Class 7 qCsOO Book k_2 copjgtitN°_ ^y^ COPYRIGHT DEPOSIT. THE TINSMITH'S HELPER AND PATTERN BOOK WITH USEFUL RULES, DIAGRAMS AND TABLES BY H. K. VOSBURGH Revised by WILLIAM NEUBECKER SE I 'EX TH EDI TION NEW YORK DAVID WILLIAMS COMPANY 239 West 39th Street 1912 r Copyright, 1906 BY DAVID WILLIAMS CO. Copyright, 1912 BY DAVID WILLIAMS CO. y\ . ■ 6 £CIA312022 INTRODUCTORY. The aim in preparing this little manual has been to make it a guide for the apprentice, journeyman and master sheet metal worker. To this end the author col- lected everything of value on the subject and then boiled it down to a well arranged series of simple problems on the different phases of pattern drafting which the mechanic has to puzzle over daily. The section on Mensuration will be found both accu- rate and complete and the rules and examples are reduced to the plainest language so that any one may understand them. Realizing the value of reliable data, he included all the tables of weights of materials, measures of area, capacity, etc., to which the sheet metal worker has occa- sion to refer, together with many excellent recipes, formulas and rules, which will be found of great service. The present edition has been carefully edited and revised by William Neubecker, expert pattern cutter and instructor at the New York Trade School. While the greater portion of the work remains intact, quite a num- ber of important changes have been made, to insure greater accuracy, and many simpler methods have been included. The Publishers. December 6, 191 1. INDEX PAGE Aluminum and copper sheets, relative weight 96-97 Aluminum solder 120 Apothecaries' weight table 109 Arc, to find the center of 7 Areas and circumferences of circles 98-104 Arithmetical signs, definitions 74 Avoirdupois weight, table 109 Balls, to. describe gores for pattern 32 Black sheet iron, standard gauges 89 Boiler block, description of 66 Boiler, oval, to find length of sheet required 26 Breasts for cans, to describe 10 Can breasts, pattern for 1 1-12 Cans one inch deep, capacity of 106 Capacities of bodies, mensuration of 85 Cement for apparatus, corks, &c 1 19 Cement for bottle corks 115 Cement for china 116 Cement for coppersmiths and engineers 115 Cement for cracks in wood 118 Cement for fastening blades, files, &c 119 Cement for fastening brass to glass vessels 119 Cement for holes in castings 115 Cement, iron rust 114 v VI Index PAGE Cement for iron tubes, boilers, &c 114 Cement for ivory, mother of pearl, &c 114 Cement for joining metals and wood 118 Cement for leather 116 Cement for marble workers and coppersmiths 116 Cement for mending earthen and glass ware 1 14 Cement for repairing fractured bodies of all kinds.. . 118 Cement for stone ware 114 Cement, gas fitters' 118 Cement, hydraulic cement paint 119 Cement, marble 116 Cement, plumbers' 115 Cement to mend iron pots and pans 117 Cement to render cisterns and casks water tight. ... 117 Cement to stop a leaky roof 119 Cement, transparent for glass 117 Center of an arc, to find the 7 Circle, to describe octagon within 9 Circles, mensuration of 79-83 Circles, tables of circumferences and areas 98-104 Circumferences and areas of circles 98-104 Cisterns and tanks, number of barrels in.. . . 107, 108, 109 Coffee pots, tables of sizes ill Cone, old German rule for patterns 18 Cone, pattern for 13 Cones and pyramids, to find the convex surface of . . 84 Cones and pyramids, to find the solidity of 86 Cones, mensuration of 73 Copper sheets, weight 9°~97 Cover, oval boiler, pattern for 2y Index vii PAGE Cubes, mensuration of 72 Cylinders, mensuration of 7°~7 l Cylinders, to find the convex surface of 83-84 Cylinders, to find the solidity of 86 Cylindrical measures 105 Cylindrical vessels, to find the contents in gallons of. 86 Decimal equivalents to fractional parts of lineal measurement 75 Definitions of arithmetical signs 74 Dippers, tables of sizes in Dish kettles and pails, tables of sizes in Druggists' and liquor dealers' measures, tables of sizes in Dry measure, table no Elbow in five sections, pattern for 58 Elbow, obtuse, to describe pattern for 60 Elbow, tapering, to describe 61 Elbow, to describe, quick method 53 Elbow, three piece, to describe 54 Ellipse or oval, to find the area of an 83 Ellipse or oval, to find the circumference of an 83 Ellipses, mensuration of 73 Flaring article, square top, rectangle base, to describe pattern 46 Flaring article, top and base rectangles, pattern for. . 48 Flaring article, with straight sides and round ends, to describe patterns 42 Flaring hexagon article, to describe pattern 44 Flaring oval vessel, two pieces, to describe pattern. . 40 Flaring square vessel, to describe pattern 45 viii Index PAGE Flaring tinware, to describe patterns for 16 Flaring vessel in three pieces 20 Flaring vessels, to describe pattern for 14 Flux for soldering tin roof 119 Four-piece elbow, to describe 56 Frustum of a cone, pattern 19-21 Frustum of a cone, to find the contents in U. S. standard gallons 87 Frustum of a cone, to find the solidity of 87 Frustum of a pyramid, to find the solidity of the. . .87-88 Frustums of cones, mensuration of j$ Funnel, rectangular, pattern for 22 Galvanized sheets dimensions 91 Galvanized sheets, weight 91 Gores for balls, to describe pattern for 32 Heart with square and compass 30 Hexagon article, flaring, to describe pattern 44 Hood for stove pipes, to cut 15 Iron, black sheet, standard gauges 89 Iron plate, weight of 89 Lead pipe, weight per foot 92 Lead, sheet, weight of 90 Lineal measurement, decimal equivalents to frac- tional parts of 75 Liquid measure, table no Measure, lip, pattern 28 Measures of capacity, dry no Measures of capacity, liquid no Measures of weight, Avoirdupois 109 Measures, tables of sizes in Index ix TAGE Mensuration, epitome of. 69 Mensuration of the circle, cylinder, sphere, &c 69-71 Mensuration of ellipses, cones, frustums, &c J$ Mensuration of solids and capacities of bodies 85 Mensuration of the square, rectangle, cube, &c 71-72 Mensuration of surfaces 76 Mensuration of triangles, polygons, &c 72 Metric system, and U. S. measures compared 110 Obtuse elbow, to describe pattern for 60 Octagon, tapering, to describe 47 Octagon, within circle, to describe 9 Octagon, within square, to describe 8 Oval boiler cover 27 Oval boiler, to find length of sheet 26 Oval flaring vessel, four pieces, to describe patterns. 43 Oval, to describe 34 - 3°\ 37 Oval, to describe by string, pins and pencil 38 Oval with diameters as 5 to 8, to describe 35 Pans, table of sizes in Pipes of various metals, weights 91 Pitched cover, pattern for 29 Plate iron, weight 89 Polygons, mensuration of 72 Polygons, to find the area of regular 78 Rectangle, mensuration of a 7 l ~7 2 Rectangular base and round top article, pattern for. . 50 Rectangular funnel, pattern 22 Right angle elbow, to describe 52 Round base and square top article, pattern for 49 Round top and rectangular base article, pattern for. . 50 X Index PAGE Round top and square base article, pattern for 51 Rules for calculating circumferences 107 Scale tray or scoop, pattern for 24 Scoop or scale tray, pattern for 24 Sheet lead, weight . 90 Sheet zinc, weight per sheet 95 Solder, aluminum 120 Solder, black 113 Solder for copper 113 Solder for steel joints 113 Solder, hard 113 Solder, pewterers' 113 Solder, plumbers' 113 Solder, silver 112 Solder, silver, for plated metal 113 Solder, soft gold 113 Solder, tinners' 113 Solder, white for raised Britannia ware 112 Solder, white for silver 112 Solder, yellow for brass or copper 112-113 Soldering fluid or flux 120 Solids, mensuration of 85 Sphere, mensuration of the J^l 1 Sphere, to find the solidity of a 88 Spheres, to find the convex surface of 85 Square base and round top article, pattern for 51 Square, mensuration of a 71 Square, to describe octagon within 8 Square top and round base article, pattern for 49 Square vessel, flaring, to describe pattern 45 Index XI PAGE Star, pattern for 31 Steamer or pitched cover, pattern 29 Strainer pail or watering pot breast, pattern 23 Stringing patterns, mode of 64 String pattern 65 Surface, mensuration of 76 Table, capacity of any cylindrical measure 105 Table, effects upon bodies by heat 112 Tables, circumferences and areas of circles 98-104 Tables, rules and recipes (See special subject) 89 Tapering elbow, to describe 61 Tapering octagon, to describe 47 Tea kettle body, to obtain length of piece 63 Three-piece elbow, to describe a 54 Tin plates, net weight per box 93~94 Triangles, mensuration of y2 Triangles, to find the areas yy Wash bowls, table of sizes in Water pressure per square inch 109 Water, weight of 107 Watering pot breasts, pattern for 23 Weights of materials (See various materials). Weights of various substances no Zinc, sheet weight of 95 