27i 40 100 20 110 4| 40 95 15 90 90 20 150 28 75 140 20 150 5 40 100 16 60 80 20 120 28i 30 90 20 ; 95 5i 40 110 16.i 80 100 20 130 30 70 140 20 150 6 40 120 16i 80 no 20 120 32 30 80 20 120 6i 40 130 17 45 S5 20 90 33 40 110 20 120 7 40 140 174 SO 100 20 140 34 30 85 20 120 7i 40 150 18 i -1^ 60 20 120 35 36 60 140 20 150 8 30 120 181 SO 100 20 150 30 90 20 il20 Table by which to determine the JVwjiber of Teeth, or Pitch of Small Wheels, by what is commonly called the Manchester Principle. Diametral Circular Diametral Circular Pitch. Pitch. Pitch. Pitch. 3 1.047 9 .349 4 .785 10 .314 5 .628 12 .262 6 .524 14 .224 7 .449 16 .196 8 .393 20 .157 168 WHEELS AND GUDGEONS. Example 1. — Required the number of teeth that a wheel of 16 inches diameter will contain of a 10 pitch. 16 X 10 = 160 teeth, and the circular pitch = .314 inch. Example 2. — What must be the diameter of a wheel for a 9 pitch of 126 teeth ? 126 -f- 9 = 14 inches diameter, circular pitch .349 inch. Note. — The pitch is reckoned on the diameter of the wheel instead of the cir- cumlerence, and designated wheels of 8 pitch, 13 pitch, &c. Strength of the Teeth of Cast Iron Wheels at a given Velocity. Strength of teeth in horse-po wer at Pitch of teeth Thickness of teeth Breadth of teeth 3 feet per 4 feet per 6 feet per 8 feet per in inches. in inches. in inches. second. second. second. second. 3.99 1.9 7.6 20.57 27.43 41.14 54.85 3.78 1.8 7.2 17.49 23.32 34.98 46.64 3.57 1.7 6.8 14.73 19.65 29.46 39.28 3.36 1.6 6.4 12.28 16.38 24.56 32 74 3.15 1.5 6. 10.12 13..50 20.24 26.98 2.94 1.4 5.6 8.22 10.97 16.44 21.92 2.73 1.3 5.2 6.58 8.78 13.16 17.54 2.52 1.2 4.8 5.18 6.91 10.36 13.81 2 31 1.1 4.4 3.99 5.32 7.98 10.64 2.1 1.0 4. 3.00 4.00 6.00 8.00 1.89 .9 3.6 2.18 2.91 4 36 5.81 1.68 .8 3.2 1.53 2.04 3.06 3.08 1.47 .7 2.8 1027 1.37 2.04 2.72 1.26 .6 2.4 .64 .86 1.38 1.84 1.05 .5 2. .375 .50 .75 1.00 WHEELS AND GUDGEONS. To find size oj Teeth necessary to transmit a given Horse Power. (Tredgold.) Horse power X 240 Diameter "'" • t/ Strength = Pitch, ins. X Revs, per min. Strength = Strength of tooth. Breadth, ins. Breadth, ins. ' (Pitch, ins.)-* The above rule will be found very suitable for a speed of circum- ference of about 240 feet per minute. For speeds above, add to 240 half tlic dinTereiice, for speeds lielow, deduct lialf the did'crence, be- tween 2 JO and the actual speed, the result being a suitable multiplier. For in-itance ; at 300 ft. per minute, 60 being the diflcrenco, 240 -}- 30 = 270 multiplier. At 160 ft. per minute, 80 being the dilTercncc, 240 — 40 = 200 multiplier. "WATER. 169 The reason being, that with iiio-her speeds, the friction, wear, and liability to shocks is increased, at lower speeds decreased, and the teeth may advantageously be proportioned accoidingly. To find the Horse Power that any Wheel will transmit. (Pitch, ins.)* X Breadth, ins. X Diameter ft. X Revs, per minute Appropriate No. according to speed, as above. = Horse Power. To find the multiplying number for any Wheel. (Pitch, ins.)2 X Breadth, ins. X Diameter ft. X Revs, per minute Horse Power = Multiplying No. as above. To find the size of Teeth to carry a given load in lbs. Load, lbs. — 1120 = Breaking strength of teeth. Load, lbs. -f- 2S0 = Strength for very low speeds, and for steady work; being 4 times the breaking strength. Load, lbs. -~- 140 = Strength for ordinary purposes of machinery ; being 8 times the breaking stiength. Load, lbs. -=- 100 = Strength for high speeds, and irregular work ; or when the teeth are exposed to shocks. As before. Strength (Pitch, ins.)' = Breadth i/ Strength , ins. V ^. ^- Breadth, ins. Pitch, ins. WATER. To find the quantity of Water that will be discharged through an orifice, or pipe, in the side or bottom of a Vessel. Area of orifice so in X ^ ^°- corresponding to height of surface ' ^' ' \ above orifice, as per table = Cubic feet discharged per minute. Height of Surface above Orifice. Multiplier. \ Height of Surface above Orifice. Multiplier. Height of Surface above Orifice. Multiplier. Ft. 1 2-25 I Ft. i 18 9-5. Ft. 40 14-2 2 3-2 20 , 10- 1 45 151 4 4-5 22 10-5 i 50 16- 6 5-44 24 II- 60 17-4 8 64 26 11-5 70 18-8 10 7 1 28 12- ! 80 20-1 12 7-8 30 123 90 21-3 14 84 32 ll7 100 22-5 16 <*• 35 13-3 15 170 WATER. To find the size of hole necessary to discharge a given quantity of Water under a given head. Cubic ft. water dischaiged » ^ ./- ivf ^1^ - JT^- w ^ . 1,1 "= Area of onnce, sq. in. jNo. corresponding to height, as per table ^ To find the height necessary to discharge a given quantity through a given orifice. Cubic ft. water discharged ^^ , . , — ; — ;- = No. corresp. to height, as per table. Area ontice, sq. inches. o > r The velocity of Water issuing from an orifice in the side or bottom of a vessel being ascertained to be as follows : -^Height ft. surface above orifice X 5-4 = i Velocity of water, ft. ° ( P^"" second. ^Height ft. X Area orifice, ft. X 324 = J ^ubic ft;^discharged per ^Height ft. X Area orifice, ins. X 2-2 = Do. Do. It may be observed, that the above rules represent the actual quantities that will be delivered through a hole cut in the plate ; if a short pipe be attached, the quantity will be increased, the greatest delivery with a straight pipe being attained with a length equal to 4 diameters, and being l-.i more than the delivery through the plain hole ; the quantity gradually decreasing as the length of pipe is in- creased, till, with a length equal to 60 diameters the discharge again equals the dischai'ge through the plain orifice. If a taper pipe be attached the delivery will be still greater, being \h times the deliv- ery thiough the plain orifice ; and it is probable that if a pipe wi'.h curved decreasing taper were to be tried, the delivery thiough it would be equal to the theoretical discharge, which is about 1-C5 the actual discharge through a plain hole. To find the quantity of Water that will run through any orifice, the top of which is level ivith the surface oftvater as over a sluice or dam. I /Height, ft. from water surface to hot- ) ^ Area of water ) ^ gig ' torn of orifice or top of dam j passage, sq. ft. ) = Cub. ft. discharged per minute. Or, Two-thirds Area of water passage, sq. ins X No. corresponding to height as per table, = Cub. ft. discharged per minute. To find the time in which a Vessel will empty itself through a given orifice. VHeight ft. surface above orifice X Area water surface, sq. ins. Area orincc, sq. in. X ^7 = Time required, seconds. The above rules are founded on Bank's experiments. MECHANICAL TABLES FOR THE USE OF OPERATIVE SMITHS, MILLWRIGHTS, AND ENGINEERS 172 DIAMETERS AND CIRCUMFERENCES OF CIRCLES,, MECHANICAL TABLES FOR THE USE OF OPERATIVE SMITHS, MILLWRIGHTS, AND ENGINEERS. The following Tables, originally dedicated to ' the JVational Asso- ciation of the Forgers of Iron Work,' England, by James Fo- DEN, will be found extremely useful to Smiths, generally, and are accompanied by Practical Examples. — Templetox. DIAMETERS AND CIRCUMFERENCES OF CIRCLES. Diam. c re. Diam. III. Circ. Diam.j Circ. Diam Circ. Diam Circ. In. Ft. In. Ft. In. Ft. Iii.'fi. In. Ft. In Ft. In. Ft. In 'fi. 111. 1 H 5.^ 1 5i 10 2 7| 1 2f 3 9i 1 6^ 4 Hi IJ 3i 5| 1 5t 1 2.^ 1 3 9h 1 7 4 111 H H 55 1 6 lOJ 2 73 1 2i 3 H If H H 1 61 10:J' 2 8i 1 23 3 m 1 n 5 li ^ 6 1 6| 10| 2 Si 1 2-^ 3 log 1 n 5 0| ll 5 10^ 2 8| 1 3 3 11 1 7| 5 05 l| 5i 6J 1 n 101; 2 9f 1 7.^ 5 1^ H 5fe 6.i 1 ^s lOi 2 n 1 31 3 114 1 n 5 It 2* 6i 6| 1 8 10| 2 101 1 3i 3 m I 73 5 2 64 1 S§ 11 2 104 1 3| 4 o\ 1 75 5 2| 2i n 6§ 1 85 1 34 4 n 1 8 5 23 H 7 H 1 9i llj 2 10| 1 3| 4 1 21 n ^« 1 94 11-J 2 lli 1 33 4 n 1 SI 5 3J 24 n 7 1 yj 11| 2 llg 1 3} 4 n 1 H 5 31 24 8i . 11^ 3 1 4 4 2i 1 83 5 4 21 H 7J 1 10| 11| 3 04 1 84 5 4J 2& 9 7.i 1 103 ll.i 3 OS 1 4i 4 n 1 8| 5 41 3 9s- n 1 llj 115 3 li 1 4i 4 3 I 83 5 5^ u 1 Uh 1 3 n 1 4g 4 3i 1 SI 5 5i 3i n 7| 1 111 1 1.^ 4 33 1 9 5 5i 3.i lOJ 7.| 2 0:J 1 OJ 3 2 1 4g 4 44 H 10.^ n 2 0| 1 OJ 3 25 1 43 4 1 91 5 G| sd lOJ 8 n 1 Og 3 2S J f^ 4 5 1 9j 5 6 3j 113 1 O.^t 3 3.i 1 5 4 5| 1 98 5 7 3? 115 8J 2 u 1 0|] 3 3g 1 94 5 7,i 3; oj 8i 2 li 1 03 3 4 1 5J 4 53 1 96 5 8 4 oi 8g 2 2.^ 1 OJ 3 4i 1 5i 4 64 1 93 5 8| 8i 2 2g 1 1 3 45 1 5i 4 6A 1 yj 5 8.^ 4ji 05 8| 2 3 I 54 4 6S i 10 5 9 4i l.i 8.^ 2 3g 1 IJ 3 "^i I 56 4 78 4i n 8J 2 :ij 1 l.i 3 n 1 5.3 4 73 1 ini 5 94 4d 21 9 2 4i 1 li 3 6 1 55 4 81 1 lo.i 5 9S .1 24 1 14 3 62 I 6 4 84 1 10| 5 lOi 21 9i 2 4g 1 1| 3 6ii 1 104 5 10| ^ 'i\ f'i 2 5 1 1.4' 3 7i 1 6i 4 8J I lol 5 11 6 ^ y| 2 5g 1 n 3 51 I 6i 4 9.i 1 103 5 llf y-i 2 5i{ I 2 3 1 63 4 n 1 10 J 6 llj H 4 !>3 2 fii 1 64 4 10 1 11 6 Oi H 43 }>ii 2 68 1 2i 3 83 1 Gg 4 log 6 ■n n 2 7 1 2.1 3 8.H 1 6:{ 4 105 1 UJ 6 Oft DIAMETERS AND CIRCUMFERENCES OF CIRCLES. 17' Diam. Circ. Diam. Circ. Ft. In. m 111 111 112- 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0| 1 1* H 13 1| 1* i| 2| 2| 2| ^1 3| 3| H 3| 07 ,4 4* 4| 4| 45 4# 4 Ft. 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 In. 1 Ft. o In. 1|2 1-1 2J- 25 3 31 33 45 4i 4 6^ 65 61 7^ 85 H 10 10| 101 Hi iif 0^ 0| II 2 23 23 3J 3^ H 43, 5i2 5^ •■;3 55 n;5 2 6 6f 65 u 73 's 75 7-5- 2 8 8* Si 8| 85 8^ 83 8J 9 9f 9i • 9 9^ 9* 9| QZ ^8 10 5|2 6^12 lOi lOi- Ft. 7 7 7 7 7 7 7 7 7 7 7 7 7 7 S 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 m. 6 75 9 9^ lOi 11' 111 lis Oi ol 0| 4 1-! 2J' 25 2| 3i 3| 4* 45 4^ 5i •^8 6 6h u n Diam. Circ. . In. lOf m 10| 103 10| 2 11' 8| 83 9i 91 10 10| 103 lU 115 Hi 11a 115 11^ 113 11^ 0^ 0^ Oi Of Oi of 01 H 1 li If 15 If 13 11 2' Ft. 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 In. 11^ 8 0^ 03 n H 9 2il0 2|10 2510 2f 10 23 10 2^10 10 3*10 3il0 3|10 3510 3*10 3310 3x10 1^ ^8 2i ^8 3 35 3f 4i ^8 51 6| '8 n 9 9| 9: lOi 105 10| 11^ 113 Oi Oi 1 Diam. Circ. 2i 2I 3? 