DIAGRAMS AND PATTERNS. To Find the Center of an Arc. Fig. i. Let H K represent the given arc. Span dividers any convenient radius and describe small arcs, as V O. Draw lines through them, as shown by dotted lines, and the in- tersection, S, will be center sought, Rules and Diagrams. To Describe an Octagon Within a Given Square, Fig. 2. Draw diagonal lines from corner to corner and the in- tersection is the center H. With the compasses set to a radius from center to corner, and one foot set successively at each corner, describe the arcs, as shown. The points at which they cut the square, as K V, will be the corners of the octagon. Draw lines from point to point to complete the figure. Rules and Diagrams. To Describe an Octagon Within a Given Circle. Fit- 3- ^ — sr« «=^-^^ \s e // > ' ^\. // \\ // \\ // \\ // \\ [' / v j V\k Ja \\ v/7 \ \ \ \ / 1 1 V / \_ V / ^ ^ ^ Draw lines at right angles passing through the center H. This divides the circle into four equal parts, which need only to be subdivided into equal parts again 'to form the corners for the octagon. This may be easily done by drawing the lines K V, bisecting, as shown, and drawing lines to the circle. The bottom will correspond in size to the size of the circle or square. Remember to allow for burr and double seam. io Rules and Diagrams. To Describe Breasts for Cans. Fig. 4. Draw horizontal line II K, another parallel to it, V O, making- the distance between the desired hight of breast. On H K lay off diameter of can, as S B. On V O, size of opening as U R, produce lines B R, S U, until they cross G. Span dividers from G to S, describe outer circle. G to U, describe inner circle. Set off outer circle equal to the diameter of the can B S. Starting at B, draw line from G, allowing for locks, as shown by dotted lines. Reference can be made to the circumference table. Rules and Diagrams. Can Breasts. Fig- 5- 11 Draw the two horizontal lines, K V and O S, and per- pendicular to them the line K H. Set off on line K V from the point K one-half the diameter of the can. On O S the point R is one-half the diameter of the opening. Produce the line U G, touching the points B and R, until it intersects H K. From U as center, with the radius U B, describe the outer circle. With the radius U R, the inner. Then span from K to B and step six times on large circle to obtain size of breast. Draw line to center and al- low for locks, as shown by dotted lines. 12 Rules and Diagrams. Can Breasts. Fig. 6. Describe circle size of can. Draw line through center H. Span dividers three-fourths of diameter and strike circle K V. Span to diameter of can and step three times on large circle. Draw line from center to points K V, allowing for edges and locks. For more or less pitch make circle K V larger or smaller. Small circle in center for opening in top. Hoods and pitched covers may be cut by same rule. Rules and Diagrams. 13 Pattern for Cone. Fig- 7. H K V represents a cone for which an envelope is wanted. Span the dividers from V to H and describe the arc O S. Set off the arc equal in length to the circumference of the required cone. Draw the lines V O and V S, allow- ing for locks or laps, as shown by the dotted lines. For the circumference, refer to the tables or obtain by some of the rules. By using the rules familiarity with them is obtained, which is desirable. M Rules and Diagrams. To Describe Pattern for Flaring Vessels. Fig. 8. For example, it is desired to describe pattern for pail 12 inches in diameter at top, 9 inches at bottom and 9 deep. Take the difference between large and small diameters (3 inches) for the first term, the hight for the second and the large diameter for the third, thus, 3 : 9 : : 12. 12x9^-3, this gives radius by which the pattern may- be described. Span the dividers (or use beam compasses, piece of wire, straight edge or any convenient device) 36 inches and strike large circle. With radius less the slant hight of pail strike small circle. Ascertain the cir- Rules and Diagrams. 15 cumference required and divide by the number of pieces to be used. Lay off on outer circle and draw lines to cen- ter, as H K V. Allow for locks, burr and wire. To Cut Hood for Stove Pipes. Span dividers size of pipe, describe circle, cut in to center, lap over and rivet. Rules and Diagrams. To Describe Patterns for Flaring Tinware. Fig. o. By this figure and rule can be drawn any article of flar- ing tinware of any diameter, large or small. It is a rule of more extensive application than any other for getting correct patterns for frustums of a cone. It is the foun- dation for all curved work, cornice, bevels, chamfers, etc. H K V O represents the elevation of an ordinary tin pan, constructed in four pieces, 15J/2 inches in diameter at the top. Below the elevation is shown the same in plan ; the pan is a frustum of a cone, and if the sides of the pan Rules and Diagrams. iy were continued down until they intersected at S, as shown, the cone would be complete. The radius of the envelope of the cone must be either S H or S K. To describe the section of the frustum which is required, place one foot of the dividers at the center S, and with the radius S H de- scribe the arc K B. With the radius S V describe O U. This gives the width of pattern and the proper sweep. To get the length of the piece, refer to the table of circumferences or find, by the rules given, the circumfer- ence of the article, which in this case is 48^6 inches. There being four pieces, divide by four, which gives 12 5-32 inches; span the dividers 1 inch, step off the 12 and add the fraction. Draw line from center S to point last ascertained. For locks, wire edge and burr allowance must be made. 18 Rules and Diagrams. The Old German Rule for Patterns for the Cone. Fig. io. Take the slant hight of the cone H K as a radius, and describe a circle. Divide the diameter of the base of the cone K V into seven equal parts and set off a space equal to twenty-two of these parts on the circle already struck. From the extremities thus measured off draw lines to the center. Allow for locks. Rules and Diagrams. Frustum of a Cone. Fig. ii. 19 Lay the square on your sheet and construct the right angle H K V. Draw line O S parallel to K V, making the distance K O the altitude. On these lines lay off one-half the diameter of the large and small ends. Draw line through points V and S until they intersect at H ; then, with H as the center, describe the semicircles B U, R G. Lay off circumference of large end on line B U and draw lines to center H. Must allow for all edges. For two sections take one-half of the piece, allowing edges on piece used for pattern. 20 Rules and Diagrams. Flaring Vessel in Three Pieces. Fig. 12. Draw line H K ; perpendicular to it, lines parallel to each other apart the hight of vessel. With the intersec- tions, as V, O for centers, describe circles size of top and bottom of vessel. Draw lines S H and B H touching on circles, and at intersection H as center, with the radius H V, describe the segment U R ; with the radius H O, the segment G F. Allow for locks, as shown by dotted lines. Rules and Diagrams. 21 Frustum of a Cone Fig- J 3- Draw perpendicular line H K, and from K lay off diameter of large end, as V O ; on the line H K the hight of frustum, as K S. Draw line parallel to V O, and on it lay off small diameter, as B U. Draw lines through points V B and O U until they intersect at H. Span compasses from H to V and draw large arc R G ; from H to B and describe small arc ; make arc R G equal to circumference of large diameter and draw lines to center H. Allow for all edges, wire, burr and locks. This forms a pattern in one piece. 22 Rules and Diagrams. Rectangular Funnel. Fig. 14. K Draw side, as H K V. Continue side lines, as shown by dots. From point of intersection as center, describe arc and chord K V and H. Draw end O K S, producing lines to intersect at B. From B as center describe arc and chord O K and S. The other side and end obtained in the same manner, as shown in cut. Can be made in two or more pieces by dividing. All locks and edges must be allowed for on the pattern piece. Rules and Diagrams. aj For Strainer Pail or Watering Pot Breast. Fig- *5- Strike circle size of pail or pot. Span dividers ij4 inches, more or less, than radius of circle, being governed by pitch desired, as from V to K, and describe the arc. Draw the chord, making the segment K O which is the pattern of the desired width. The breast may be cut out if preferred, as shown by dotted lines. 24 Rules and Diagrams. Scale Tray or Scoop. Fig. 16. Construct a sectional view of the scoops, as H K V; it being made in two pieces as O, let H S B represent one-half elevation of it. Continue the lines B S and K H until they cross at U. Divide H K V into any given number of spaces, continuing the same to the line H B, as shown by short lines. Draw lines from the division Rules and Diagrams. 25 points on H B to the joint U, thus obtaining the inter- sections on the line S H. With the T square at right angles with H U, drop the points thus obtained on H S, onto the line B S. With U as center and U B as a radius describe the arc B R. Step off upon this arc spaces equal to those in H K V, using dividers, which gives the length B R. Draw radial lines from U to space marks on line B R, as shown. With U as center and the various points on S B as radii, describe arcs, intersecting similar radial lines as shown. Then a line traced through the points thus obtained, together with the arc B R, will be the outline of the required pattern. Allow for edges, as shown by dotted lines. 26 Rules and Diagrams. To Find Length of Sheet Required for Oval Boiler. Common Method. Fig. 17. Describe bottom, length and width desired, then burr and from H as a starting point roll on the bench to obtain circumference. If three piece- are to be used, divide the circumference into three parts and allow edges; if made in two pieces, divide by two. Always divide the circum- ference by the number of pieces desired. Cut the cover the same size as bottom. Rules and Diagrams. 27 Oval Boiler Cover. Fig. 18. Draw line A K, and from R as center describe circle G U, size of boiler outside of rod. Make A K equal to one-half of entire length of boiler, and KS ^ inch or more if more pitch is desired. Through S draw the per- pendicular line H V. Lay corner of square on line H, one blade at K, the other touching circle, describe lines U H K; in similar manner obtain K V G. Allow for locks and notch for edges. 28 Rules and Diagrams. Measure Lip. Fig. /o. Draw line H K and upon it, with V as center, describe circle size of measure. With S as center, being the half distance from V to H, describe semicircle B. U. Make R K the desired width. With V as center describe G O. Cut on B U and G O to obtain the lip. Rules and Diagrams. 29 Steamer or Pitched Cover. Fig. 20. Strike circle 1 inch larger than rim burred. Draw line through center H, and from either side cut 1 inch on circle to 1 inch from center K. Draw lines and cut out. Or, strike circle the same or larger. Draw line through center and cut on it to center. After burring put in rim; draw up and mark, cut out triangular piece and solder, Much quicker and equally as good. 30 Rules and Diagrams. Heart with Square and Compass. Fig. 21. Draw line H K the breadth of the heart and on it two semicircles. Span dividers from H to K and make sweep toV. Rules and Diagrams. 3* To Describe a Star. Fig. 22. From V as center strike circle size of star desired. Divide circle in five parts and draw lines to points. There is a rule for finding the points of a star other than stepping, but I do not give it. I have found the mode given to be the quickest and most accurate. 32 Rules and Diagrams. Pattern for Cutting Balls. — To Describe the Gores. Fig- *3- Erect perpendicular line H K equal to one-half the cir- cumference oi the ball; divide this line into one-half the number of pieces required in full ball ; make the line Y O equal to one of these pieces, cutting H K through the center at right angles; then with II and K as centers, with radius greater than one-half the distance K S, describe the two arcs B U; with V and O as centers, arcs R G; draw Rules and Diagrams. $$ lines through these points, as shown by dotted lines. From points of intersection describe arcs H V K and H O K, and you obtain pattern for one piece. Allow for laps or seams. The more pieces used the better globe produced. Good results obtained by slightly raising the pieces. 34 Rules and Diagrams. To Describe an Oval. Fig. 24. Draw horizontal line F K, span the dividers one-third the required major diameter, and from V and O as centers describe circles, as shown; then span dividers two-thirds entire length, and, with one foot at the intersection of the circles, as S and B, draw the arcs G H and U R, which completes the oval. The proportion of the diameters is about as 3 to 4. Rules and Diagrams, 35 To Describe Oval with Diameters as 5 to 8. Fig- 2 5- Draw horizontal line H K. Span compasses one- quarter the long diameter and describe three circles with that radius, as shown by diagram. Then draw lines through centers of outer circles and their intersections, as shown. The oval is completed by drawing the arcs con- necting the outer circles from points V and O as centers. 3« Rules and Diagrams. To Describe an Oval. Another Method. Fig. 26. Draw horizontal line H K and perpendicular to it V O. Let H K equal the long or transverse diameter, and S B the short or conjugate. Lay off the distance S B on the line H K, as from H to U. Divide the distance U K into three equal parts. From R, the center, set off two of the parts each side, as G F. On the line Y O set off the dis- tance G F from R, as R Y and R O. From V and O draw lines passing through G and F, as shown. From the points V, O, G, F as centers describe the arcs that complete the ellipse. Rules and Diagrams. To Describe an Oval. Another Method. Fig. 27, 37 Construct the parallelogram equal in length and width to the long and short diameters of the oval desired. Di- vide it into four equal parts by drawing lines through the center, crossing at H. Mark the points K and K one-third the distance from V to H, and draw lines from the corners through these points until they intersect, as shown at O. Then from O and O as centers describe the arcs SUB and SUB; from K and K as centers the segments B V B and S V S. 38 Rules and Diagrams. To Describe Oval by Means of String, Pins and Pencil. Fig. 28. Erect perpendicular line H K equal to short diameter and at right angles to it V O. Span dividers one-half the length of the oval, and with H and K as centers describe the arcs S and B. Set pins at these points, and, with a string (one that will not stretch) tied around them so that the loop when drawn tight will reach H or K, as shown, draw the figure with pencil, keeping string equally tense while going around. Of all the apparatus invented Rules and Diagrams. 39 for oval drawing I think the string is the best. The best results, at least, are obtained. To attempt to draw a per- fect oval or ellipse by the use of compasses is vain. It cannot be done so that the line will be true, or the propor- tion or shape satisfactory to one with an eye for correct- ness or uniformity. The so-called trammels are the next best thing, but no better. A few rules for drawing ovals by the use of dividers have been given in this work so the mechanic may take his choice, and after a little prac- tice with the string and nails will find them the best tram- mels yet invented for the purpose. 4° Rules and Diagrams. To Describe Pattern for Flaring Oval Vessel. Two Pieces. Fig. 29. Draw plan according to rule given in Fig. 24, or any other method. Construct right angle triangle T H 1 S 1 and parallel to H 1 S\ draw H 1 O 1 , the distance between hight of article. Lay off on H 1 S 1 the distances H S and V S in plan and on H 1 O 1 the distances H O and V O in Rules and Diagrams. 41 plan. Draw lines through these points to intersect the line R 1 T at U and T. Using T as center draw the arcs O 1 K 1 and S 1 R\ making the distance along the arc S 1 R 1 equal to U R in plan. Draw line from R 1 to T. Take radius V 1 U on the lines R 1 T and S 1 T and obtain centers B and C. with which describe the arcs R 1 G 1 and S 1 G\ which make equal in length to G R or U B in plan. Draw lines to centers B and C. Allow for all edges, locks, wire and burr. 42 Rules and Diagrams. To Describe Pattern for Flaring Article with Straight Sides and Round Ends. Two Pieces. Fig- 30. Erect two perpendicular lines, H V, K O, distance between the length of sides A B ; at right angles to these, two lines, distance between the slant highl of article C D. On II V and K O set off the radius C E as Y and O. From V and O as centers, with radii V B, V II and O S, < » K, draw the arcs B J, H G and S U, K R. Make the arcs H G and K R equal to one-half the circumference of the ends M N and draw lines to Y and O. Allow for all edges, locks, wire and burr. Rules and Diagrams. To Describe Pattern for Oval Flaring Vessel. Four Pieces. Fig- 3*- 43 Describe bottom as by Fig. 27. Obtain length of arcs SUB and S V S, also length of corresponding arcs at the top of vessel. Draw horizontal lines H K and V O, making the distance between the desired slant hight. Make H K equal in length to that of the piece at the top, and V O to that of the bottom, for the sides. S B and U R for the end pieces. Produce lines through these points to intersect at G and G\ Describe the arcs from these points. Allow for all edges, locks, wire and burr. 44 Rules and Diagrams. To Describe Pattern for Flaring Hexagon Article. Fig. 32. Let V O represent width of the bottom of one side and R G the width of the top of one side, the distance between the slant hight. Produce side lines until they cross in the center, as shown by dotted lines. Span dividers from center to O, and describe circle H O U; span to G and describe inner circle ; span again from V to O and step on the outer circle three spaces each side from O, as K, H, B, S, U. Draw lines from these points tending toward center, and connect by chords as H K, K O, etc. Cut out piece H U, allowing for locks, as shown. Pattern for a pentagon article may be described bv the same rule. Rules and Diagrams. 