3t 4 4.^ H In.^Ft. 4 10 4*10 4il0 43 ^8 45 4^ ^8 43 42. 5° 10 10 10 10 10 10 In 5f 6| 63 7-^ I* 8^ 84 5*10 5il0 5|10 5|10 5310 5*10 6 10 6* 6i ^*, 6511 6f 1 631 6*1 7'il T*l 73 ] 8 , 751 7|1 731 7*1 8 11 8*1 8|l 85 1 8|1 84:1 8|;i 8*;i 9 1 9*;i 9il 9|1 9i ^8 95 ^8 10| 103 11* 115 lU "5 0^ li 15 12- 2 ^3. H 4| 5 ^r 5i 4 65 7 7a '8 n 8* 8| 9i 10* 105 Diam. Ft. In. 3 9.^ 9^ circ. 3 93 3 91 3 10 3 101 lOi 3 lOf 3 lOA 3 lOf 3 103 3 101 3 11' 3 Hi 3 llf 3 115 3 114 3 11* Ft In. 11 1U| 11 Hi 11 uj 12 12 oi 4 12 4 12 4t 12 43 12 5A 12 55 12 6 12 64 12 61 01 12 7i Of 05 12 12 12 ■7-1 71 si It 1^^ ^8 15 I ^8 2 2* 2i 2| 25 95 --s 23 97 12 83 12 91 12 95 12 91 12 lOi 12 10| 12 11 12 lU 12 11| 13 Oi 13 0| 13 1^ 13 li 13 1* 13 2| 13 2| 13 3 13 3| 13 3| 15* 174 DIAMETERS AND CIRCUMFERENCES OF CIRCLES. Diam.j C re. Diam. Circ. Diam. Circ. Diam. C re. D am. Circ. Ft. IiiJpt. In. Ft. In. Ft. III. Ft in. Ft. In. Ft. In. Ft. In. Ft ■ In.iFt. In. 4 3il3 4* 4 85 14 lOi ■5 2il6 3A .> H 17 yi 6 1|,19 24 4 3^13 5 4 8f 14 m 5 2116 3i 5 8 17 H 6 1419 21 4 3|13 5| 4 9 14 11 5 U 16 M 6 1119 3i 4 3i^l3 H 5 2f 16 H 5 S^ 17 10 6 if 19 3f 19 4 4 3|13 4 9^ 14 "1 5 25 16 5^ 5 81 17 1C| 6 1| 4 3^ 13 4 94 14 114 5 ^ 16 H 5 8|17 10^ 6 2^ 19 4| 4 3113 H 4 9| 15 Oi 5 3 16 ^ 5 8il7 lU 4 4 13 H 4 9| 15 Of 5 S% 17 IH 6 2i 19 43 4 9| 15 1 5 3^ 16 6i 5 s^ln 111 o| 6 24 19 54 4 4113 4 4il3 75 4 9:1 15 If 5 34 16 H 5 8118 6 2|19 o§ 24!l9 6 ^8 4 91 15 n 5 3| 16 7 5 9 IS n 6 4 4|13 ^J 4 10 15 H 5 3i 16 8^, 6 2f|19 63 4 4| 20 3 4 7.1 14 5 OJ 15 111 ll| 5 Gi 17 ■il 6 18 10j^6 H 20 3| 4 7114 H 5 1 15 5 6.J 17 54 6 5& 20 35 4 7i 14 6.i 5 6| 17 6 0^ 18 10.i6 53 20 4\ 4 n 14 6.=i 5 1* 16 5 6i 17 n 6 01 18 10i;6 5J20 4f 4 73 14 7i 7A 5 M 16 21 5 6J 17 6 6 o;;- 18 Hi 6 6 ,20 5 4 7114 5 i;; 16 5 7 17 n 6 OA 18 Hi 4 8 14 ^1 5 l.x 16 1^ 6 0|l9 »i 6 6' 20 51 5 ]": lii li 5 7^ 17 6h^ 6 03 19 Oi 6 6\ 20 5| 4 8^ 14 8i 5 1?, 16 IJ 5 7{ 17 7.1 6 0119 016 fiil 20 fii 4 84 14 ^a 5 11 16 2.? 5 7;;- 17 'g 6 1 19 l.ifi 6^ 20 65 4 8| 11 9 5 2 16 5 ll 17 8 |6 1^20 7 4 8^ 14 9i 5 T'i 17 si 6 1^ 19 2 16 63 20 73 4 k|i4 '4 .5 2|16 3| 5 7.1 17 6 14 19 H 20 73 DIAMETERS AND CIRCUMFERENCES OF CIRCLES. 175 Diaia. 176 DIAMETEKS AND CIRCUMFEHENCES OF CIRCLES. Diam.l Circ. Dia. \ Circ. Diam. Circ DIAMETERS AND CIRCUMFERENCES OF CIRCLES. 177 Diaxn. Circum. Diani. Circum. I Diam. Ft Ivi. 11 2| 11 2i 11 3 11 11 11 11 11 11 11 11 3^ ^8 3d H 34 ^8 Ft. 35 35 35 35 35 35 35 3f 35 " 35 35 35 11 41 11 H 11 4| 11 H 11 4| 11 4i 11 u 11 5 11 11 11 11 11 5^ 4 5| In. n 6 U 35 7| 35 8 35 35 35 35 9h 35 10 35 10| H 35 35 35 35 36 10| lU llj 'J* 111. I Ft. In. 5i 36 0| Sff 26 1| 6 36 Ij^ 11 11 7| 8' 36 6^ 74 Ft. In. 11 8| 11 8| 11 9 11 91 11 9i 11 9| 11 9i U 9| 11 95 11 9| 11 10 11 101 11 10^ 11 10| II lOA 11 lOf 11 lOSi 11 101 11 11 11 11 11 11 11 1% Hi 11^ ^^8 114 iif circum. I Diam. Circum Ft. In. 36 10| 36 10.^ 36 101 36 111 36 Hi 37 01 37 37 37 37 37 li n 37 2i 37 21 37 4 37 37 37 4| 37 4| 37 5i 37 37 37 37 37 5^ 6 61 71 '8 Ft. In. Ft. Ill 11 11.^ 37 7h 11 111 37 7| 12 37 61 12 0^ 37 8| 12 0^ 37 91 12 0|| 37 9| 12 oil 37 91 12 Of 12 Oi 12 01 12 l' 12 11 12 H 12 If 12 14 12 If 12 li 11 12 12 12 12 12 12 12 2^ P 24 21 37 10:^ 37 10| 37 111 37 114 37 115 38 Oi 38 0| 38 1 38 If 38 l| 38 2i 38 2| o ■~± o 2 = - o_ If a Hoop of larger diameter than 12 feet is required, double some number. Observations on Tables relating to the Diameters and Circumferences of Circles. I do not intend to enter into any labored argument to prove the general utility of these Tables, as their simplicity and clearness are sufficient to stamp their value to the artist and mechanic. It will be clearly perceived, on inspection, that the Table commences with as small a diameter as is gen- erally used in hoops and rings, viz. one inch, and increases by the regular gradation of one-eighth of an inch, to upwards of twelve feet; and in the column marked Circumference, against each Diameter stand the respective circumferences : hence all that is necessary on inspecting these Tables is to enter into them with any proposed diameter or circumference, and an answer to the inquiry is immediately obtained. Example. — Required the circumference of a circle, the diameter being 8 feet 7 7-8 inches ? In the column of circumferences, opposite the given diameter, stands 27 feet 2:^ inches, the circumference required. But it will be necessary to observe, that in the formation of hoops tind rings a contraction of the metal takes place. Now, the just allowance for this contraction is the exact thickness of the metal, which must be added to ihe diameter. Ex. — In making a hoop whose diameter inside is 6 feet 9 1-8 inches, the thickness of the iron being 4 inch, this 4 inch must be added to the given diameter, which will make it 6 feet 9 5-8 inches} this will allow 1 5-8 inch 178 DIAMETERS AND CIRCUMFERENCES OF CIRCLES. for the contraction in bending in a hoo^ of the above diameter, pivinff the circumference or length of iron required for the hoop, 21 feet 4 3-8 iiicnes. The foregoing example appertains to the formation of hoops or iron bent on the flat; but in the formation of rings or iron bent on the edge, the same rule must also be followed, only taking care to add the brtadlh instead of the thickness. As for example : To make a ring whose inside diameter is 8 feet 2.] inches, the breadth of the iron being 2^ inches ; by adding the 2!^ inches to the given diameter, will increase it to 8 feet 4| inches ; opposite to this diameter in the column of circumferences stands 26 feel 4^ inches, being the length of iron necessary for the ring. The foregoing observations relate more particularly to plain hoops and rings ; but as respects the hoops that are on the wheels of radway carriages, a difference must be observed, which is as follows : These hoops having a flange projecting on the one edge of the surface, it will be necessary, in addition to the thickness of the metal, to add two-thirds of the thickness of tlie flange to the diameter, as the flange side would contract considerably more than the plain surface ; this is supposing the tires are in a straight form, but, in general, they come from the iron-works in a curved state. In the latter case, it will be only necessary to add the thickness of the bare metal, as the aforesaid portion of the thickness of the flange is allowed for in the curve. It has been found that the curve may be exactly obtained, by using four times the circumference of the hoop as a radius. If the tire has not been previously curved, it may easily be done in the operation of bending ; the smith must pay particular attention to this, or he will have his hoop bent in an angle. But the practical utility of this Table is not confined to smiths alone ; to the millwright it will be found equally useful and expeditious, as on a bare inspection of the Table he may ascertain the diameter of any wheel thaJ may be required to be made, the pitch and number o( teeth being given. Ex. — Suppose a wheel were ordered to be made to contain sixty teeth, the pitch of the teeth to be 3 7-8 inches, the dimensions of the wheel may be ascertained simply as follows; Multiply the pilch of the tooth by the number of teeth the wheel is to contain, and the product will be the circumference of the wheel ; thus 3^ inches pilch of the tooth, 10 X 6 = 60 the number of teeth, Feet 19 4J the circumference of the wheel. However, by inspecting the column marked Circumference, I find the nearest number to this is 19 feet 4 .3-8 inches, which is the cighlli of an inch less than the true circumference ; but if this 1-8 were divided into (JO equal pirls, it would not make the difference of a single hair's-brcadln in the size of each tooth ; so that it is sufficiently near for any practical purpose. The diameter answering to this circumference is 6 feet 2 inches ; consequently, wilh onc-h;ilf of this number as a radius, the circumference of the wheel will be described. The manner in which the foregoing Table of Circumferences is found is as follows : Taking the diameter at unity, we have by decimal proportion in. in. Asl :31HG :: 1- :3141G, and the decimal 1 HG multiplied by 8, gives the circumference for 1 inch of diaincler 3 1-8 inches. In these 'Jables tiie number S-HIG is divided by 8, which gives .3927 Tb:H decimal [iroportion has been used as a constant, and tin- sum niiiltiplicd by 8 gives the excess above the decimal value in cigluiis of an inch CIRCUMFERENCES FOR ANGLED IRON HOOPS. 179 CIRCUMFERENCES FOR ANGLED IRON HOOPS. ANGLE OUTSIDE. Diam. Circ. Diam.l Circ. Diam Cin;. Diam. Circ. Diam. Ciri'. Ft In. Ft. In. Ft. In.lFt. In. Ft. In Ft. In. Fl. In. Ft. in. Ft. In. Ft. In. 6 1 5i 1 6 4 4:1 2 6 7 31 7 4| 3 6 10 3 4 6 113 24 i 1 64 4 51 i i JO- 3| 4'l3 3 h 1 7 4 6^ 4 61 4 7| h 7 5| 7 4 i 10 4i 413 3| 1 1 7| 1 i 1 10 54 |13 4| 4 7 13 5| 413 51 7 1 8i 1 7 2 7 7 6g 3 7 10 6 i 1 H i 4 St 4 91 4 91 4 7 U 4 10 65 h 1 9| h i 7 84 4 10 74 413 6| 1 I io| 1 * 7 9 1 10 84 3,13 7| 8 : 1 HI 1 8 4 10| 4 n| 2 8 7 9| 3 8 10 8| 10 9| 4 8 13 8i i 2 Oi i i 7 lOi k 4 13 81 h 2 Oi h 5 h 7 114 h 10 10| 10 ll| 10 ll| H of 11 l| 4 13 9| 2 l| i 5 0.^ 1 8 I 1 13 104 9 i 2 2| 1 9 5 1^ 2 9 8 0| 3 9 4 9 13 11 • 2 3 4 5 24 4 8 1| 4 k 13 111 % 2 3| i 5 3 d 8 ■ 2| ^ 4 14 o4 I 2 .4i 3 5 3| 1 8 21 1 11 2' I 14 U 10 2 5i 1 10 5 4f 5 5! 