45 To Describe Pattern for Flaring Square Vessel. Fig- 33- Let K Y and B U represent the width of the bottom and top of one of the sides, the distance between the slant hight. Continue lines until they intersect at R. With radius R B. strike circle U B G. Span dividers from K to V ana set orr on outer circle the distance, as V O, K S, etc. ; draw lines through these points tending toward the center R, also the chords, as shown by dotted lines. Allow for edges. Can be made in two pieces by dividing and allowing for extra lock or seam. 46 Rules and Diagrams. To Describe Pattern for Flaring Article with Square Top and Base a Rectangle. Two or Four Pieces. Fig- 34- Draw rectangular base H K and square top Y in center of base. Draw perpendiculars O S and R U. Also place the hight of the article O B and R G. Place the slant hight B S on B 1 S 1 and draw lines a and b which intersect as shown, which gives pattern for end. Place G U on G 1 U 1 , draw lines a' and b' which intersect as shown, which gives pattern for side. Join half of end pattern to either side of side pattern as shown by similar letters, which gives half pattern. Rules and Diagrams. 47 To Describe Tapering Octagon Article. Fig- 35- Draw bottom K II and top V of one side, with dis- tance between the slant hight, and continue side lines until they intersect at O. With O as a center and the radii O V and O H, describe inner and outer circles. Set off on them distances equal to H K and V, and connect by chords, as shown by dotted lines. Allow for locks and edges. 4 8 Rules and Diagrams. Flaring Article, Top and Base a Rectangle. Two Pieces. Fig- 3<5. Draw side elevation, as H K, V O, of the longest side. Span dividers the difference between the shortest side of the base and longest side of top. From Y and O as cen- ters describe arcs S and S. With blade of square resting on arcs and the corner at 1 1 and K, draw lines H B and K G. Set off H B and K G equal one-half of shortest sides of base and draw lines B U and G R at right angles to H B and K G ; also lines U V and R O at right angles to U B and G R. Allow for locks, as shown by dotted lines. For a strictly accurate pattern proceed as in Fig. 34. Rules and Diagrams. 49 Round Base and Square Top Article. Two Pieces. Fig. 37- Erect perpendicular lint. Span dividers to three- quarters diameter of base and describe semicircle H K V. Make K V and K H each equal to one-quarter the circum- ference of the round base and draw lines to center. Span dividers to three-quarters size of top from corner to cor- ner and describe inner circle. Lay out sides of top, size required, on circle, as shown. Allow laps. 5° Rules and Diagrams. Rectangular Base and Round Top Article. Two Pieces. Fig- 38- Draw horizontal lines H K, V O. Make H K equal to the longest side of base, V O equal to one-fourth the circumference of the top, the distance between slant hight ; draw side lines through these points. With radii one-half the difference between V O and the shortest side of the base, describe the arcs S, B ; with blade of square resting on arcs, and corner at H and K, draw lines K R, H U, equal to one-half the short side ; at right angles to K R, H U, draw lines R G and U G ; U G and R G pro- duced will intersect ; from this point span dividers to line V O and describe the arc. Allow for locks and edges. Rules and Diagrams. 5* Square Base and Round Top Article. Two Pieces. 'Pig- 39- Draw horizontal lines H K, V O; H K equal to the length of one side of the base, V O equal to one-fourth the circumference of the top, the distance between the slant hight ; draw lines through these points. With radii one-half the difference between K H and O V, describe arcs ; with blade of square resting on arcs and the corner at H and K, draw lines H S and K B, equal to one-half the base ; at right angles to H S and K B draw S U and B R, produced to intersect at G. Span dividers from G to line V O and describe the arc. Allow for locks and edges. 5 2 Rules and Diagrams. To Describe a Square or Right Angle Elbow. Two Pieces. Fig. 40. Draw the elevation of the elbow, as B S, O V, K H. Draw line from V to O. Divide one-half of the plan into a convenient number of equal parts, as shown by dotted lines ; erect lines to intersect O V. Make the line B R equal rn length to the circumference of the elbow. Set off on this line spaces corresponding to those in the plan, the same number each side of the center line ; then draw lines parallel to the arm of the elbow, cutting the corresponding lines as indicated. By tracing through these points the irregular line U G the pattern is obtained. Allow for locks or rivets. The general principle for cutting elbow patterns is the same throughout, and to understand the principle is to be able to describe pattern for any elbow, at any angle and of any number of pieces. It is the design of this work to make the principle clear. Rules and Diagrams. 53 Quick Method. Fig. 4i> K T U /f] V B Lay out on sheet length required for elbow, as H K V O. Describe semicircle S the desired size of pipe, which divide into four parts. Space the length of the sheet into twice the number of squares in S, and draw vertical and horizontal lines until they intersect. OBU R V is then an accurate pattern. Allow for flanges. 54 Rules and Diagrams. To Describe Three-Piece Elbow. Fig. 42. Let H K be the throat and K V the diameter of the elbow. Draw the quadrant Y O, which divide into four equal parts, as shown by i, 2, 3. Draw miter lines through 1 and 3 as H R and H G. Draw the circle B equal to diameter of elbow and divide one-half of B in equal parts, as shown ; draw lines to intersect miter line R U. Rules and Diagrams* 55 Fig. 43- _R_ R' 9 8 7 6 5 4 8 4 5 6 7 8 Construct parallelogram H K V O equal in length to the circumference of B. Through the spaces on H K draw parallel lines as shown. Measuring from V K, take the various distances to the miter line R U and place them on similar lines measuring from H K. H S B K is then the pattern for the end. Double the distance from 3 to R 1 and place it from S to G and B to U and transfer the miter line S R 1 B to G R U. Place H S as shown by G O and U V and draw O V, which completes the three patterns. 5* Rules and Diagrams. To Describe a Right Angle Elbow. Four Pieces. Fig. 44. v b Let H K be the throat and K V the diameter of the elbow. Draw the quarter circle V O, which divide into six equal parts, as shown by a b c d e. Draw miter line* through a, c and e, as shown by II B, H G and H F Draw the circle R, which space as shown, and draw lines to intersect the miter line B U. Rules and Diagrams. 57 Fig- 45- 7 6 5 4 3 4 5 t> 7 Construct parallelogram H K V O, equal in length to the circle R, as shown by similar figures on H K, through which draw parallel lines as shown. Measuring from V K, take the various distances to the miter line B U and place them on similar lines in the pattern, measuring from H K, and obtain B S B. Double i S and place at B U and B U and trace the miter cut B S B as shown by U G U. Place S G at U T and U T and trace UGU as shown by T A T. Make T O and T V equal to S i and draw line O V, which completes the four patterns. Allow for locks. 5» Rules and Diagrams. Elbow in Five Sections. Fig. 46. Draw throat H K and diameter K V. Draw quad- rant H Y R, which divide into eight parts as shown from a to g ; draw miter lines HU,HB,HS and H O. Divide profile A into equal spaces, and draw lines to miter line HO. Rules and Diagrams. 59 Fig- 47- F C — < u o G B H K 3 4 5 6 7 5 4 3 2 1 Make I i equal to circumference of profile A. Draw parallel lines as shown in pattern. Use dividers and meas- ure various distances from V K to miter line H O, which transfer to similar lines measuring from i i, and obtain miter cut H K V. Double 7 K and place at H O and V S and draw miter cut O B S. Place KBatOU and S R and draw miter cut U G R. Make U A and R D equal to H O and draw miter cut A C D. Make A F and D E equal to H i and draw F E, which completes the five pat- terns. Allow for locks. 6o Rules and Diagrams. To Describe Pattern for Obtuse Elbow. Fig. 48. When the pattern for an obtuse elbow is desired it it only necessary to draw a correct representation of the elbow and obtain the miter line, as follows : With H as center, draw the arc K V. With any desired radius, and using K and V as centers, intersect arcs at O. Draw the miter line H O S. Place the half profile B in position as shown, which space, and draw parallel lines to the miter line H S. Then proceed as by the rules already given, and the result will be satisfactory. Rules and Diagrams. 61 To Describe a Tapering Elbow Fig. 49. 62 Rules and Diagrams. Draw elevation of elbow at any angle desired and draw miter line H K as shown. Establish hight and diam- eter of small end as Y O and extend the lines i-V and 7-O until they meet at B. Draw half profile S, which space into equal parts and draw vertical lines to 1-7, from which draw radial lines to the apex B, which will cross the miter line H K as shown. From these intersections draw horizontal lines to the side B-7 as shown from 1 to 7. With B-7 as radius, draw the arc y'-f equal to the circumference of the circle S. From the points on j'-J draw radial lines to the apex B, which intersect by arcs struck from B as center, with radii equal to the points between 1 and 7. U R G O is the pattern for the upper arm and R G y'-y' pattern for the lower arm. Allow for locks. Rules and Diagrams. «3 To Obtain Length of Piece for Tea Kettle Body Fig. 50. \ ,—. (' -J u '7 The way in general practice is to roll the bottom after burring on the bench to obtain circumference, and use strip 24 i ncn l ess m length, as shown by figure. H repre- sents the pit ; K V the length of the strip or sheet. $4 Rules and Diagrams. Mode of Stringing Patterns. Fig- 51- This cut represents the three pieces of a 6-quart pan usually cut from one sheet of 10 x 14 tin. Instead of using one piece for pattern and placing it three times, three pieces are fastened together by soldering on two strips of tin with a heavy hem on each side, and all placed at once, thus saving time and vexation. To use to advantage begin at the bottom of the string pattern and mark around on the outside first, and then mark in the centers. Rules and Diagrams. 65 String Pattern. Fig. 5 2 - H2 This figure represents a string of rim or hoop pat- terns, fastened as shown in the same manner as described on page 64. Rims of any width can be put together in this manner and a great saving of time is the result when once properly done. Patterns for all articles of tinware should be strung in this way, when more than one piece is obtained from a sheet, that the marking out may be ex- pedited and less tedious. 66 Rules and Diagrams. Description of Boiler Block. Fig- 53- Tiy this figure is represented a block for truing - up boilers after they are formed up in the rollers and locked together. Many mechanics depend upon the stake and the accuracy of the eye, but after using this method would not abandon it, as better results are obtained and in much less time. The block is made of 2-inch [lank, by placing one on another and securing with four long bolts passing through them. The proper dimensions are as follows : Bottom, 13 inches wide, 25 inches long. Top, 10 " " 19 " Hight, 12 " APPENDIX. EPITOME OF MENSURATION. OP THE CIRCLE, CYLINDER, SPHERE, ETC. i. The circle contains a greater area than any other plane figure bounded by an equal perimeter or outline. 2. The areas of circles are to each other as the squares of their diameters. 3. The diameter of a circle being 1, its circumference equals 3.1416. 4. The diameter of a circle is equal to .31831 of its circumference. 5. The square of the diameter of a circle being 1, its area equals .7854. 6. The square root of the area of a circle multiplied by 1. 1 2837 equals its diameter. 7. The diameter of a circle multiplied by .8862, or the circumference multiplied by .2821, equals the side of a square of equal area. 8. The number of degrees contained in the arc of a circle multiplied by the diameter of the circle and by .008727, the product equals the length of the arc in equal terms of unity. 9. The length of the arc of a sector of a circle multi- plied by its radius equals twice the area of the sector. 10. The area of the segment of a circle equals the area of the sector, minus the area of a triangle whose vertex 70 Epitome of Mensuration. is the center and whose base equals the chord of the seg- ment. 1 1. The sum of the diameters of two concentric circles multiplied by their difference and by .7854 equals the area of the ring or space contained between them. 12. The circumference of a cylinder multiplied by its length or hight equals its convex surface. 13. The area of the end of a clyinder multiplied by its length equals its solid contents. 14. The area of the internal diameter of a cylinder multiplied by its depth equals its cubical capacity. 15. The square of the diameter of a cylinder multiplied by its length and divided by any other required length, the square root of the quotient equals the diameter of the other cylinder of equal contents or capacity. 16. The square of the diameter of a sphere multiplied by 3.1416 equals its convex surface. 17. The cube of the diameter of a sphere multiplied by .5236 equals its solid contents. 18. The hight of any spherical segment or zone, multi- plied by the diameter of the sphere of which it is a part and by 3.1416, equals the area or convex surface of the segment ; or, 19. The hight of the segment multiplied by the cir- cumference of the sphere of which it is a part equals the area. 20. The solidity of any spherical segment is equal to three times the square of the radius of its base, plus the square of its hight. multiplied by its hight and by .5236. 21. The solidity of a spherical zone equals the sum of the squares of the radii of its two ends and one-third Epitome of Mensuration. 71 the square of its bight, multiplied by the hight and by 1.5708. 22. The capacity of a cylinder, 1 foot in diameter and 1 foot in length, equals 5.875 United States gallons. 23. The capacity of a cylinder, 1 inch in diameter and 1 foot in length, equals .0408 United States gallon. 24. The capacity of a cylinder, 1 inch in diameter and 1 inch in length, equals .0034 United States gallon. 25. The capacity of a sphere 1 foot in diameter equals 3.9168 United States gallons. 26. The capacity of a sphere 1 inch in diameter equals .002266 United States gallon ; hence, 2J. The capacity of any other cylinder in United States gallons is obtained by multiplying the square of its diame- ter by its length, or the capacity of any other sphere by the cube of its diameter and by the number of United States gallons contained as above in the unity of its measurement. OF THE SQUARE, RECTANGLE, CUBE, ETC. 1. The side of a square equals the square root of its area. 2. The area of a square equals the square of one of its sides. 3. The diagonal of a square equals the square root of twice the square of its side. 4. The side of a square is equal to the square root of half the square of its diagonal. 5. The side of a square equal to the diagonal of a given square contains double the area of the given square. 6. The area of a rectangle equals its length multiplied bv its breadth, 72 Epitome of Mensuration. 7. The length of a recangle equals the area divided by the breadth ; or the breadth equals the area divided by the length. 8. The solidity of a cube equals the area of one of its sides multiplied by the length or breadth of one of its sides. 9. The length of a side of a cube equals the cube root of its solidity. 10. The capacity of a 12-inch tube equals 7.48 United States gallons. OF TRIANGLES, POLYGONS, ETC. 1. The complement of an angle is its defect from a right angle. 2. The supplement of an angle is its defect from two right angles. 3. The three angles of every triangle are equal to two right angles : hence the oblique angles of a right angled triangle are each other's complements. 4. The sum of the squares of two given sides of a right angled triangle is equal to the square of the hypothe- nuse. 5. The difference between the squares of the hypothe- nuse and given side of a right angled triangle is equal to the square of the required side. 6. The area of a triangle equals half the product of the base multiplied by the perpendicular hight. 7. The side of any regular polygon multiplied by its apothem or perpendicular, and by the number of its sides, equals twice the area. Epitome of Mensuration. 73 OF ELLIPSES, CONES, FRUSTUMS, ETC. 1. The square root of half the sum of the squares of the two diameters of an ellipse multiplied by 3.1416 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 circumference 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 the product of its base multiplied by its altitude or hight. 