5 5| 5 6| 5 81 2 10 8 3| 3 10 11 25 4 10 14 2 k 2 6 i 4 8 4 8 5i 8 si 4 11 34 4 14 2l h 2 65 1 1 <^ 11 44 4 14 3i 2 7.i 1 1 11 5 1 14 4t' 11 2 Si 2 8| I n 2 11 8 6i 3 ll'* 11 55 4 11 14 4f 1 i i 8 74 4 11 64 4 14 5{ 14 6 ^ 2 9| h 5 81 5 9| k 8 8 i 11 7J 4 1 2 lOl 2 ll| % 1 8 81 11 71 11 s| 14 7; I 2 5 104 3 8 94 4 5 14 7 k 2 lU 3 of 3 l| i 5 Jl 4 8 104 4 11 9f 11 101 11 101 i 14 S 1 5 111 6 Oi 1 8 11 8 Ilf 9 of 9 ll 9 11 1 4 I 14 9] 14 10 1 1 3 2 2 1* 6 U 3 1 4 1 11 ll| 5 1 14 ]0| ^ 3 2| ^ 6 2 4 4 12 04 4 14 114 ^ 3 3i i 6 2| 1 4 12 1 4 15 04 % 3 44 1 6 3| 1 9 2| 5 12 1| 1 15 1 1 2 3 5 2 2 6 4J 3 2 9 3| 4 2 12 24 5 2 15 If 15 2| i 3 55 i 6 41 i 9 41 4 12 34 4 h 3 6^ i 6 5| 1 9 4| ^ 12 4 4 15 %■ % 3 n 3 7| 1 6 6| 9 5J 1 12 45 15 3, 15 4^ 15 5; 1 3 2 3 6 74 3 3" 9 64 4 3 12 54 5 3 i 3 8|| ^ 6 11 i 9 7 1 12 6| 4 / 3 9| 3 loj 1 6 8| h 9 1% i 12 6J 4 15 Gy 1 1 6 94 I 9 8i i 12 71 1 15 6^ 1 4 3 101 2 4 6 10 3 4 9 94 4 4 12 8| 3 4 15 7; 1 3 111 ^ 6 ]0| ;. 9 91 k 12 9! 4 15 S i 4 04 •i 6 11^ 1 ; 9 ]0| h 12 91 4 15 9 1 4 1 I 7 04 1 9 ll| I 12 lo| 1 15 9% 1 5 4 IS 2 5 7 1 3 5 10 o| 10 01 4 5 12 114 5 5 1 15 104 ^ 4 2i 1 7 11 i 4 13 415 114 1 4 34 d 7 2^ iio 1| ^ 13 0| 4I16 1 4 4 I 7 3| §10 2| 113 HI |ll6 Of 180 CIKCUMFERENCES FOR ANGLED IRON HOOPS. CIRCUxMFERENCES FOR ANGLED IRON HOOPS. ANGLE INSIDE. Diam . Circ. Diam.j Circ. Diam Circ. Diam . Circ. Diam. Circ. Fi. in . Ft. In Ft. In. Ft. In . Ft. in Ft. In Ft. In Ft. In . Ft. In. Ft. In. 6 1 S.J 1 6 5 1| 2 6 8 6^ 3 6 11 111 4 6 15 4| J \ 1 n - i 5 2.3 i 8 7A i 12 Oj 415 5| i 1 10; \ i ^ 5 3^ h 8 8| i 12 1.3 i 15 7, i E 1 H ■ i E 5 4j I 8 9J 12 2| 7 I Hi 1 7 5 5 2 7 8 104 3 7' 12 3; 4 7 15 8; i E 2 05 ; I 5 53 4 8 U 4 12 4 415 9j t 2 1| > ■ 5 q\ A 8 \n d 12 4^ A 15 10 .1 2 2^ i 5 7i 1 9 0| 2 8 9 l.i 3 12 5| 3il5 101 8 2 3| 1 8 5 8^ 3 8 12 6| 4 8 15 ll| i 2 44 i 5 9J i 9 2| 4 12 7i 4 16 o| h 2 5 h 5 lOi i 9 34 d 12 8| dl6 l| 1 2 52 1 5 11 1 9 4i 3 12 94 3!l6 2i 9 2 el 1 9 5 11^ 2 9 9 5 3 9 12 10 4 9 16 3A 16 4" i 2 7| i 6 0^ f 9 51 4 12 lOi 12 ll| h 2 8i d 6 l| h 9 6j; •i 16 41 1 2 9| 2 lol a 4 6 21 ^ 9 ll ^1 13 Of 13 n 3il6 5| 10 1 10 6 34 2 10 9 8| 3 10 4 10 16 6| 16 7| k 2 11 i 6 4J 4 9 94 4 13 2| 4 h 2 1]| 3 0| il 6 5 i 9 lOi A 13 34 dll6 8i i I 6 5Z .? 9 11 5 13 4 1 16 9A 11 3 n 1 11 6 6.1 2 11 9 111 3 11 13 4| 4 11 16 10 ^ 3 2| 4 6 7g 410 o| 4 13 5| 4 16 lOJ jl 3 3g i 6 83 6 9| d'lO Id i 13 6f A 16 113 1 3 4i 5 ^ 10 25^- .^ 13 U 1 17 0| I 3 5 2 6 lOJ 3 10 34 4 13 8| 13 94 5 17 lA ^ 8 51 4 6 11 4 10 4a 4 4 17 2^ 1^ 3 61 d 6 in A'lO 5 d 13 10 1 d 17 3| 17 4" ? 3 71 4 7 0| 310 5| I 13 lOi 1 L 1 3 8^ 2 1 7 Jg 3 1 10 6| 4 1 13 115 5 1 17 Ax i 3 9| i 7 22 410 7^ 4 14 of 417 5| d 3 lol t 7 3| ijio ^ %\\0 9^ dli4 Id dl7 6| % 3 11 •^ 7 4 il4 2| 1 17 7T 2 3 115 2 2 7 5^ 3 2 10 10^ 4 2 14 3| 5 2 17 84 4 4 03 4 7 55 410 11 4 14 4 4 17 sf 17 10^ d 4 IS h 7 6g i'lO 11.? ^1-4 4| d 1 4 2i I 7 7i \n o| i 14 53 i 17 lOj 17 ui 3 4 3| 2 3 7 8g 3 3 11 l| 4 3 14 65 5 3 ^ 4 4J 4 7 9-} 411 n 414 7a dl4 8| i'l4 9^ 4 18 Oi A 4 5 h 7 10^ ill 34 d 18 l| 1 4 5J A 7 ir ■111 H 3 18 24 4 •1 i\i I 4 7 ii-i 3 4 11 5 4 4 ] 4 10 5 4 18 3i 4 4 7S ;} 8 0.3 411 53 ; 1 4 102 4 11.^ 4 18 4' |!18 4| 4 8i ^ 8 li ilil H . ] 1 4 9g •1 8 2* in n i 15 Oft i 18 6: 6 4 K'^ } 5 8 A 3 5 11 81 - 1 5 |15 Id 5 5 18 6. :} 4 11 4 8 4| 411 94 415 24 418 7 i 4 Ul A 8 5 iiii loA d 15 H 4 18 8 3 5 0§ 1 8 bl 3I11 102 il5 4 III8 9, CIRCUMFERENCES FOR ANGLED IRON HOOPS, 181 Observations on Table containing the Circumferences foi Angled Iron Hoops. — Angle Outside. As this Table will be useful to those smiths who chiefly work angled iron, it will be necessary to remark, that the observation made on Tables relatinst to the Diameters and Circumferences of Circles, respecting addmg the thickness of the iron to the diameter, must be attended to in this, with this difference, — the breadth of the angle must be added to the diameter. Example. — Suppose a hoop is wanted to be made of 2^ inch angled iron, whose diameter inside must be 12 inches. Here the 2^ inches must be add- ed to the 12 inches, which raises the number to 1 foot 2^ inches. I-ooking into the Table, I find the circumference, or length of iron requisite for the hoop, is 3 feet 6:^ mches. Observations on Table containing the Circumferences for Angled Iron Hoops. — Angle Inside. The observations respecting this Table are the reverse to those on the preceding one, — viz. the breadth of the angle must be taken from the diam- eter, — for tl>is reason, that the diameter is taken from outside to outside of the ring. Suppose a ring is to be made of angled iron, whose diameter outside is to be 12 inches, the breadth of the angle 2^ inches; then, by talking 2^ inches from 12 inches, we have left 9.i inches. Looking into the Table in the col- amn of diameters, I find in the circumference column, opposite 9^ inches, 2 feet 8J inches, which is the length of iron necessary for the ring. It his been already observed, that between angled and plain iron a con- siderable diflerence exists with regard to the proportion of the circumference to the diameter : this is owing to the angle or flange on one side of the bar, and when the iron is formed into a hoop : it contracts more or less, as the angle or flange may be mside or outside of the hoop. From repeated ex periments on this subject, I have ascertained that the proportions of the diameters to the circumferences are as follows : — For the angle inside as 1 : 3-4243, and for the angle outside the hoop, as 1 : 2-9312 : : Diam : Circ'f. Problem — ^To find the circumference of an ellipse, or an oval hoop or ring. Rule. — Add the length of the two axes together, and multiply the sum by 1-5708 for the circumference; or as it may be used in the Table of Circum- ferences, take half the sum of the axes as a diameter, with the breadih ot the iron added, and enter the Table of Circumferences where it will be found. Ex. — Required the circumference of an elliptical hoop, whose axes are 18^ and 13 inches, the thickness of the iron being 2^ inches. ISi -f 13 = 31i -^ 2 = 153 -f 21 = 18i inches the diameter. Entering into the Table of Diameter with 18| inches, the circumference will be found to be 4 feet 9j- inches. In constructing elliptical hoops of angled iron, with the angle outside, reference must be made to the Tables for hoops of angled iron ; the opera- tion will be similar to the above example. Bui in hoops where the angle is inside, the thickness of the iron must be taken from halt the sum of the axes. Note. — It must be observed, that in the examples given in the Observa- tions on Table relating to the Diameters and Circumferences of Circles, and also on hoops formed of angled iron, that those circumferences are nothing more than the ends of the iron meeting together; therefore, ever}- smith must allow for the thickening of the ends of the metal previous to scarving the same in order to weld it IG 182 SHIP AND RAILROAD SPIKES, AND HORSE SHOE&- SHIP AND PvAILHOAD SPIKES. NUMBER OF IRON SPIKES PER 100 POUNDS. Manufactured by Philip C. Page, Mass., and Sold by Page, Briggs & Babbitt, Boston. Ship Spikes or Hatch Nails 1-4 in. sq're. Ship SpikeS or Hatcli Nails 5-lG in. sq. Ship Spikes or Deck Nails 3-8 in. sq're. Ship Spikes 7-16 inch square. Ship Spikes 1-2 inch square. Ship Spikes 9-lG inch square. Ship Spikes 5-8 inch square. size Nil. size No. 1 ,sizei No. 1 size No. 1 size No. size No. size] No. in 1 in 10 in |1 in 10 0, in 1 in 10 in 1 inc lbs. inc. lbs. j inc. lbs. inc. lbs. inc. lbs. inc. 8 lbs. inc. lbs. 3 jl900 3 1000 4 540 5 340 !6 220 140 1 10 80 3^1.580 3.i 960 1 4k 500 5i 310 6.i 200 9 120 15 60 4 [1320 4 800, 5 460 6 300 7 190 10 110 — — 4i 1220 U 600 5i 420 6* 280 n 180 11 100 — — 5 1020 5 680 6 400 7 260 8 170 — . — — — 6 520 i 6h 320 1 u 240 Sh. 160 1 — — [ ._ — — — — — — 8 J 220 9 150 — — 1 1 — — — — — — i — , — 10 140 — — — ■ Mail Road Spikes 9-16lhs square 5.^ inches 160 per 100 pounds. Rail Road Spikes 1-2 inch " 5.^ " 200 per 100 pound.s. BURDENS PATENT SPIKES AND HORSE SHOES. Manufactured at the Troy Iron and Nail Factory, Troy, New York. Boat Spikes. Size in No. in inches. K)0 11)s. 3 1750 84 1468 4 1257 44 920 5 720 H 630 6 497 64 47S 7 S62 n 337 8 295 84 290 9 210 10 198 COPPERS, TUBING, CAST IRON AND STEEL. 183 COTFEB.S. —Dimensio7is and TT'ci ghlfrom 1 to 208 Gallons. Indies Weight Inches ■Weight Inches Weight lag Gallons. m lag Gallons. in hie Gallons. in to brim. pounds. ito brim. pounds. to brim. pounds. 9\ 1 14 24 15 224 294 29 434 Ui 2 3 24* 16 24 30 30 45 14 3 44 25 17 254 32 36 54 15i 4 6 254 IS 27 34 43 644 16i 5 74 26 19 28h 35 48 72 174 6 9 26.^ 20 30 36 53 794 m 7 104 26| 21 314 37 58 87 19h S 12 27 22 33 38 63 944 20| 9 134 27i 23 34.1 39 67 1004 21 10 15 274 24 36 40 71 1064 214 11 164 27$ 25 374 45 104 1.56 22 12 18 28 26 39 50 146 219 224 13 194 2S4 27 404 55 208 312 234 14 21 29 28 42 COPPER TUBING. — Weight of the usual Thicliness. When the inside diameter, is | of an inch, 3 ozs. ; f do., 5 ozs. \ ^io 6 ozs. ; I do., 8 ozs. ; % do., 10 ozs. per foot. BRASS, COPPER, STEEL AND LEAD.— Weight of a Foot. BRASS. COPPER. STEEL. LEAD. Diam'ter Weight Weight Weight Weight ,' Weight Weight Weight Weight and Side of of of of of of of of of Sq're. Round. Square. Round. Square. j Round. Square. Hound. Square. Inches. Lbs. Lbs. j Lbs. Lb3. Lbs. Lbs. Lbs. Lbs. ^ .17 .22 .19 .24 .17 .21 I ..39 .50 .42 .54 ' .38 .48 X .70 .90 .75 .96 .67 .85 . 1.10 1.40 1.17 1.50 1.04 1.33 ' ■ 1.59 2.02 1.69 2.16 1..50 1.91 I 2.16 2.75 2.31 2 94 2.05 2.61 1 2.83 3.60 3.02 3.84 2.67 3.40 3.87 4.93 u 3.58 4.56 3.82 4.86 3.38 4.34 4.90 6.25 n 4.42 5.63 4.71 6. 4.18 5.32 6.06 7.71 n 5.35 6.81 : 5.71 7.27 5.06 6.44 7.33 9 33 14 6.36 8.10 6.79 8.65 6.02 7.67 8.72 11.11 1^ 7.47 9.51 7.94 10.15 , 7.07 9. 10.24 13.04 n 8.66 11.03 ; 9.21 11.77 8.20 10.14 11 87 15.12 n 9.95 12.66 i 10.61 13.52 9.41 11.98 13.63 17.36 2 11.32 14.41 12.08 15.38 ; 10.71 13.63 15.51 19.75 2J 12.78 16.27 13.64 17.36 12.05 15.80 17.51 22.29 H 14.32 18.24 15.29 19.47 13.51 17.20, 19.63 25. 