5. The square of the diameters of the two ends of the frustum of a cone added to the product of the two diame- ters, and that sum multiplied by its hight and by .2618, equals its solidity. DEFINITIONS OF ARITHMETICAL SIGNS USED IN THE FOLLOWING CALCULATIONS. = Sign of Equality, and signifies as 4 + 6 = 10. Addition, " Subtraction, " Multiplication, " Division, ' k Square Root, " to be squared, " to be cubed, " as 6 + 6 = 12, the Sum as 6 — 2=4, Remain- der. as 8 x 3 = 24, Product. as 24 + 3 = 8, Extraction of Square Root. thus 8 2 = 64. thus 3 3 = 27. DECIMAL EQUIVALENTS TO FRACTIONAL PARTS OF LINEAL MEASUREMENT. .8333 .75 .0666 .4166 .3333 .25 ONE INCH THE INTEGER OR WHOLE NUMBER. ,96875 equal T s and 3-32 .46875 equal % and 3-32 9375 T . and 1-16 .4375 " %and 1-16 ,90625 % and 1-32 .4iT.LT, " % and 1-32 S75 % .37r, " % ,84375 % and 3-32 .34375 " V 4 and 3-32 8125 % and 1-16 .3125 " *A and 1-16 78125 % and 1-32 .28125 " y 4 and 1-32 .75 % i' 5 " hi 71875 % and 3-32 .21875 " % and 3-32 ,6875 % and 1-1<; .1ST:. " V 8 and 1-16 ,65625 %and i 32 .15625 " %and 1-32 ,625 ' .12.-. " Vs .59375 & and 3-32 .09375 " 3-32 .5625 & and 1-16 .0625 " 1-16 .53125 .5 ' %and 1-32 .03125 " 1-32 ONE FOOT OR TWELVE INCITES THE INTEGER. 9166 equal 11 inches. .1666 equal 2 inches. 11 inches. .Ki.;t; 10 .0833 9 .<»7L'91 8 .0625 7 " .05208 6 " .04166 5 " .03125 4 .02083 3 " .01041 1 % % 833 7 " .05208 " % MENSURATION OF SURFACES. Mensuration is that branch of Mathematics which is employed in ascertaining the extension, solidities and ca- pacities of bodies capable of being measured. MENSURATION OF SURFACES. To Measure or Ascertain the Quantity of Surface In Any Right Lined Figure whose Bides are Parallel to Each Other. Rule.— Multiply the length by the breadth or perpen- dicular higlit, and the product will be the area or superfi- cial contents. Application of the Rule to Practical Purposes. The sides of a square piece of iron are gji inches in length, required the area. Decimal equivalent to the fraction ]/$ — .875, and 9.875 X 9.875 = 97.5, etc., square inches, the area. The length of a roof is 60 feet 4 inches and its width 25 feet 3 inches ; required the area of the roof. 4 inches = .333 and 3 inches = .25 (see table of equiv- alents), hence, 60.333 X 25.25 = 1523.4 square feet, the area. Epitome of Mensuration. 77 TRIANGLES. To Find the Area of a Triangle When the Base and Per- pendicular are Given. Rule. — Multiply the base by the perpendicular hight and half the product is the area. The base of the triangle is 3 feet 6 inches in length and the hight 1 foot 9 inches ; required the area. 6 in. = .5 and 9 in. = .75, hence, OD _ = 3.0625 2 square feet, the area. Any Two Sides of a Right Angled Triangle being Given, to Find the Third. When the Base and Perpendicular are Given to Find the Hypothenuse. Add the square of the base to the square of the perpen- dicular and the square root of the sum will be the hypothe- nuse. The base of the triangle is 4 feet and the perpendicular 3 feet ; then 4 2 + 3- = 25, V25 = 5 feet, the hypothenuse. When the Hypothenuse and Base are Given to Find the Perpendicular. From the square of the hypothenuse subtract the square of the base, and the square root of the remainder will be the perpendicular. The hypothenuse of the triangle is 5 feet and the base 4 feet ; then 5 2 — 4 2 = 9, and V9 — 3, the perpendicular, 78 Epitome of Mensuration. When the Hypothenuse and Perpendicular are Given to Find the Base. From the square of the hypothenuse subtract the square of the perpendicular, and the square root of the re- mainder will be the base. OF POLYGONS. To Find the Area of a Hegular Polygon. Rule. — Multiply the length of a side by half the dis- tance from the side to the center, and that product by the number of sides; the last product will be the area of the figure. Example. — The side of a regular hexagon in 12 inches, and the distance therefrom to the center of the figure is 10 inches; required the area of the hexagon. — X 12X6 =360 square inches = 2 l / 2 square feet. Ans. 2 To Find the Area of a Regular Polygon when the Side Only I* Given. Rule.— Multiply the square of the side by the multi- plier opposite to the name of the polygon in the ninth column of the following table, and the product will be the area. Table of angles re 1 ative to the construction of Regular Polygons with the aid of the sector, and of coefficients to facilitate their construction without it ; also, of coefficients Epitome of Mensuration. 79 to aid in finding the area of the figure, the side only being given. ! *„ s a - h *S-*i Si i* .c o> a> + J o 5 -a ^do °o ° • a 02 tig "Si S"3 £2* •dS^-dag' g'S Names. ^ <<3 ^^^^ <- Triangle 3 120 60 .2SS68 1.782 .5773 2. .433012 Square 4 90 90 .5 1.414 .7071 1.414 1. Pentagon 5 72 108 .GSS2 1.175 .8506 1.238 1.720477 Hexagon 6 60 120 ..S66 1. 1. 1.156 2.598076 Heptagon 7 513-7 128 4-7 1.0382 .8672 1.152 1.11 3.633912 Octagon 8 45 135 L2071 .7654 1.3065 1.08 4.828427 NonagOD 9 40 140 L3737 .684 1.4619 1.06 6.181824 Decagon 10 36 144 L.53S8 .618 1.618 1.05 7.694208 Undecagon 11 32 8-11 147 3-11 1.7028 .5634 1.7747 1.04 9.36564 Dodecagon 12 30 150 1.866 .5176 1.9318 1.037 11.196152 Note. — " Angle at center" means the angle of radii passing from the center to the circumference or corners of the figure. " Angle at circumference " means the angle which any two adjoining sides make with each other. THE CIRCLE AND ITS SECTIONS. Observations and Definitions. i. The circle contains a greater area than any other plane figure bounded by the same perimeter or outline. 2. The areas of circles are to each other as the squares of their diameters ; any circle twice the diameter of an- other contains four times the area of the other. 3. The radius of a circle is a straight line drawn from the center to the circumference. 4. The diameter of a circle is a straight line drawn 8o Epitome of Mensuration. through the center and terminating both ways in the cir- cumference. 5. A chord is a straight line joining any two points of the circumference. 6. The versed sine is a straight line joining the chord and the circumference. 7. An arc is any part of the circumference. 8. A semicircle is half the circle cut off by a diameter. 9. A segment is any portion of a circle cut off by a chord. 10. A sector is a part of a circle cut off by two radii. General Rules in Relation to the Circle. 1. Multiply the diameter by 3.1416, the product is the circumference. 2. Multiply the circumference by .31831, the product is the diameter. 3. Multiply the square of the diameter by 7854 and the product is the area. 4. Multiply the square root of the area by 1. 12837, tne product is the diameter. 5. Multiply the diameter by .8862, the product is the side of a square of equal area. 6. Multiply the side of a square by 1.128, the product is the diameter of a circle of equal area. Application of the Rules to Practical Purposes. 1. The diameter of a circle being 5 feet 6 inches, re- quired its circumference. 5.5 X 3- I 4 I 6 — 17.27880 feet, the circumference. Epitome of Mensuration. 81 2. A straight line or the circumference of a circle being 17.27880 feet, required the circle's diameter corresponding thereto. 17.27880 X -31831 = 5.5000148280 feet, diameter. 3. The diameter of a circle is 9^ inches; what is its area in square inches? 9-375 2 = 87-89, etc., X .7854 = 69.029, etc., inches, the area. 4. What must the diameter of a circle be to contain an area equal to 69.029296875 square inches ? V 69.02929, etc., = 8.3091 X 1-12837 = 9.375, etc., or g}i inches, the diameter. 5. The diameter of a circle is 15^ inches; what must each side of a square be to be equal in area to the given circle? 15.5 X .8862 = 13.73, etc., inches, length of side. 6. Each side of a square is 13.736 inches in length; what must the diameter of a circle be to contain an area equal to the given square ? 13736 X 1.128 = 15.49, etc., or 15^ inches, the diameter. Any Chord and Versed Sine of a Circle being Given, to Find the Diameter. Rule. — Divide the sum of the squares of the versed size and one-half the chord by the versed sine ; the quo- tient is the diameter of corresponding circle. 7. The chord of a circle equals 8 feet and the versed sine equals i l / 2 ; required the circle's diameter. 8 2 + 1.5 2 = 66.25 -7- 1.5 = 44.16 feet, the diameter. 8. In the curve of a railway I stretched a line 80 feet in length and the distance from the line to the curve I found to be 9 inches ; required the circle's diameter. 82 Epitome of Mensuration. 8 ° 2 + 75 2 = 640.5625 H-2 = 320.28, etc., feet, the di- ameter. To Find the Length of Any Arc of a Circle. Rule. — From eight times the chord of half the arc subtract the chord of the whole arc, and one-third of the remainder will be the length, nearly. Required the length of an arc, the chord of half the arc being 8^2 feet and chord of whole arc 16 feet 8 inches. 8.5X8 = 68.0 — 16.666 = 5 — 33 ^ = 17.111V, cubic feet, the length of the arc. To Find the Area of the Sector of a Circle. Rule. — Multiply the length of the arc by half the length of the radius. The length of the arc equals 9J/2 inches and the radii equal each 7 inches ; required the area. 9-5 X 3-5 = 33- 2 5 inches, the area. To Find the Area of a Segment of a Circle. Rule. — Find the area of a sector whose arc is equal to that of the given segment, and if it be less than a semi- circle subtract the area of the triangle formed by the chord of segment and radii of its extremities ; but if more than a semicircle add area of triangle to the area of the sector, and the remainder or sum is the area of the seg- ment. To Find the Area of the Space Coutalned Between Two Concentric Circles or the Area of a Circular Ring. Rule I. — Mutlply the sum of the inside and outside diameters by their difference and by .7854; the product is the area. Epitome of Mensuration. 83 Rule 2. — The difference of the area of the two cir- cles will be the area of the ring or space. Suppose the external circle equal 4 feet and the in- ternal circle 2 l /> feet, required the area of space contained between them or area of a ring. 4 + 2.51=6.5 and 4 — 2.5=1.5, hence, 6.5 X 1.5 X .7854 = 7.65 feet, the area ; or, The area of 4 feet is 12.566; the area of 2.5 is 4.9081. (See table of areas of circles.) 12.566 — 4.9081 = 7.6579, the area. To Find the Area of an Ellipse or Oval. Rule. — Multiply the diameters togther and their prod- uct by .7854. An oval is 20 x 15 inches, what are its superficial con- tents ? 20 X 15 X 7854 = 235.62 inches, the area. To Find tiie Circumference of an Ellipse or Oval. Rule. — Multiply half the sum of the two diameters by 3.1416 and the product will be the circumference. Example. — An oval is 20 x 15 inches, what is the cir- cumference. 20+ 15 2 ference. = 17.5 X 3-1416= 54.978 inches; the circum- OF CYLINDERS. To I in. I ih. Convex Surface of a Cylinder. Rule. — Multiply the circumference by the flight or length, the product ivill be the surface. Example. — The circumference of a cylinder is 6 feet 84 Epitome of Mensural ion. 4 inches and its length 15 feet, required the convex sur- face. 6-333 X 15 = 94-995 square feet, the surface. OF CONES AND PYRAMIDS. To Find the Convex Surface of a it i- in Cone or Pyramid. Rule. — Multiply the circumference of the base l\r the slant hight and half the product is the slant surface; if the surface of the entire figure is required, add the area of the base to the convex surface. Ex \milk. — The base of a cone is 5 feet diameter and the slant hight is 7 feet, what is the convex surface? 5 X 31416 = 15. 7Q circumference of the base and 1 ^ 70 yc 7 - = 54.95 square feet, the convex surface. To Find the Convex Surface of a Fruatum of a (one or Pyramid. Rule. — Multiply the sum of the circumference of the two ends by the slant hight and half the product tvili be the slant surface. The diameter of the top of the frustum of a cone is 3 feet, the base 5 feet, the slant hight 7 feet 3 inches ; re- quired the slant surface. 2s 12 X 72s 9.42 + 15.7 = — /- = 91.06 square feet, slant surface. Epitome of Mensuration. 85 OF SPHERES. To Find the Convex Surface of a Sphere or Globe. Rule. — Multiply the diameter of the sphere by its cir- cumference and the product is its surface; or, Multiply the square of the diameter by 3.1416; the product is the surface. What is the convex surface of a globe 6 l / 2 feet in di- ameter? 6.5 X 3-i4i6 X 6.5 = 132.73 square feet; or, 6.5 2 = 42.25 X 3-i4i6 = 132.73 square feet, the convex surface. MENSURATION OF SOLIDS AND CAPACITIES OF BODIES. To Find Ihe Solidity or Capacity of Any Figures In the Cubical Form. Rule. — Multiply the length of any one side by its breadth and by the depth or distance to its opposite side, and the product is the solidity in equal terms of measure- ment. Example. — The side of a cube is 20 inches ; what is its solidity? 20 X 20X 20 = 8000 cubic inches, or 4.6296 cubic feet, nearly. A rectangular tank is in length 6 feet, in breadth 4 l / 2 feet and its depth 3 feet ; required its capacity in cubic feet ; also its capacity in United States standard gallons. 6X4.5X3 = 81 cubic feet; 81 X 1728 = 139,968 -f- 231 = 605.92 gallons, 86 Epitome of Mensuration. OF CYLINDERS. To Find the Solidity of Cylinders. Rule. — Multiply the area of the base by the hight and the product is its solidify. Example. — The base of a cylinder is 18 inches and hight 40 inches; 18 2 X 7854 X 4 n = 10.178.7840 cubic inches. To Find the Contents In Gallons of Cylindrical Vessels. Rule. — Take the dimensions in inches and decimal parts of an inch. Square the diameter, multiply it by the hight, then multiply the prod net by .0034 for wine gallons. or by .002785 for beer gallons. Example. — How many United States gallons will a cylinder contain whose diameter is [8 inches and length 30 inches ? 18- X 30 = 97 2 o X -0034 = 33.04. etc., gallons. OF CONES AND PYRAMIDS. To Find the Solidity of a tone or a Pyramid. Rule. — Multiply the area of the base by the perpen- dicular hight and one-third the prod net will be the solidity. Example. — The hast- of a cone is j ! .j feet and the hight is 3M feet, what is the solidity? 2.2s 2 X 7854 X 3-75 „ .: f 4 rf — - = 4-97 cubic feet, the solidity. Epitome of Mensuration. 8 7 To Find the Solidity of the Frustum of a Cone. R ULE . — Jo the product of the diameters of the ends add one-third the square of the difference of the diame- ters; multiply the sum by .7854 a ' ui t,lc product will be the mean area between the ends, which multiplied by the per- pendieular hight of frustum gives the solidity. Example. — The diameter of the large end of a frus- tum of a cone is 10 feet, that of the smaller cud is 6 feet and the perpendicular hight 1 2 feet, what is its solidity? I0 6 = 4 2 =i6-i- 3= 5-333 square of difference of ends ; and 10X6 + 5.333 = 65-333 X 7854 X 12 = 615.75 cubic feet, the solidity. To Find the < oiitent* in I . 8. Standard Gallons of the Frustum of a Cone. r ule . — Jo the product of the diameters, in inches and deeimal parts of an inch, of the ends, add one-third the square of the difference of the diameters. Multiply the sum by the perpendicular hight in inches and decimal parts of an inch and multiply that prod net by .0034 for wine gallons, and by .002785 for beer gallons. Example.— The diameter of the large end of a frus- tum of a cone is 8 feet, that of the smaller end is 4 feet and the perpendicular hight 10 feet; what are the contents in United States standard gallons? 96 — 48 = 48' = 2304 -f- 3 = /68 ; 96 X 48 + 768 = 5376 X 120 X .0034 = 2193.4 gallons. To Find the Solidity of the Frustum of a Pyramid. Rule. — Add to the areas of the two ends of the frus- tum the. square root of their product, and this sum multi- 88 Epitome of Mensuration. plied by one-third of the perpendicular hight will give the solidity. Example. — What is the solidity of a hexagonal pyra- mid, a side of the large end being 12 feet, one of the smaller ends 6 feet and the perpendicular hight 8 feet ? 374.122 X 93-53 = v 34,99i-63 = ^7-o6. 17+122 + 93-53 + 187.06= ^321 ><_§ = 1745.898 cubic feet, solidity. To Find the Solidity of a Sphere. Rule. — Multiply the cube of the diameter by .5236 and the product is the solidity. Example. — What is the solidity of a sphere, the di- ameter being 20 inches ? 20 3 = 8000 X -5236 = 4188.8 cubic inches, the solidity. TABLES, RULES AND RECIPES. BLACK SHEET IRON. Black Sheets are rolled to the following Standard Ganges adopted by the United States, taking effect July 1, 1893. , THICKNESS. > , WEIGHT. ^ Approxi- Approximate mate thick- Weight per Weight per thickness ness in dec- square foot square foot Number infractions imal parts in ounces in pounds of gauge. of an inch, of an inch, avoirdupois, avoirdupois. 10 9-64 .140625 90 5.625 11 1-8 .125 80 5. 12 7-04 .109375 70 4.375 13 3-32 .09375 60 3.75 14 5-04 .0781 25 50 3.125 15 9-128 .0703125 45 2.8125 16 1-16 .002.-, 40 2.5 17 9-160 .05625 36 2.25 18 1-20 .05 32 2. 19 7-160 .04375 28 1.75 20 3-80 .0375 24 1.50 21 11-320 .< 134375 22 1.375 22 1-32 .03125 20 1.25 23 9-320 .028125 18 1.125 24 1-40 .025 16 1. 25 7-320 .