21 15.96 20.32 17.03 21.69 15 05 19.17 21.80 27.80 24 17.68 22.53 ; 18.87 24.03 16.68 21.21 24.24 30.86 2| 19.50 24.83 20.81 26.50 18.39 23.41 26.72 34.02 21 21.40 27.25 22.84 29.08 20.18 25.70 29..33 37.34 n 23.39 29.78 24.92 31.79 22.06 28.10 32.05 40.81 8 25.47 32.43 i 27.1S ' 34.61 24.23 30.60 34.90 44.44 184 WEIGHT OF CAST IRON & lEON AND BRASS BALLS. CAST IRON. Weight of a Foot in Length of Flat Cast Jrcn. Width Thick, Thick, Thick, Thick, Thick, Thick, Thick, Of Iron. nth inch. 3-Sths inch Pounds. 1-2 inch. S-Sths inch. Pounds. 3-4ths inch. 7-8ths incli. Pounds. 1 incli. Inches. Pounds. Pounds. Pounds, Pounds. 2 1-.56 2-34 312 3-90 4-68 5-46 6-25 2i 1-75 2-63 3-51 4-39 5-27 615 7-03 2* 1-95 2-92 3-90 4-S8 5-85 6-83 7-81 21 214 322 4-29 5-37 6-44 7-51 8-59 3 2-34 351 4-68 5-85 7-03 8-20 9-37 3i 2-53 3-80 5-07 6-34 7-61 8-88 10-15 3* 2-73 4-10 5-46 683 8-20 9-57 10-93 35 293 4-39 585 732 S-7S 10-25 11-71 4 312 4-68 6-25 7-81 9-37 10-£>3 12-50 4| 3-32 4-97 6-64 S-30 9-96 11-62 13:28 4h 3-51 5 27 7-03 8-78 10 54 12-30 14-06 4^ 371 5-56 7-42 9-27 11-13 12-98 1484 £ 3-90 5-86 7-81 9-76 11 71 13-67 15-62 5;J 410 615 8-20 10-25 12-30 14-35 16-40 - 5.^ 4-29 6-44 8-59 10-74 12-89 1503 17-18 S.'v 4-49 673 8-98 11-23 13-46 15-72 17-96 6 4-68 703 9-37 11-71 1406 16-40 1875 CAST IKON. Weight of a Superficial Foot from \ to 1 inches thicK. Size. Weight. Pounds. Size. AVeight. Poumls. Size. Ins. AVeight. Pounds. Size. ■\Vci?lit. Size 1d<.. Ins. Ins. pounds. Ins. ii 9.37 i 23.1.5 1 37.50 1^ 51.56 1:1 1 14.06 5 28.12 IJ 42.18 1*. 56.25 n h 18.73 I 32.81 l.i 46 87 1| 60.93 2 CAST IRON, COPPER, BRASS, AND LEAD BALLS. Weight of Cast Iron, Copper, Brnss. and Lead Balls, from 1 inch to 12 inches in Diameter. 5 ■S 6^ o. o o 1 '6 el pounds. •214 i 5 Cast Iron. Copper. g a 1 Ins. 1 pounds. •136 pounds. -166 I)oundH. •158 Indies. 7 pounds. 46-76 pounds. 57- 1 pounds. 54-5 pounds. 73-7 u •46 •562 •537 •727 n 57-52 70-0 67 11 900 2 1-09 1-3 1-25 1-7 8 69-81 85-2 81-4 110-1 2* 213 2-60 2-50 3-35 8^ 83-73 102-3 1000 1 .'52-3 3 3-68 45 43 5-8 9 P9.4 121-3 1159 156-7 3* 5-84 7-14 6-82 923 H 116-9 1430 1.36-4 ISl 7 4 8-72 10-7 10-2 13-8 10 l.'56-35 166-4 1590 21.50 4* 12 42 15-25 14-5 19-6 10.^ 1.57-84 193-0 184 250-0 5 1704 20-8 19-9 26-9 11 181-48 221 8 211-8 2S6-7 H 22-68 27-74 26-47 36-0 m 207-37 233-5 242-0 327-7 6 29-45 35-9 34-3 46-4 12 235-62 288-1 275-0 372-3 eh 37-44 4576 43-67 6913 WEIGHT OF ROUND AND SQUAEE CAST IRON. 185 CAST IRON. — Weight of a Foot in L mgth of Sq uare and Round. SQUARE. ROUND. Size. Weight. „ Size. Weight. Size. Weiglit. 1 Size. Weight Inches Square Poundj. Inches Square. Pounds. Inches Diam. Pounds. * Inches Diam. Pounds. d •78 45 74-26 4 •61 1 45 58-32 1 1-22 5 78-12 1 -95 5 61-35 i 1-75 5^ 82-08 i 1-38 5i 64-46 I 2-39 H 86-13 I 187 H 67-64 I 312 H 90-28 1 2-45 5| 7009 n 3-95 5h 94-53 n 3 10 54 74-24 H 4-8S H 98-87 u 3 83 5ft 77-65 If 5-90 51 103-32 If 4-64 5| 81-14 n 7-03 55 107-86 14 5-52 ^ 84-71 if 8-25 6 112-50 ii 6-48 6 88-35 11 9-,57 H 12208 11 7-51 H 95-87 n 10-98 H 13203 n 8-62 H 103-69 2 1250 64 142.38 2 9-81 6| 111 82 2k 14-11 7 153-12 2i 1108 7 12026 2k 15-81 7.i 164-25 2i 12-42 H 129- 2| 17-62 n 175-78 21 1384 u 138-05 24 19-53 7| 187-68 24 15-33 n 147-41 2| 21-53 8 200- 2| 1691 8 15708 21 23-63 H 212-56 2| 18-56 8| 167-05 25 25-83 84 225-78 21 20-28 84 177-10 3 28- 1 2 8| 239-25 3 22-08 8| 187-91 Si 30-51 9 2.53 12 3J 23-96 9 198-79 H 33- H 267-38 H 25-92 H 210- 31 35-59 94 282- 31 27-95 94 221-50 H 38-28 n 29707 34 30-06 91 233-31 3| 4106 10 312-50 H 32-25 10 245-43 31 43-94 lOi 328-32 3| 34-51 m 257-86 H 46-92 104 344-53 H 3685 104 270-59 4 50- 10| 361-13 4 39-27 1 10| 283-63 4i 53-14 n 378-12 4J 41 76 11 296-97 4^ 56-44 Hi 395-50 4i 44-27 lU 310-63 ^ 59-81 114 413-28 41 46-97 114 324-59 ^ 63-28 111 431-44 44 49-70 m 3.38-85 4| 66-84 12 450- 4| 52-50 12 35343 4i 70-50 4| 55-37 STEEL. - - Weight of a Foot in Length of Flat. • Size. Thick, 1-4 inch. Thick, 3-Sths. Thick, 1-2 inch. Thick, 1 o-Sths. 1 Size. Thick, 1-4 inch. Thick, 1 Thick, 3-Sths. Il-2ineh. Thick, ."i-Sths. Inches 1 pounds. •852 pounds. 1 27 pounds. 1-70 pounds. 2.13 Inches. 24 pounds. 2-13 pounds. 3-20 pounds. 4-26 . pounds. 5-32 n -958 1-43 1-91 2-39 , m 234 3-51 4-68 5-85 H 1-06 1-59 2 13 2-66 3 2-55 .3 83 5-11 639 n 1 17 1 75 234 2-92 3^ 2-77 4-15 5 53 6-92 n 1 27 1 91 255 3-19 34 2-98 4-47 5-98 7-45 n 1-49 2-23 2^98 3 72 n 319 4-79 6-38 7-98 2 170 2-55 3-40 4-26 4 3-40 5-10 6-80 8-32 2| 191 2-87 3-83 4-79 16-^ 186 PARALLEL AND TAPER ANGLE IKON. WEIGHTS OF ROLLED IRON Per lineal foot, in pounds and decimal parts, of sections of Parallel Angle Taper Angle, Parallel J, Taper J, and Sank Iron and Rails. Table I. — Parallel Axgle Iron, of Equal Sides. f il Lena:ih of sides. Uniform lliickness Weinrht of one A B, in inches. throug'hoLit. lineal foot. in. in. 3 3_ 80 2| 70 2i 8 575 2i 5-16ths 4-5 2 d full 3-75 li k 30 li i 25 ll No. 6 wire guage 1-75 li 8 1-5 1* 9 1 25 1 10 10 1 10 •875 11 •625 4 11 •563 \ 12 ■5 A Table II. — Parallel Angle Irox, of Unequal Sides. L'^h of side L'eth of side Uniform Weight of 1 A in inches. Bin inches. thickness throu-rhoul. lineal loot. in. in. in. 3.i 5 3 975 3 5 1 5^75 3 4 5-l«ths 7-5 2.i 4 5-16ths 675 2.i 4 h 5-75 2 4 k 5-5 2i 3 k 4-75 2 2i i 3-375 1.^ 2 k 2-875 1-i 2 3-16ths 2-23 A , s^^^ B Table III— Tap^r Angle Iron, of Equal Sides L'gih of sides 'I'hickness of Tliickness of Weiprht of 1 A.A, ill inches. edifes at B. root at c. lineal foot. in. in. 171. 4 h i 110 3 h 1 io:n5 2.1 7-16lh9 a-iethit 8-25 2i J h e-5 2.1 5-HiiJis,full 7-l()llis 5 ■> ,i lull .0-16!hi full 3-S7.> H .i 5-l()tli.s 3-25 Ih i bare 5-16lh,ljare 2 625 WEIGHT OF PARALLEL AND TAPER T IRON 187 WEIGHl^ OF PARALLEL AND TAPER T IRON. Table /F. -Parallel J iron, of Unequal Width and Dtpxa Width Total Uniform Uniform Weijrht of ot top depth thickness thickness one lineal table A. B. top table c of rib D. foot. in. in. in. in. 5 6 h h 1.5-75 4i H h 9-16ths 13-25 4 3 3 t 8-875 3i 3 J 825 3i 4 h ^ 12 5 u. 3 i ffuU 7-0 n 2 5-16ths 4-5 2 1-^ 5-16ths 5-16tlis 4-0 11 2 i i 3-125 14 2 k i 2-875 n li i k 2-375 1 H 3-16!hs 3-16ths 1-5 1 1 3-16ths 3-16ths 1 125 l\^'^x^;^-: -|px\-^ X.. ^d Table V. — Parallel J Iro.v, of EquAL Depth and Width. Width of top ta- Uniform Weight of • ble, and total thickness one depth A, A. throughout lineal foot. in. in. 6 h 5 7-16ths 13-75 4 ! g 9-75 34 S-5 3 7-5 24 5-l«ths 4-625 2i 5-16th3 4-5 2 5-16ths 3-75 1| 4 30 14 i 2-25 n i 1-75 1 3-16ths 10 t 1 •725 •625 -A— ^ '/^yy9/> / ^'-A/'///'A Table VI. — Taper T Ikon Width Total Thickness Thickness Uniform | Weight of top depth of top table of top table thicknesof of one table A B. at root c. at edges D. nb E. lin.foot. in. %n. in. in. in. 3 H 4 I 7-16ths 8-0 3 •^ 7-16ths 3 8 4 8-0 2 3 7-16ths 5-16ths 5-16th. 1125 A 10 9-16ths 10 1 1 * h •75 Table VIII — Rails ec^ual top and bottom Tables. -B- Depth A ill inches. in. 5 4i 4i Width across top and Ijottom, BB, in inches. in. 2| 2i Thickness of rib c. Weight of 1 lin. foot. in. \ \ 25-0 2.'J-,3.3 21-66 I^ K - -B / L f L- •u- TaUe IX. — Temporary Rails. Top width a. Rib width B. tn. in. Bed width c. 171. 3 4 4 Total depth D. in. 2 2i .•} 3 Thickness of bed E. Wcig-ht of L lin. foot in. 7-16ths h 90 12 160 173.3 WEIGHT OF FLAT IRON. 189 WEIGHT OF A LINEAL FOOT OF MALLEABLE REC- TANGULAR OR FLAT IRON. From an Eighth of an Inch to Three Inches Thick. T designates the thickness, B. the breadth. T. B. Weig)it. T. 1 B. in. j Weight. T 'TIT Weight. T 1 ^' in. Weight. in. in lbs. ozs. in. lbs. ozs. in lbs. ozs. in Jbs. ozs. * 1 1.6 i 10:] 4 7-3 i 94 7 141 i 8| 10 13-8 o 2-4 11 4 9-0 n 8 1-4 9 11 2.8 1 3-3 Hi 4 10-7 10 8 4-8 H 11 7-8 1 4-1 n-i 4 12-3 loi 8 8-1 94 11 127 i 5-0 m 4 14-0 lOi 8 11-4 95 12 1-7 i 5-8 12 4 15-6 io| 8 14-7 10 12 67 1 6-6 11 11. i 9 2-0 9 5-4 lOi 104 12 11 6 13 0-6 8-3 1 4 i 6-6 H 9-9 8-3 114 9 8-7 103 13 56 i| 11-6 1 100 115 9 12 11 13 10-5 2 13-2 I 11 6 12 9 15-3 Hi 13 15-5 24 14-9 1 u 13-2 114 111 14 J-'i ■^4 2h 1 0-6 1 0-6 Y % • 14-9 14 94 2| 1 2-2 u 1 3-9 I 1 1-3 12 14 14-4 3 1 .^-9 11 2 1 7'> 1 1 3-8 1 8-8 H 1 55 X 1 ad 1 10.5 4 1 1 10-4 H 1 7-2 2i 1 13-8 • 14 1 13-8 H 2 11 31 1 8-9 24 2 1-2 13 2 2-7 14 2 7-7 4 1 105 21 2 4-5 2 2 7-7 i| 2 14-3 4i 1 12-2 3 2 7-8' 2i 2 12-7 2 3 4-9 4h 1 13 8 3i 2 IM 24 3 1-6 2d 3 11-6 44 1 15-5 3h 2 14-4 25 3 6-6 24 4 2-2 5 2 12 31 3 1-8 3 3 11-6 25 4 8.8 5i 2 2-8 4 3 51 3-i 4 0-5 3 4 15-4 5^ 2 4-5 H 3 8-4 34 4 5-5 H 5 61 51 2 61 4h 3 11 7 31 4 10-5 34 5 12-7 6 2 78 4| 3 15-0 4 4 15-4 35 6 3.3 6i 2 9-5 5 4 2-4 44 5 4-4 4 6 9-9 6;^ 2 111 5i 4 5-7 44 5 9-4 4i 7 0-6 61 2 128 54 4 .90 45 5 14-3 44 7 7-2 7 2 14-4 55 4 12-3 5 6 3-3 45 7 13 8 7i 3 1 6 4 15-6 5i 6 8-3 5 8 4-4 7i 3 1-8 6i 5 3-0 54 6 13-2 5i 8 111 7| 3 3-4 64 5 6-3 55 7 2-2 54 9 1-7 • 8 3 51 6l 5 96 6 7 7-2 55 9 8-3 8i 3 6-7 7 5 130 64^ 7 12-2 6 9 149 8i 3 8-4 7i 6 02 64 8 11 H 10 5-6 8;| 3 10 1 74 6 .3-6 65 8 6-1 64 10 12-2 9 3 11-7 7| 6 7-0 7 8 111 65 11 2 8 9.i 3 13-4 8 6 10-2 7.i 9 00 7 11 94 9i 3 150 8i 6 13-5 7.-i 9 50 7ii 12 00 9| 4 7 84 7 0-8 7.5 9 lO-O 74 12 6-7 10 4 2-4 Si 7 4-2 8 9 14-9 75 12 1.3 3 lOJ 4 4-0 j 9 7 7-5 8.1 10 3-9 8 13 39 lOi 4 5-7 1 H 7 10-8 84 10 8-9 H 13 10-5 190 WEIGHT OF FLAT IRON. T. designates tne thickness. B. the breadth. T B. in. Weight. T in B. in. Weight. ' r. B. n. in. Weight. ' r. B. 1. in. Weight. in lbs. ozs. lbs. ozs. i lbs. ozs. i lbs. ozs. i 8^ 14 1-2 1 9k 19 10-6 1 io| 26 11-2 1 2 6 10-0 H 14 7-8 93 20 2.9 11 27 5-1 24 7 7-2 9 14 14 4 10 20 11-2 114 27 151 2i 8 4.4 H 15 50 104 21 3-«t Hi 28 9-0 n 9 1-7 H 15 11-7 m 21 11-7 111 29 30 3 9 14-7 n 16 23 105 22 40 12 29 12-9 34 10 12-2 10 16 8-9 1 1 22 12 3 - 3i Si 11 9-4 12 67 1'-' KM 16 15-5 1 1. 114 23 4-6 l^ 5 11 10^ 17 6-2 Hi 23 128 2 5 12 7 4 13 39 10$ 17 12-8 m 24 51 24 6 8-3 44 14 1-2 11 IS 3-4 12 24 13-4 2i 7 3.9 4i 14 14-4 114 m 18 lOO ? 7 15-5 8 11.1 4| 5 15 11 7 16 89 19 0-7 i| li 3 11-6 m 19 7-3 IJ 4 5-5 34 9 6-7 54 17 6-2 12 19 13-9 2 24 4 15-4 5 9-4 10 2.2 10 13-8 5i 53 18 3-4 19 0-7 '— 1 H 2 9-4 2i 6 3-3 4 11 9-4 6 19 139 u 3 1-6 21 6 13 2 H 12 5-0 64 20 11-2 n 3 9-9 3 7 7-2 4 13 0-6 6i 21 84 2 4 22 34 8 11 n 13 12-2 6i 22 5.7 24 4 10-5 3i 8 111 5 14 78 7 23 2-9 2* 5 2-8 35 9 50 H 15 3-4 74 24 0-2 2i 5 110 4 9 14-9 4 15 150 7i 24 13-4 3 6 3.3 44 10 8-9 4 16 10-6 n 25 10-6 34 6 11 6 4i 11 2-8 6 17 62 8 26 7-9 Si 7 3-9 4| 11 12-7 64 18 1-8 84 27 51 n 7 122 5 12 6 7 4 18 13 4 8i 28 2-4 4 8 4-4 54 13 0-6 H 19 8-9 Si 28 156 44 8 12.7 5i 13 10-6 7 20 4-5 9 29 12-9 4i 9 50 51 14 4-5 74 21 01 9.1 30 101 4^ 9 13-3 6 14*14-4 7i 21 11.7 9i 31 7-4 5 10 5-6 64 15 S-4 7| 22 7-3 9:i 32 4-6 54 10 13-8 6i 16 2-3 8 23 2.9 10 33 1-9 5ii 11 61 63, 16 12-2 84 23 14-5 104 33 151 5ii 11 14 4 7 17 62 4 24 101 lOi :J4 12 4 6 12 6-7 74 18 01 H 25 57 105 35 9.6 64 12 150 7i! 18 10-0 9 26 1-3 11 36 69 6i 13 7-2 n 19 40 94 26 12 9 H.1 37 4-1 6.^ 13 15-5 8 19 13-9 9A 27 8.5 Hi 38 1-4 7 14 7-8 84 •20 7-8 H 28 4-0 11:1 3S 14-6 74 15 0.1 8i; 21 1-8 10 28 15-6 12 39 119 7i 7-4 15 8-4 8;{ 9 21 11-7 22 5.7 lot 29 11-2 - 30 6-8 1 i 16 0-6 '" 1 lOi ^ 2.i 8 6-1 8 16 8-9 94 22 15 6 lof 31 2-4 2i 9 50 84 17 12 9i 23 9-5 11 81 140 2.1 10 3 9 8.i 17 9-5 9:1 24 3.5 ll.{ 32 9-6 3 1 1 2-8 «ii 18 18 10 24 13-4 Hi 33 5-2 31 12 1-7 9 1 18 10.0 10.1 25 7-3 11=1 31 0-8 H 13 0-6 ».ll 19 2 3 lOi 26 1-3 1 12 34 12.4 35 13 15-5 WEIGHT OF FLAT IRON. 191 T. designates the thickness, B. tlie breadth. T. B. in. AV eight. T. in. B. j in. Weight. T. in B. in. w eight. . T. ' B. in. AV eight. in. lbs. ozs. lbs. ozs. 'lbs. ozs. in. lbs. • ozs. H 4 14 14-4 H 6i 25 140 If 83 39 13-5 u Hi 57 21 4i 15 13-3 6h 28 14-5 9 40 15-7 113 58 5.9 4i 16 122 d'i 27 151 H 42 20 12 59 98 43 5 17 111 7 28 15-6 93 43 4-2 ■ Ig 100 7i 30 0-2 44 6-4 H H 17 7-8 5i 19 8-9 u 31 0-8 10 45 8-6 H IS 13-4 H 20 7-8 n 32 13 101 46 10-8 33 20 29 53 21 6-8 8 33 1-9 lOi 47 130 4 21 8-4 6 22 5-7 H 34 2-4 103 48 15-2 4i 22 13-9 H 23 4-6 H 35 30 11 50 1-5 4h 24 3 5 eh 24 3-5 83 36 3-6 1I5 51 3-7 43 25 90 6| 25 2-4 9 37 41 Hi 52 59 5 26 145 7 26 13 H 38 4-7 113 53 81 H 28 40 7i 27 0-2 H 39 5-2 12 54 10-3 4 29 9-6 27 151 93 10 40 5-8 53 30 151 4-6 28 140 41 6-4 li 3 14 14.4 "•1 6 32 8 29 12-9 10| 42 6-9 H 16 2-3 H 33 10-2 H 30 11-8 m 43 7-5 H 17 6-2 6i 34 15-7 H 31 10-7 103 44 8-0 3| 18 lO'O 63 36 5-2 8| 32 9-6 11 45 8-6 4 19 139 7 37 10-7 9 33 8-5 114 46 9-2 4| 21 1.8 n 39 0-3 H 34 7-4 lu 47 9-7 4i 22 5-7 u 40 5-8 H 35 6-3 113 48 103 43 23 95 n 41 113 n 36 5-2 12 49 10-8 5 24 13.4 8 43 0-9 10 •^7 41 30 54 5i 26 27 1-3 51 8i dS 6-4 11-9 m O 1 38 n 23 12 8-3 °4 8i 45 lol S9 1-9 3 13 10-6 53 28 90 S3 47 14 10| 40 0-8 H 14 12-8 6 29 12-9 9 48 70 11 40 15-7 H 15 15-0 H 31 0-8 H 49 12-5 Hi 41 14-6 33 17 1-2 H 32 4-6 H 51 20 Hi 42 13-5 4 18 34 63 33 8-5 93 52 7-6 113 43 12-4 H 19 5-6 7 34 12-4 10 53 131 12 44 11-4 4h 20 7-8 7i 36 0-2 lOi 55 26 43 21 101 H 37 41 loi 56 8-1 " H o^ 10 5-6 5 22 12-3 n 38 8-0 103 57 13-7 23 11 61 H 23 14-5 8 39 11-9 11 59 3-2 3 12 6-7 H 25 0-7 H 40 15-7 114 60 8.7 H 13 7-2 53 26 2-9 8i 42 3-6 Hi 61 14-2 H 14 7-8 6 27 51 83 43 7-5 113 63 3-8 33 15 8-4 H 28 7-4 9 44 11-4 12 64 9-3 4 16 8-9 6k 29 9-6 94 45 15-2 H 17 9-5 6| 30 11-8 47 3 1 I4 u 20 4-5 4i 18 100 7 31 14-0 n 48 70 3:1 2] 11-7 43 19 10-6 U 33 0-2 10 49 10-8 4 23 2-9 5 20 11-2 u 34 2-4 K'i 50 14-7 44 24 101 5i 21 11-7 n 35 4-7 io| 52 2-6 4i 26 1-3 H 22 I2:i 8 36 6-9 103 53 6-5 43 1 27 8-5 53 23 128 Si 37 91 11 54 10-3 5 i 28 15-6 6 24 13-4 8i 38 11-3 Hi 55 14 2 5il 30 6-8 ly d WEIGHT OF FLAT IRON. T. designates the thickness, B. the breadth. T. B. W eigrht. JT.; B. w eight. T. in. B. in. W eight. T. in. B. W eiglit. ill. in lbs. 1. ozs. in. in. lbs. ozs. lbs. ozs. iu. lbs. ozs. 1| o.i 31 140 n 9 55 14-2 2i 44 ^31 10-7 n 85 65 32 5iJ 33 5-2 9i 57 70 45 33 6-3 9 67 10 6 ;34 12-4 i>4 58 15-9 5 35 30 9i 68 14-9 61 36 3-6 n 60 8-7 5^ 36 15-2 94 70 12-7 6i 37 10-7 10 62 1-6 54 38 113 95 72 10-5 6| 39 1-9 m 63 10-4 55 40 7-5 10 74 8-3 7 40 91 104 65 3-2 6 42 3-6 m 76 61 7.i 42 0-3 10| 66 121 6.i 43 15 8 10.4 78 3-9 74 43 75 11 68 4-9 64 45 119 lOij SO 1-7 n 44 14.7 lU 69 13-8 65 47 8-1 11 81 15-5 8 46 5-8 114 71 6-6 7 49 4-2 m 83 13-3 Si 47 13»0 111 72 15-4 74 51 0-4 114 85 111 8i 49 4-2 12 74 S-3 74 52 12-5 113 87 8-9 8| 50 11-4 75 8 54 56 8-7 12 89 6-7 52 J. J. ^ 2-6 2 4 r^R 7-9 2-4 1 4-8 »7 9.\ 53 9-8 4i 28 8i 58 *4 10 n I5 37 5-8 H 55 1-0 44 29 12-9 8.h 59 131 5 39 5-2 n 56 81 41 31 7-4 85 61 9-3 H 41 4-7 10 57 15-3 5 33 19 9 63 5-4 54 43 4-2 lO.i 59 6-5 H 34 12-4 9.i 65 1-6 55 45 3-6 10.4 60 13-7 54 36 6-9 94 66 137 6 47 31 l()l 62 4-9 53 38 14 95 68 9-9 6i 49 2-6 11 63 12 1 6 39 11-9 10 70 60 64 51 20 Hi 6.5 3 2 6.i 41 6-4 10.^ 72 2-2 65 53 15 llh 66 10-4 64 43 0-9 104 73 14-3 7 55 10 llf 68 1-6 65 44 11-4 10.5 75 10-5 n 57 0-4 12 69 8-8 7 46 5-8 11 77 66 74 58 15-9 7i 74 48 0-3 "J 11.4 79 2-S 75 60 15-3 1| 35 23 4-6 49 10-8 80 150 8 62 14-3 O 4 24 13-4 7.5 51 5-3 115 82 HI s\ 64 143 •1.! 26 62 8 52 15-8 12 84 7-3 84 66 13-7 4h 27 15.1 8i 54 10-3 — 85 68 13-2 ±*J ad 4:1 29 7-9 84 56 4-8 2-i 44 33 8-5 9 70 12-7 5 31 0-8 85 57 153 45 35 63 9J 72 121 5.i 32 9-6 9 59 90 5 37 4 1 94 74 116 54 34 2-4 ^\ 61 4-3 5.i 39 19 95 76 11 1 5ii 35 11-3 o.\ 62 14-8 54 40 157 10 78 10-5 6 37 4-6 95 64 93 55 42 13 5 10 1 80 100 6i 38 130 10 66 3-8 6 44 11-4 104 82 9-4 64 40 5-8 m 67 143 6.^ 46 92 105 84 8-9 G'i 41 14-6 lOi 69 8-8 64 48 70 11 86 8-4 7 43 ► 7-5 105 71 33 65 50 4-8 HI 88 7-8 7i 45 0-3 11 72 13-8 7 , 52 2-6 114 90 7-3 74 46 9-2 11-i 74 8-3 7.i 54 04 115 92 6-8 n 4S 20 1 114 76 2-8 1 74 55 14 2 1 1 12 94 6-2 49 51 10-8 37 115 12 77 79 13 3 7-8 75 8 i 57 !•> 1 ' 59 1 M V 98 -'4 5 1 41 6-4 8A liO 125 5-4 84 <;i 7-6 m j.-i 7.5 85 54 ^\ 4.i| 29 14 5 0, \f » 84 ' 63 • 1 \t 5 4 O.J ,-- 54145 8.6 WEIGHT OF FLAT IRON. 19- T de: .ignates the thickne ss, B . the breadth. T. B. ill. Weight. T. in. B. We ght. T. in. B. in. We ?ht. T. ir.. in. We gilt. in. lbs ozs. in. lbs. ozs. lbs. ozs. lbs. ozs. 2i 51 47 9-7 2| 7 60 13-7 n H 77 6-6 91 ~8 i"4 97 9-6 6 49 10-8 74 63 0-5 83 79 111 lo.i 99 15-7 6i 51 120 U 65 3-2 9 81 15-5 103 102 5-7 6h 53 131 n 67 60 94 84 3-9 11 104 11-8 n 55 14-2 8 69 8-8 H 86 S-4 114 107 19 7 57 153 8.i 71 11-6 n 88 12-8 ii-i 109 8-0 n 60 0-4 8h 73 14-3 10 91 1-2 111 111 141 u 62 1-6 SI 76 11 104 93 5-7 12 114 4-2 u 64 2-7 9 78 3-9 10^ 10| 95 10 1 8 66 3-8 n 80 6-7 97 14-5 3 6 59 98 Si 68 4-9 H 82 9-4 11 100 30 64 62 16 Sh 70 6-0 9:1 84 12-2 114 102 7.4 6d 64 9-3 Si 72 7-2 10 86 15-0 114 104 lis 61 67 1-0 9 74 8-3 104 89 1-8 111 107 0-3 7 69 8-8 9i 76 9-4 lOh 91 4-6 12 109 4-7 74 72 0-5 9-i 9^ 7S 80 10-5 11-6 105 11 03 7-3 7i 7:1 74 77 S-3 00 95 101 01 51 54 120 10 82 12-8 114 97 12-9 6 57 21 8 79 7-8 m 84 13-9 uh 99 15-7 64 59 8-2 84 81 15-5 m 86 150 m 102 2-4 6h 61 14-2 8i 84 7 3 m 89 0-1 12 104 5-2 f 74 64 4-3 n 86 150 11 91 1-2 66 69 10-4 0-5 9 94 89 91 6-7 14-5 Hi 93 2-4 2:1 5h 50 1 5 lid 95 3:5 5:1 52 5-9 n 71 6-6 9.i 94 6-2 111 97 4-6 6 54 10-3 7:1 73 12-7 91 96 140 12 99 5-7 64 56 14-8 8 76 2-S 10 99 5-7 6h 59 3-2 84 78 8-9 104 101 13.5 ■ 2| 54 45 10-3 6| 61 7-6 8i 80 15.0 lOi 104 5.2 5i 47 130 7 63 121 8| 83 5-0 103 106 13.0 54 49 15-8 74 66 0-5 9 85 111 11 109 4.7 6 52 2-6 U 68 4-9 94 88 1-2 114 111 12.4 6i 54 5-4 7% 70 9-4 9i 90 7-3 ii-i 114 4.2 6d 56 8-1 10-9 8 72 13-8 91 92 134 11:1 116 11.9 6| 58 84 75 2-2 10 95 3-5 12 119 3.7 OBSERVATIONS ON TABLE OF FLAT IRON. The wei£;hts here given are in poitnds, ounces, and decimal parts, avoir- dupois ; and it will be seen, on inspecting- the Tabic, that the first numbers in each page are those which applj' to nul iron, and that the breadth in- creases by 4 of an inch. The last numbers in each page show the weight of a square foot, according to the respective thickness of each bar. Hence the weight of any length of a bar of rectangular iron may be ascertained gimply, as follows : Rule. — Multiply the tabular weight, according to the thickness and breadth, by the number of feet in the bar, the product will be tne weight required. Example — In a bar of iron whose thickness is 2} inches, the breadth 61^ inches, and the length 18 feet, what is the weight thereof?. In the Table for 2 [inches thick, and opposite G^ inches, stand 48 lbs. 7 ozs.; being the weight of one lineal foot. Multiply this number by 18 feet, and we have as follows ; 48 lbs. 7 ozs. X IS = 871 lbs. 14 ozs. 194 ELASTICITY OF STEAM. ELASTIC FORCE OF STEA.M. lable of the Elastic Force of Steam, and corresponding Tempera- ture of the Water ivith ivhich it ts in Contact-. 1 Elastic 1 Volume of Elastic Volume of Pressure in force in Temper- Steam ] Pressure in force in Temper- Steam pounds Inches ature compared ] pounds Inches ature compared per sij. in J of Fahreu't. with Vol. per sq. in. of Fahren't. with Vol Mercury. of Water.! Mercury. of Water- 14.7 3U.IJU 212.0 170U 63 128.52 299.2 44 9 15 30.00 212.3 1609 04 130.56 300.3 443 16 32.64 216.3 1573 05 132 00 301.3 437 17 34.68 21i).6 14SS 00 134.64 302.4 431 18 3a.72 222.7 1411 07 130 .'58 303.4 425 19 33.76 225.6 1343 03 138.72 304.4 419 20 40.80 229.5 1281 69 140.70 305.4 414 21 42 84 231.2 1225 70 142.S0 3f)0.4 403 22 44.83 233.8 1174 71 144.S4 307.4 403 23 46.92 2:36.3 1127 72 140.88 303.4 393 24 43.96 238.7 105*4 73 143.92 309.3 393 25 51J0O 241.0 1U44 74 150.90 310.3 383 26 53.04 243.3 1007 75 153 02 311.2 383 27 55.08 215.5 973 70 155.00 312.2 379 23 57.12 247.6 941 77 157.10 313.1 374 29 59.16 249.6 911 73 159.14 314.0 370 30 61.21 251.6 883 79 161.18 314.9 360 31 63.24 853 6 857 SO 103.22 315 8 362 32 65.28 255.5 833 81 10.5. 26 310.7 353 33 67.32 257.3 SlO 82 107.30' 317.6 354 34 69.36 259.1 788 83 109.34 318.4 350 35 71.40 260.9 J67 84 171.38 319.3 346 36 7344 202.6 743 85 173 42 320.1 342 37 75.48 264.3 729 SO 175.10 321.0 330 33 77.52 265.9 712 87 17 7. .50 321.3 335 39 79.56 267.5 695 88 179.54 392 6 3:12 40 81.60 269.1 679 89 181.58 32:) .5 329 41 83.64 270.0 604 90 133.02 321.3 325 43 85.63 272.1 019 91 185.00 325.1 322 43 87.72 273.6 035 92 137.70 325.9 319 44 89.76 276.0 022 93 189.74 326.7 316 45 .91.80 270.4 010 94 101.78 327.5 313 46 93.81 277.8 593 95 193.S2 328.2 310 47 95.83 279.2 530 90 195.60 329.0 307 43 97.92 230.5 575 97 197.90 329.8 304 49 99.96 281.9 564 93 199.92 330.5 301 50 102.00 283.2 551 99 201.90 331.3 298 51 104.04 284.4 544 100 204.01 332.0 295 52 106.03 2S5.7 534 110 221.40 339.2 271 53 1(18.12 280 9 525 120 241. 82 345.8 251 54 11010 258. 1 516 130 203.23 352.1 233 55 1 12.20 239.3 503 HO 2S5.GI 357 9 218 56 114.21 29!l.5 500 150 306.03 363.4 205 57 116.23 291.7 492 100 320.42 368.7 193 58 118.32 292.9 4Sl 170 310.80 373.6 133 59 120.30 204 2 477 180 307.25 378.4 174 CO 122.40 295.6 470 190 .387.61 382.9 166 61 121.44 290.9 403 200 403.01 337.3 153 62 120.43 298 1 456 1 Water ii ililmcr im puriiies in solution lends to ret ard its at ainin^ l)i c nuriform stale, and so impair: the amount of its cla.sllc force al an cqi al lenipcr aturc. Common v Sea waler Common \ Sea wmcr /tiXCT. . . . boilinp point, 212° F ut 212 " boiling' point, 210° F al 210 " . ( clastic 1 • force, 30 ' 23 32 ' 21 inches. .05 " I'atrr. . , , .5 " '.'.'.'.'.'.'. .0 " PROPERTIES OF STEAM. 195 PRODUCTION AND PROPERTIES OF STEAM. When water in a vessel is subjected to the action of fire, it readily im- bibes the heat or fluid principle of which the fire is the immediate cause, and sooner or later, according to the intensity' of the heat, attains a tempe- rature of 21 i** Fahrenheit. If at this point of temperature the «atcr be not enclosed, but exposed to atmospheric pressure, ebullition wil' take place, and steam or vapor will ascend throufih the water, carryins: with it the superabundant heat, or that which the water cannot under such circum- stances of pressure absorb, to be retained and to indicate a higher teinpera- tUre. Water^ in attaining the aeriform state, is thus uniformly confined to the same laws nnderevery degree of pressure ; but as the pressure is augmented, so is the indicated temperature proportionately elevated : hence the various densities of steam, and corresponding degrees of elastic force. The preceding Table is peculiarly adapted for estimating the power of steam engines on the condensing principle, because in such the efft-ctive force of tlie steam is the difl^erence between the total force and the resisting vapour retained in the condenser. The following Table is more adapted for estimating the effects of non-condensing engines, as, in such, the atmo- spheric pressure is not generally taken into account, engines of this principle being supposed to work in a medium; or, the atmospheric pressure on the boiler, to cause a greater density of steam, is equal to the resisting atmo- sphere which the effluent steam has to contend with on leaving the cylinder. Table of the Elastic Force of Steam, the Pressure of the Atmosphere not being included. Elastic Force in Atmospliere. lbs. square inch 1.1'J 2.5 1.22 3 1.29 4 1.36 5 1.70 10 2.04 15 2.-38 20 8.72 25 3.06 30 3.40 35 3.74 40 4.08 45 • 4.42 50 4.76 55 5.10 60 inch, of Mer. Temperature [ Volume of in degrees of Steam Water Fahr. I being 1. 5.15 CIS S.24 10.3 20.6 30.9 412 51.0 61.8 72.1 82.4 92.7 103.0 113.3 123.G 230 222 225 223 2.40 251 2150 268 275 282 288 294 299 304 309 1496 1453 1.366 12S2 1044 853 767 678 609 553 506 468 435 407 382 Cubic in. of "Water in a cubic foot of Steam. 1.14 1,18 1.25 1..33 1.64 1.93 2.23 2.52 2.8 1 3.09 3.38 3.6G 3.93 4.20 4.43 Steam, independent of the heat indicated by an immersed thermometer, also contains heat that cannot be measured by any inslrument at present known, and, in consequence of which, is termed latent or|concealcd heat •, the only positive proof we have of its existence being that of incontestable re- sults or effects produced on various bodies. Thus, if one part by weight of steam at 212° be mixed with nine parts of water at 62*^, the result is water at 178 6° ; therefore, each of the nine parts of water has received from the steam IIGG" of heat, and consequently the steam has diffused or given out UG.G X 9 = 10494 — 33.4 = 1016° o"f heat which it must have contained. Again, it is ascertained by experiment, that if one gallon of water be trans- formed into steam at 212", and that steam allowed to mix with water at 52°, the whole will be raised to the boiling point, or 2 12". From these and other experiments, it is ascertained that the latent heat in steam varies from 940" 196 CONSUMPTION OF COAL. to 1044°, the ratio oT accumulation advancing from 212°, as the steam be- comes more dense and of greater elastic force 5 hence the severity of a scald by steam to tliat by boihiig water. The rules formed by experimenters as corresponding with the results of their experiments on tlie elastic force of steam at given temperatures vary, but appro.ximate so closely that the following rule, because of being simple, may in practice be taken in preference to any otiier. lirt/e. — To the temperature of the steam in degrees of Fahrenheit, add 100. divide the sum by 177, and the 6th power of the quotient equals the force in inches of mercury. Ex. Required the force of steam corresponding to a temperature of 312°, 312 -f 100 ~ 111 — 2.o27" = h')d inches of mercury. But the Table is much belter adapted to practical purposes, as the vari- ous results or effects are obtained simply by inspection. CONSUMPTION OF COAL. TABLE for finding the CONSUMPTION of COAL per Hour in Stcamera either Paddle or Screw (the same Screw being used throughout,) at any Kate of Speed, the Consumption lor a particular Rate being known. (At a given Amount of Cord, the Engineer may determine tiie most pru- dent Rate of Engine for reaching next coaling Port.) — Engineer's and Contractor's Pocket Book, London. Speed. Consumption of Coal. Speed. Consumption of Coal. Explanation. 3 .216 9 5.83 3 1-2 .3 13 9 1-2 6.86 The speed for the consump- 4 .512 10 1 8.00 tion of a unit of coal is sup- 4 1-2 .729 10 1-2 ' 9.26 posed here to be 5, which may 5 1 .000 11 10.65 ' be 5 miles or knots, or 5 times 5 1-2 1 .;i.ii 11 1-2 1'2.15 any number of miles or knots ; i; 1 728 12 13.82 then if 5 of sudi number of 6 1-2 2.197 12 1-2 15.61 miles require 1 unit of coal 7 274I. 13 17 58 per hour. 9 of such units will, 7 1-2 3.375 13 1-2 19.08 jy the table, retiuirc 5.83 units 8 4.096 14 2195 of coal, and 3 of them .21& 8 1-2 4.910 units of coal. It will be evident that this Table is calculated on the principle that the horse power varies very nearly as tlie cube of the speed ; the enormous in- crease of consumption at increased velocities is in liict a little greater than that shown by the Table. The advantages indicated above to be obtained at low velocities arc evidently independent of those obtained at those velocities by using the steam expansively. EVAPORATIVE POWER OF COAL AND RESULTS OF COKING. Under the authority of an Act of the American Congress, approved Sept. 11, 1841, an extensive series of experiments was conducted by Prof .fohn- son upon the evaporative power of sevi'ral kinds of coal. The number of samples tried was 41 , including 9 anthracites from Pennsylvania; 12 free- burning or semi-bituniinous coals; II biluminons from \ir";inia; (i foreign bituminous coals, viz. 1 from Sydney, Nova Scotia, sent by llie Cuniird (.'oal Mming Company; 1 of Pictou Coal, sent by tin; same ; I ol'Scolch; 1 of Newcastle ; 1 ol Liverpool ; and 1 of Piclou. From one to six trials were EVAPORATIVE POWER OF COAL. 197 made on each sample, the average ciuantity used per trial being 978 lbs. The experiments occupied 144. days, during each of which continuous obser- vations were made during 12 or 14 hours. The coals were burnt under a steam boiler, fitted with apparatus for com- plete regulation, the supply of water and coals being determined both by weight and measure. The standard adopted to measure the heating power of each tind of coal was the weight of water which a given weight of each evaporated from the temperature of 212^ Fahr. The following Table gives the results of five comparisons in each of which that coal which ranks the highest is stated as 1000, and the others in deci- mal parts of the integer. Comparison Comparison Comparison Comparison Comparison 1. 2. t. . 4. 5. 3 O ■a t»> 0) CI o EC o o Si es s £•9 ll 4 O Cm O tn CO Kinds of Coal. 'si fir" GS 11, evaporativ I weights of oir steam f d by 1 cubi 2° ll i quired to b steady ac i t II O OJ a 'p. £ . 11 .11 Pounds water at of fuel. Relative for equa Pounds produce each. Relative for equa u a > Time re boiler to hours. li it ll 5 >» Anthracites : Atkinson and Terapleman's ) 10 70 1.000 566.2 I.OOO 1 7.96 .633 0.99 .505 5.1 .725 52.92 Beaver Alea- i dow (No. 5). J Bituminous and 9.38 .923 556.1 .982 6.74 .748 2.42 2.07 6.12 .060 56.19 free burning : Newcastle . 8.66 .809 439.6' .776 5.68 .887 0.84 .595 10.7 .346 .50.82 Pictou . . . HA-i .792 417.9 .738 12.06 .418 0.85 .588 3.7 i.noo 49.25 Liverpool 7.84 .733 375.4 .663 504 1.000 0.86 .581 11 1 .333 47.88 Cannelton, (In) 7.34 .636 348.8 .616 5.12 .984 0.50 1 .000 6,4 .578 47.65 Scotch . . 6.9.5 .649 353.8 .625 10.10 .499 0.96 ..•)21 5.7 .649 51.05 Dry pine wood. 4.69 .436 98 6 .475 0.307 16.417 The same report states some results of coke-burning, from which it ap- pears that by burning in uncovered heaps, and only covering up the ignited mass when flame ceases to be emitted (as in many of the iron works of Great Britain, France, &c.), the loss in weight at Plymouth has been found to be 17 per cent. ; at Penn-y-darran, 20 per cent. ; and at Dowlais Cwhere it may be presumed the abundance of coal admits of an uneconomical man- agement), 34: per cent. By coking in stacks, or well covered heaps of coal from 10 to 15 ft. diameter, as followed in Staffordshire, highly bituminous coals lose from 50 to 55 pr. ct. weight, and those of a drier nature from 35 to 40. By coking in close ovens, a coal which, in an uncovered heap, yields only 45 to 59 per cent., yields 69 per cent. In the close oven the gain in bulk is from 22 to S!3 per cent. ; and while highly bituminous coals yield only 40 to 45 percent, in open heaps, and actually /ose in hulk, \hey yield in close ovens from G5 to 66 per cent., and gain in bulk. By coking fn gas retorts, the Deane Coal of Cumberland gains nearly 30 per cent, in bulk, and loses in weight 25 per cent. Carlisle coal nearly the same. Cannel and Cardiff coals gain 30 per cent, in bulk, and lose 36.5 in weight. Bewick's Wallsend loses 30, and Russell's Wallsend, 30.7 per cent, by the same process. 17* 198 POV/ER OF STEAM. POWER OF STEAM. Mr. Trcdgold gives the following- Table, which will show how the power of tlie steam as it issues from the boiler, is distributed. IN A NON-CONDENSING ENGINE. Let the pressure on the boiler be 10.000 Force required to produce motion of the steam in the cylinder will be O.OiiO Loss by cooling in the cylinder and pipes O.IGO Loss by friction of the piston and waste 2.000 Force required to expel the steam into the atmosphere 0.0G9 Force expended in opening the valves, and friction oftlie various parts 0.G23 Loss by the steam being cut oiTbefore the end of the stroke 1.000 Amount of deductions 3.920 Effective pressure 6.060 IN A CONDENSING ENGINE. Let the pressure on the boiler be 10.000 Force required to produce motion of the steam in the cylinder 0.070 Loss by cooling in the cylinder and pipes 0.160 Loss by friction of the piston and waste 1.250 Force required to expel the steam through the passages 0.070 Force required to open and close the valves, raise the injection water, and overcome the friction of the axes 0.630 Loss by the steam being cut off before the end of the stroke 1.000 Power required to work the air pump 0.500 Amount of deductions 3.680 Effective pressure 6.320 If wc now suppose n cylinder whose diameter is 21 inches, the area of this cylinder and consequently tiie area of the piston in scjuare inches, will be, 24" X .7854 = 452.39 Let us also make the supposition that sloam is admitted into the c^dinder of such power as exerts an cfTeclivc pressure on the piston of 12 lbs. to the square inch ; therefore, 4-52.39X12 = 5128.08 lbs., the whole force with which the piston is pressed. If wc now suppose that the Icnnlh of the stroke is five feet, and the engine makes 44 single or 22 double strokes in a minute, then the piston will, move through a space of 22 X 5 X 2 = 220 foot in a minute ; the power of the engine being equivalent to a weight of 5428 lbs. raised through 220 feet in a minute. This is the most certain measure of ihc powor of a steam engine. It is usual, however, to estimate the ed'cct as e(|uivalenl to the power of so many horses. This method, liowever siini)lc and naturnl it may appear, is yet, from (lifTereuccs of opinion as to the power of a horse, not very accurate ; and its employment in calculation can only be accounted for on the ground, that when steam engines were first employed to drive machinery, they were substituted instead of liorses ; and it becanic tlius necessary to eslimate what size of a steam engine would give a power e<]nal to so many horses. 'J'liere arc various opinions as to the power of a liorsc. According to Smeaton, a horse will raise 22,'JIG lbs. one foot iiigh in a minute. Doaagu- licrs makes the number 27,500; and Watt makes it larger still, that is lU.OOO. Thcre.is reason to believe that oven this nnndicr is too small, and that we may add at least 11,000 to it, which g'vcs 41,000 lbs. raised one fool higli per minute. — drier. RULES AND TABLES FOR GAUGING, ULLAGING, &c GAUGING OF CASKS. 201 GAUGING OF CASKS. In takinc; the dimensions of a Cask it must be carefully observed : 1st, That the bung-hole be in the middle of the cask; 2d, That the bung-stave, and the stave opposite to the bung-hole, are both regular and even within; 3d, That the heads of the Cask are equal, and truly circular; if so, the distance between the inside of the chime to the outside of the opposite stave will be the head diameter within the Cask, very near. Rule. — Take, in inches, the inside diameters of a Cask at the Head and the Bung, and also the Length; subtract the head -diameter from the bung-diameter, and note the difference. If the measure of the Cask is taken outside, with callipers, from head to head, then a deduction must be made of from 1 to 2 inches for the thickness of the heads, according to the size of the Cask. 1 1/ the stave.i of the Cask, between the bung and the head, are considerably curved, (the shape of a Pipe), multiply the difference between the bung and head, by .7. 2 If the staves be of a medium curve, (the shape of a Molasses Hogshead), multiply the difference by .65. 3. 1/ the staves curve very little, (less than a Molasses Hogs- head), multiply the difference by .6. 4. If the staves are nearly straight, (almost a Cylinder), mul- tiply the difference by .55. 5. Add the product, in each case, to the head-diameter ; the sum will be a mean diameter, and thus the Cask is reduced to a cylinder. 6. Multiply the mean diameter by itself, and then by the length, and multiply if for Wine gallons, by .0034. The difference of dividing by 294 (the usual method), and multiplying by .0034 (the most ex- peditious method), is less than 500ths of a gallon in 100 gallons. EXAMPLE. Supposing the Head-Diameter of a Cask to be 24 inches, the Bung- Diameter 32 inches, and the Length of Cask 40 inches; What is the content in Wine Gallons ? 1st variety. Bung-Diameter, 32 brought up 876.16 24 Length, 40 ~8 35046.40 .7 .0034 Head-Diameter, Difference, Multiplier, 5.6 Head-Diam., 24 multiply 29.6 by 29.6 carry up Square, 876.16 14018560 10513920 119.157760 Jlns. 119 galls. 1 pint. To obtain the contents of a similar Cask in Ale Gallons, multiply 35046.40 by .0027S5, and we get 97.6042, (or 97 gallons 5 pints.) 202 GAUGING OF CASKS. GAUGING OF CASKS IN IMPERFAL (BRITISH) GALLONS. AND ALSO IN UNITED STATES GALLONS. Having ascertained the variety of the Cask, and its interior dimen- sions, the following Table will facilitate the calculation of its capacity. Table of the Capacities of CasJ:s, ivhose Bung Diameters and Lengths are 1 or Unity. n. 1st Var. 2d Var. 3d Yar. ■ith Var. .50 .51 .5-2 .53 .54 .5.5 .5(i .5/ .53' .59 .OU .GI .6> m .01 .G.J .00 .07 .03 .09 .70 ^ .73 .74 .75 .00212441 .0021310 .0021 I37I .0021530' .0021037 .0021740 0021315 .0021951 .0022000; .0022170' .0022233! .00223971 .00225 13i .0022031' .0022751 .0022373; .00229971 .002;3122 .00232.)0 .0023379! .0023510 .00230431 .0023778 .002:3915 .0021051! .0024195 .0020300 .0020433 .0020507 .0020702 .0020333 .0020975 .0021114 .0021253 .0021394 .0021530' .0021079 ,0021323' .0021903 .0022114 .0022202 .0022110 .0022500 .002271 1 .0022303 .0023010 .0023170 .0023320 .0023432 .002)040 .0023799 .00239.59 .0017704 .0017347 .0017993 .0018141 .0018293 .0013447 .0013004 .0018704 .0018927 .0019093 .0019201 .0019433 .0019007 .0019784 .0019901 .0(120147 .0020332 .0020.521 .0020712 .0020900 .0021103 .0021302 .0021.505 .0021710 .0021913 .0022129 .0010523 .0010713 .0010905 .0017098 .0017294 .0017491 .0017090 .0017391 .0018094 .0013299 .0018500 .0018715 .0018925 .0019133 .0019352 .0019503 .0019730 .0020000 .0020228 .0020452 0020073 .0020905 .0021135 .0021306 .002)599 .0021834 II. 1st Var. 2d Var. I 3d Var. I 4tli Var. .70 .77 .73 .79 .80 .81 .82 '33 .84 .85 .80 .87 .38 .89 .90 .91 .92 .93 .94 .95 .90 .97 .98 .99 1. 00 .0024337 .0024482 .0024023 .0024777 .0024927 .0025079 .0025233 .0025383 .0025540 .0025700 .0025307 .0020030 .0020190 .0020303 .0020532 .0()2(i703 .O020'<75 .0027050 .0027227 .0027405 .0027535 .0027703 .0027952 .0023133 .0023320 .0024120 0024232 .0024445 .0024010 .0024770 .0021942 .0025110 .0025279 .0025449 .0025021 .0025793 .0025907 .0020141 .0020317 .0020491 .002(5072 .0020351 .0027032 .0027213 .0027390 .0027579 .0027704 .0027950 .0028137 ,0028320 .0022343 .0022500 .00227.-0 .0023002 .0023227 0023155 .00231)30 .0(I2:>920 .00241.56 .0024390 .0024033 .0021333 .0025131 .002.5331 .0025035 .0025-91 .0020150 .0020412 .0020077 .0020945 .0027215 .00274.39 .0027705 .0028044 .0023320 .0022071 .002a310 .0022551 .002279 4 .002:3033 .0023285 .002:S533 .0023733 .0024035 .0024269 .0024545 .0024803 .0025003 .0025324 .00255'-3 .0025-5:3 .0021120 .0020389 .0020000 .0020933 .0027208 .0027484 .0027703 .0023013 .0023320 Divide the head by the hung diameter, and opposite the quotient in the column II, and under its proper variety, is the tahular number for unity. Multiply the tabular number by the square of the bung diameter of the given cask, and by its length, the product equals its capacity in Imperial gallons. Required the number of Gallons in a Cask, {\st variety,') 21 inches head diameter, 32 bung diameter, and -10 inches in length i ■ 32) 2 1.0 (.75 see Table for tabular No. .002419.5 tabular No. for unity. 82 X 32 is 1024 square of bung diam. ytnso 4S390 24195 2.4775(J80 40 Inches long. 99.1027200 Imperial Gallons. 1.2 Note. — Mulliply- ing Imperial gallons by one &. two-tenths (1.2) will convert them into U.S. gallons; and U. S. gallons multiplied by ■8.33 equal Imperial gallons. 1982054400 991027200 I18.9232(JI00 United States Gallons. ULLAGE OF CASKS. 203 TO ULLAGE, OR FIND THE CONTEXTS IN GALLONS OF A CASK PARTLY FILLED. To find the contents of the occupied part of a lying cask in gallons. Rule. — Divide the depth of the liquid, or wet inches, by the bung di;inietcr, and if the quotient is under .5 deduct from the quotient one- fourth of what it ii less than .5, and multiply tlic remainder, by the whole capacity of the cask, this product will be the number of gallons in the cask. But if the quotient exceeds .5, add one-fourth of that excess to the quotient, and multiply the sum, by the whole capacity of the cask, this product will be the number of gallons. Example i. — Suppose the bung-diameter of a cask, on its bilge, is 32 inches, and the whole contents of the cask 118.80 U. S. standard gallons; requiied the ullage of 15 wet inches. 32) 15.00 (.46875 .5 — .46875= .03125 -4- 4 = .0078125 .46875 — .0078125 =.4609375 X 118.80 = 54.759375 U. S. Gallons. Example ii. — Required the ullage of 17 wet inches in a cask of the above capacity ? 32) 17.00 (.53125 — .5 = .03125 -=-4 = .0078125+ .53125 = .5390625 X 118.80 = 64.040625 U. S. Gallons. Proof — 64-040625 + 54-759375 = 118-80 gallons. To find the ullage of a filled part of a standing Cask, in gallons. Rule. — Divide the depth of the liquid, or wet inches, by the length of the cask; then, if the quotient is less than .5, deduct from the quotient one-tenth of what it is less than .5 and multiply the re- mainder, by the whole capacity of the cask, this product will be the number of gallons. But if the quotient exceeds .5, add one-tenth of that excess to the quotient, and multiply the sum, by the whole capac- ity of the cask, this product will be the ullage, or contents in U. S. standard gallons. Example. — Suppose a cask, 40 inches in length, and the capacity 118.80 gallons, as above: required the ullage of 21 wet inches? 40) 21.000 (.525 — .5 = .025-=- 10= .0025+ .525=. 5275 X IIS.SO = 62.667 U. S. Gallons. Note. — Formerly the British V/inc and Ale Gallon measures were sim- ilar to ihose now used in the United States and British Colonies. Ttie following Tables exhibit the comparative value between the United States and the present British measures. TJ. S. measure for British (Im.) measure. wine, spirits, &c. galls, qts. j>ts. gills. 4-2 gulls. = • lierce, = 34 3 13 63 =1 lio-!sh. = .5'2 113 120 = 1 pipe, = 104 3 13 252 =1 tun, =209 3 1 2 U. S. measure for British (Im.) measure. ale and beer. sails, qts. pts. gills. 9 galls. = 1 firkin, =" 9 1 1 30 =1 b;irrel,= 36 2 3 54 =1 liogsh. = 54 3 1 1 108 =1 bult, =109 3 3 To convert Imperial Gallons into United States Wine Gallons multiply the im- perial by 1-2. To convert U. S. Gallons into Imperial multiply the U. Slates Wine gallons by -feSS. 51 U. S. Ale Gnllons equal 60 Imperial Gallons, therefore to convert one into other add or deduct 1-COth. 204 PLOUGHING, PLANTING. — WEIGHT OF WOOD, &C. PLOUGHING. Tabic showing the distance Travelled by a horse in Ploughing an Acre of L-and ; also, the quantit}' of Land worked in a Day, at the rate of 16 and 18 miles per day of 9 hours. B'dth of Furrow Spaco travel- led in Ploush- Extent rioughed B'dth of Furrow Space travel- led in IMoueh- Extent Ploughed Elice. ing an Acre. slice ing an Acre. Miles. Inches. Miles. 18 Miles. 16 Miles. Inches. 18 Miles. iO Miles. 7 14 1-2 11-4 11-8 14 7 2 1-2 2 1-4 8 12 1-2 1 1-2 1 1-4 15 6 1-2 2 3-4 22 5 9 11 13-5 1 1-2 10 6 1-G 2 9-10 2 3-5 10 9 9-10 14-5 13-5 17 5 3-4 3 1-10 2 3-4 11 9 2 1 3-4 18 5 1-2 3 1-4 2 9-10 12 8 1-4 2 1-5 19-10 19 5 1-4 3 1-2 3 1-10 13 7 1-2 2 1-3 2 1-10 20 4 9-10 3 1-5 3 1-4 PLANTING. Table showing the number of Plants required for one Acre of Land, from one Toot to Twenty-one Feet disicmce from Plant to Plant. Feet No. of Feet No. of Feet No. of Feet No. of) Feet No. of Distance. Hill-. Distance Hills. Distance. Hills. Distance. Hills. Distance Hills 1 43, .560 4 2,722 7 889 10 436 17 151 Ij^ 19,360 4.^ 2,151 ih 775 lOi 361 18 135 2 10,890 5 1,742 8 680 12 302 20 108 2.i 6,969 5.^ 1,440 sh C02 14 223 21 99 3 4,840 6 1,210 9 538 15 193 25 69 3^ 3,556 fi-i 1,031 94 482 1.6 171 30 48 WEIGHT OF A CORD OF WOOD. Table of the Weight of a Cord of different kinds of Dry Wood, and the comparative vahie per Cord. A Cord of Hickory, - - 4469 poun ds, - - Carbon - - 100 Maple, - - - 2863 - - *'. - - 54 Wliile Birch, - 2360 - - " - - 48 " Beech, - 3236 - - " - - 65 " Ash, - - 3450 - - " - - 77 Pitch Pine, - - 1904 - - " - - 43 White Pine, - 1868 - - " 42 Lombard V Poplar 1774 - - " 40 While Oak - - 3821 - - " - - HI Yellow Oak, - 2919 - - " - - (iO . Red Oak, - - 3254 - - " - - 09 Note. — Nearly oiii; lialf of tlie weight of a ijrowhipr Oak tron consists of sap. Oriliiiary Dry Wood contains about one-fourtli of its wciijlil in water. CHAIICOAL. Oak, Maple, Hecch, and Chostnnt make llie best qiialilj. Do- twccn 15 and 17 per cent, of coal can be obtained when tlie %von(l is propcM-ly l)nine(!. A bnsliel of coal (Voiii Iini-d wood wi ii;hs between 29 and 31 lbs., and Iroin lioni pine between 28 and 3U lbs. ADDITION TO TINMAN'S MANUAL. TINMAN'S TWELVE POUND BILL, OR BILL OF DAY'S WORK No. of Articles for Day's Work. 12 lb. 16 Sixteen quart Large Dish Kettles, 84 10 Water Pots, 75 18 Twelve quart Pails, 67 18 Large Dish Kettles, 67 20 Foot Stoves, 67 24 Ten quart Pails, 58 24 Ten quart Pans, 68 18 Gallon Coffee Pots, 58 18 Six quart Covered Pails, . 58 18 Large Sauce Pans, 58 24 Gallon Measures, 39 30 Six quart Pails, 39 36 Common Size Milk Pans, . 39 20 Large AVash Bowls, 39 20 Lanterns, 39 24 Small Dish Kettles, six qt. 39 20 Cullenders, 39 24 Three quart Coffee Pots, . 39 24 Large Pudding Bags, ... 39 24 Roasters, 39 40 Lantern Pans, 36 24 Two quart Coffee Pots, . , 34 20 Three qt. Covered Pails, . 34 24 Small Wash Bowls, 34 24 Small Sauce Pans, 34 30 Half gallon Measures, ... 25 48 Half gallon Pans, 25 24 Half gallon Dippers, 25 36 Half gallon Funnels, 25 30 Thi-ee pint Coffee Pots, . . 25 24 Two quart Covered Pails, 25 86 Large Blow Horus, 25 36 Three quart Pails, 25 48 Round Pans, 18 100 Square Pans, 18 108 Scollop Pie Pans, 18 48 Sausage Horns, 18 86 Quart Coffee Pots, 18 48 Square Toast Pans, 18 No. of Articles for Day's Work. 12 lb. 36 Round Toast Pans, 18 40 Quart Covered Pails, 18 36 Round Flat Bottom Tea Pots, 18 72 Second Size Horn, 18 48 Sailor Pots, 18 36 Quart Lamp Fillers, 18 36 Water Ladles, 18 36 Sugar Scoops, 18 36 Milk Strainers, 18 72 Quart Measures, 14 48 Large Skimmers, 14 72 Quart Funnels, 14 72 Small Horns, 14 72 Basins, 12 144 Quart Scollops, 12 144 Quart Grease Pans, 12 60 Round Handled Dippers, 12 120 Half Square Pans, 10 84 Half Sheet Funnels, 10 72 Half Sheet Dippers, 10 120 Half Sheet Scollops, 10 96 Pint Funnels, 8 84 Pint Measures, 8 96 Pint Cups, 8 168 Pint Scollops, 8 48 Flour Boxes, 8 96 Half Pint Measures, 5 108 Half Pint Cups, 5 96 Half Pint Dippers, . . 5 120 Half Pint Funnels, 5 96 Gill Measures, 5 48 Blisters, 5 96 Small Skimmers, 5 124 Flat Candlesticks, 5 120 Needle Cases 5 84 Pepper Boxes, 5 120 Hearts, 3 144 Rounds, 3 98 Rattle Boxes, 3 [The 6 Pound Bill is one-half of the 12 Pound Bill.] ADDITION TO TINMAN S MANUAL. No. of Articles for Day's Work. 121b. 12 Six quart Coffee Boilers, 1.00 12 Five quart Coffee Boilers, 83 12 Four quart Coffee Boilers, (37 12 Three qt. (ioffee Boilers, 50 12 Two quart Coffee Boilers, 42 12 Six quart Coffee Pots,. . . 83 12 Five quart Pots, 75 12 Large Dutcli Buckets,. . . 12 Small Dutch Buckets,. . . 12 Small AVater Pots, 12 Ten quart Covered Pails, 84 18 Five quart Covered Pails, 50 26 Three pint Covered Pails, 20 30 One pint Covered Pails,.. 14 30 Five quart Open Pails, . . 50 32 Gall. Open Pails, 40 Three Pint Open Pails,. . 121b. No. pf Articles for Day's Work. 24 Nine quart Pans, 16 Twelve qt. Pans, handles, 20 Seven qt. Pans, handles, 36 Five quart Straight Pans, 40 Two quart Straight Pans, 48 Three pint Straight Pans, 20 Handled Wash Boards,. . 18 Twelve qt. Dish Kettles,. 18 Ten qt. Dish Kettles, 24 Four qt. Dish Kettles, . . . 40 Three pint Dish Kettles, . Twelve qt. Cov. Buckets, 1.00 Oak Leaf Cake Cutters, . . 10 One quart Tea Pots, 34 One gallon Fluid Cans,. . Half gallon Fluid Cans, . . 80 50 39 67 58 39 18 1.— WEIGHTS OF IRON WIRE PER 20 FEET. Manufactured by Ichabod Washbukn & Moen, Worcester, Mass. No. 0. .5 lbs. No. 6.. .lib. 14 ozs. No. 12. . 9 ozs. No. 1. .4 lbs. 2 ozs. No. 7.. .lib. 10 ozs. No. 13. .6 ozs. No. 2. .3 lbs. 8 ozs. No. 8.. .1 lb. 7 ozs. No. 14. .5 ozs. No. 3. .2 lbs. 15 ozs. No. 9.. .lib. 2 ozs. No. 15. .44 ozs. No. 4. .2 lbs. 8 ozs. No. 10.. 14 ozs. No 16. .3i^ ozs. No. 5. .2 lbs. 5 ozs. No. 11.. • 10 ozs. No. 17. .3 ozs. 2.— WEIGHT OF IRON WIRE PER LINEAL ROD. N09. Diameter in 1-100 of an Inch. Weight per Lineal Rod. 4 lbs. 2 OZS. 3 " 10 " 2 " 15 " 2 " 8 " 2 " 5 " 1 " 15 '' 4 " 9 " Nos. 1 8 9 10 11 12 1 13 Diameter in 1-100 of an Inch. .18 .16 .15 .13 .12 .10 Weight per Lineal Rod. 1 2 3 4 5 6 .32 .30 .27 .25 .24 .22 1 lb. 4 OZS. 1 " " «« 14 " " 10 " " 9 " ♦« 6 " 7 .20 1 33 R^ H A. T A. . Page 35. — To find tiik Solidity of a Pyramid or Cone. Role.— Multiply the area of the base by the height, and one-ihird of the product will be the solid eoiilenl. ExAMPi-E.— Required the solid conlent in inches of a Cone or Pyramid, the diameter of the base being 8 inches, uiid perpendicular height 18 inches ? &X8 = 0IX .7854X19 = ''*'>' "^03^ 3 =301 59.% inches -^ 2.31 = 1 gall, li qts. Page 92 No. 38.— For Tin 61 lbs. Copper I lb. rtad Copper 64 lbs. Tni 1 lb. GETTY CENTER LIBRARY CONS T 49 B98 1861 *5 c 1 Butts. I R (Isaac The tinman- s manual and Builder s and me 3 3125 00181 4025 ?^:v:MliSa=iP ] \