( >21875 14 .875 20 3-160 .01875 12 .75 27 11-640 .0171875 11 .6875 28 1-64 .015625 10 .625 29 9-640 .0140625 9 .5625 30 1-80 .0125 8 .5 31 7-040 .0109375 7 .4375 32 13-1280 .0101 5625 6V 2 .40625 A variation of 2% per cent, either way is allowed. Plate Iron. The following table gives the weight per square foot for iron plates 1-16 inch up to Y / 2 inch thick. Thickness. Weight in lbs. Thickness. Weight in lba. 1-16 2.50 > 5-16 12.50 1-8 5.00 3-8 15.00 3-16 7.50 7-16 17.50 1-4 10.00 1-2 20.00 Tables, Rules and Recipes. WEIGHT OF SHEET LEAD. The thickness of lead is in common determined or understood by the weight, the unit being that of a square or superficial foot ; thus : 4 lbs. lead is 1-16 inch in thickness ; 6 do. 1-10 do. ; 7y a do. 1-8 do. ; 11 do. 3-16 do. ; 15 do. 1-4 do. DECIMALS EQUIVALENT TO THE FRACTIONAL PARTS OF A POUND. 03125 %o z. .28125 4% 08. .53125 S% oz. .78125 12% 0625 1 .3125 5 " .5623 9 ' .8125 13 00375 1% * .34375 f,i . ■■ 9Vj ' 84375 13Mi 125 2 ' .375 6 •• ,625 10 • .ST.". 14 L5625 2% .40625 .;i, •• .65625 1MI, • ' 14'... 1875 3 ' a.;::, 7 " .6875 11 ' .9375 15 21875 3% .46875 7% '• .71875 11% ' .96875 15% 25 4 ' .5 8 " .75 1-' ' 1. 16 DECIMALS EQUIVALENT TO THE FRACTIONAL PARTS OF AN INCH WHEN DIVIDED [NTO 32 TARTS; LIKEWISE nil-: DECIMALS EQUIVALENT TO THE FRACTIONAL PARTS OF A FOOT. Parts of an Parts of an Parts <>f Decimals. inch. Decimals. inch. Decimals. a foot. .03125 1-32 .53125 '..and 1-32 ., •• 4% - Size. 2qt. 3pt. 1 " Die Diam. of top. 9 in. 8% - 6% - 9 " Diam. of bot. 6 in. 4 " 7', " Ilight 3% in. 2% - 1% " DISH KETTLES A XI) I 'AILS. Size. 14 «)t. 10 " Diam. of top. 13 in. 11% - Diam. of bot. 9 in. 7 Bight 9 in. COFFEE Si/.'. ti.|t. ■ > .. POTS. Diam. of top. 9% in. Diam. of bot. 5% in. 4 • Hight. 6% in. 4 " Size. lgal. Diam. »if top. 1 in. Diam. of bot. 7 in. Hight. 8% in. Six.-. :; qt. I Ham. of toll. 3% in. I Main. of hot. 6 in. Ilight. 8% in. WASH BOWLS. Size Large wash bowl in] i * ■ 1 1< i •> ■' l Ham. ..f top. . 11 in. 11 9% - Diam. of bot. .-,'•, in. Hight. 5 in. Small Milk - wash bowl if ralner . . . DIPPERS. Size. % gal. Diam. of top. 6% in. Diam. of bot. 4 in. Hight. 1 in. Size, lpt. Diam. of top. 1', in. Diam. of bot. 3* in. Highl 2$ in. MEASURES. Size. 1 gal ',■ ' 1 qt. Diam. of top. . 5% In. 4 " 3% •• Diam. of bot. C'.in. 1% - 4 Right. In. g ■« Size. i pt. Diam. of top. 2% in. 2% ■ Diam. of Lot. ::•-, in. 2% - Ilight 4% in 3% " druggists' and liquob : dealers' measures Size. 5 gal. 3 " 2 " 1 " Diam. of top. 8 in. 7 •• 6 " 3% " 1 Ham. of bot. 13% in. 11 1.. '• io% •• Hight. 12% in. 10% - 8% " 7% '• Size. %gal. i" -it. l pt. Diam. of top. 3% in 2% - 2 " 1% " Diam. of bot. 6% in. 4 " 3% " Hight. 6 in. 4% - 4 " 3% " Tables, Rules and Recipes. 93 X 1'. -1 X /< to X tl M 6 X X I- Tl H 6 2 *—> m K 00 ti d 2 < Tl CU d o Z £ :i o o •— i M CO H -r 6 X rl y. O t-T 1 H cc •' I - ' d « M £ 0) — BO — o CO H ifi 6 - Tl £> 55 O . 3 Tl "t Tj :: 3 — d £ « ~ Z H £ CO CO H EC d X 'a 03 jO z - o -f X CO r^ ^ e« m tr ti c r. r. c ti ti tr vr -t- -t ii x jo t- rroco £h S S CO 01 H CO CO 01 Tl T I T I T I T I Ct CT -t 1 1 Ol CO CO .^ , _ -,-f Mr-o »o >o Lt ti g ti £ ti r: .- tf2 ^ j 01 01 01 ^ — i ^ r-TlTITITITI — Tlr-TI— Tl- I. 1 r- i-i i-l ri rl a ' s -- .iSaaaaa Hgaasaaassaaaaa ^■^OQaSSSSS^HiHSrHtHrHrHT-lrHrHTHiHrHINNtN 94 Tables, Rules and Reap es. X 1". -- r. X 6 z X 1— 1 vr ■- X X d i - X M r- £ X '.' !_: X x. •— ' '/. -. X 6 r — /. y '^. 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'-ririri'M n o B ^ 1 ' — 1-53SIS9 rj tj r i £ © © C -r s So* -t 5 -- - A r nrir :: :: — ~ - • - x Z " tf — = •_ - - -.-J: r - - — x r- |^9fi - — ''Jr. -■ — 1 1 "i M i :i n :i -. i :: fc. :i tj Z7rh.fl-----: — ^JtHt-Hri , s a 6 6 6 6 r*yy./ss Tables, Rules and Recipes. 95 3 3 - <-• - O ._. « O 1-1 CO -/. :: -■ - " CI — - 8 g to ci c 12 a ri '- - r. ::i- : r — / d tfi -- vi - .- oj i - r. 7 ,?. 35 © e§ o .(coiinrHt-. _ _ ^j^THrH uaeq B ' i B s. 7 i 50 0>MCJHO'Qt> CO "^ ro m _J ~ i-.i-iV.I-/1-ZI-ZX05hS - I>00 CI XL- M N v gi B i i -' ga B i i a B i d r-i © i - i 3 77* - -' -,-' i - ' - EC i - X i - v i - i - >; £\ f - ■ - — i ■ I I -■_■■- x _r — — (O —J ~ i — j i - — '■ r >C i _ ' i - — ' r- - j — ' / - — i - ;.;• -:i:i r-ir~o>cotc /- — h : : CO X — : : O ' LO y' > ":' r :' c-i i - i -' i - - i NcoM :: M . : — . -. H ,"- , 7 — i - -Ir • ! — lO 0€ "i r : r. 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S -=3 ■° a A •d a a ° a ia ■° a 0J « g its .£f S u> £Pfl to .tc a a '35 O c .M o> , a> " CD "35 'S "35 ^ rt '35 C O) "2 '35 u '35 "S OS- CD C o o §5 0) ^3 . ^ CD ►1 . *S ^05 p, 5 « .2 CO 1) bo - to a* CO .2 ed 3 3 §« 3 =* s^ §. 2 O ^ •- ^ O "w '-' co r^ "^ os ^ 05 f 3 ^ CO es w to ^ M*JB c « -9 Cl ~ '- t O eS 1 i t £ es £3 O N n a ^j Q. j;, _ SO jg i a n« j a ^ Qm .a a .a a « a a £ a» rZ H o O 05 02 02 02 02 02 02 02 z: Xi 35 .00537 4 1.22 1.16 0.35 2 0.61 3.12 0.96 4.50 1.38 6 1.83 33 .00806 6 1.83 1.75 0.53 3 0.92 4.68 1.43 6.75 2.06 9 2.75 ::i .0107 8 2.44 2.33 0.7 1 4 1.22 6.25 1.91 9 2.75 12 3.66 29 .0134 10 3.05 2.91 0.89 5 1.53 7.81 2.38 11.25 3.43 15 4.57 27 .0161 12 3.66 9.37 4.12 26 .0183 14 4.27 10.93 15.75 4.80 21 6.40 24 .0215 16 4.88 4.66 1.42 8 2.44 12.50 3.81 18 5.49 24 7.32 23 .0242 18 5.49 5.25 1.60 9 2.75 14.06 4.29 20.25 6.17 27 8.23 22 .0269 20 6.10 5.83 1.7 3 10 3.05 15.62 4.76 22.50 6.86 30 9.14 21 .0322 24 7.32 7 2.14 12 3.66 18.75 5.72 27 8.23 36 11.00 in .0430 32 9.75 9.33 2.85 16 4.88 25 7.62 36 11.00 48 14.70 18 .053S 40 12.20 11.66 3.56 20 6.10 31.25 9.52 45 13.75 60 18.30 16 .0645 48 14.65 14 4.2 J 24 7.32 37.50 11.45 54 16.50 72 22.00 15 .0754 56 17.10 16.33 4.98 28 8.53 43.75 13.35 63 19.20 84 25.60 14 .0860 64 19.50 18.66 5.69 32 9.75 50 15.30 72 21.95 96 29.30 13 .095 70 21.35 35 10.70 55 16.80 79 24.10 105 32.00 12 .109 81 24.70 40% 12.40 63 19.20 91 27.75 122 37.20 11 .120 89 27.15 • 44% 13.60 70 21.35 100 30.50 134 40.85 10 .134 100 30.50 50 15.30 78 23.80 112 34.20 150 45.70 9 .148 110 33.55 55 16.80 86 26.20 124 37.80 165 50.30 8 .165 123 37.50 61 18.60 96 29.30 138 42.10 184 56.10 7 .180 134 40.85 67 20.40 105 32.00 151 46.00 201 6130 6 .203 151 46.00 75i/o 23.00 118 36.00 170 51.80 227 69.20 5 .220 164 50.00 82 25.00 .'28 39.00 184 56.10 246 75.00 4 .238 177 53.95 88V 2 27.00 138 42.10 199 60.70 266 81.10 3 .259 193 64.30 96 29.30 151 46.00 217 66.10 289 88.10 2 .284 211 67.95 105V 2 32.20 165 50.30 238 72.50 317 96.60 1 .300 223 77.10 llli/o 34.00 174 53.10 251 76.50 335 102.20 .340 253 1261/o 38.60 198 60.40 285 86.90 380 116.00 One ounce per square foot aluminum sheet is 0.0044 inch thick and corresponds to about No. 37 B. & S. gauge. Tables, Rules and Recipes. 97 SHEET COPPER. Official table adopted by the Association of Copper Manufac- turers of the United States. Rolled copper has specific gravity of 8.93. One cubic foot weighs 558 12 7iooo pounds. One square foot, of 1 inch thick, weighs 46 51 /ioo pounds. 6C .2 Oj 2^ . " ft .d « M ^ 50 — T « « p .m.5 s c ^ '2 a> «m 35 00537 33 00806 31 0107 29 0134 27 0161 26 0188 24 0215 23 0242 22 0269 21 0322 19 0430 18 0538 16 0645 15 0754 14 0860 13 095 12 109 11 120 10 134 9 148 8 105 7....... .180 6 203 5 220 4 238 3 259 2 284 1 300 340 *- 2 a> o 4 6 8 10 12 14 16 18 20 24 32 40 48 56 64 70 81 89 100 110 123 134 151 164 177 193 211 223 253 £* 1.16 1.75 2.33 2.91 3.50 4.08 4.66 5.25 5.83 7 9.33 11.66 14 16.33 18.66 2S i m 2 3 4 5 6 7 8 9 10 12 16 20 24 28 32 35 40% 441/2 50 55 61 67 75y 2 82 88 1/ 2 96 105i/o 111% 1261/2 C SQ 50,0 CO -t-> 02 -s, -t-> bfi 4).— 0> 4> 3.12 4.68 6.25 7.81 9.37 10.93 12.50 11.06 15.62 18.75 25 31.25 37.50 43.75 50 55 63 70 78 86 96 105 118 128 338 151 165 174 198 5.2 CO-w •*-> W) O) 4; tit 4.50 6.75 9 11.25 13.50 15.75 18 20.25 22.50 27 36 45 54 63 72 79 91 100 112 124 138 151 170 184 199 217 238 251 285 4 j *r Of 4* 6 9 12 15 18 21 24 27 30 36 48 60 72 84 96 105 122 134 150 165 184 201 227 246 266 289 317 335 380 TABLES OF THE CIRCUMFERENCES OF CIRCLES, TO THE Nearest Fraction of Practical Measurement; also, the areas of circles, in inches and decimal parts, likewise in felt and decimal parts, as may be required. Rules that may render the following tables more gen- erally useful. 1. Any of the areas in inches, multiplied by .052, or the areas in feet multiplied by 7.48, the product is the num- ber of gallons at 1 foot in depth. 2. Any of the areas in feet, multiplied by .03704, the product equals the number of cubic yards at 1 foot in depth. Dia. in Circum. Area in Side of Dia. in Cir. in Area in Area in inch. in inch. sq. inch. = sq. inch. ft. in. sq. Inch. sq. ft. 1-16 .196 .0030 .0554 1 in. 3% 7v, 4 7 /s l 8 .392 .0122 .1107 Lfc :;>., .9940 % and 3-32 3-36 .589 .0276 .1661 W4 3% 1.227 1 in. 1-4 .785 .0490 .2115 3 414 1.484 1 3-16 5-16 .981 .0767 .2669 4% 1.707 1 5-16 3-8 1.178 .1104 .3223 1% 5V 8 2.074 1 7-16 7-16 1.374 .1503 .3771 1% 5% 2.405 1 9-16 1 7 > 5% 2.761 1 11-16 1-2 1.570 .1963 .4331 2 in. 6^4 .°..141 1% 9-16 1.767 .2485 .4995 2% O-'s 3.546 l 7 /s 5-8 L963 .3068 .5438 - 1 . 7 3.976 2 in. 11-16 2.159 .3712 .6093 2% 7% 4.430 2y 8 3-4 2.356 .4417 .6646 J'., T ; . 1.111 IN 2 3-16 13 16 2 552 .5185 .7200 2^ 8V4 5.412 2 5-16 7-8 2>48 .6013 .7754 2% 8% 5.939 2 7-16 15-16 2.945 .0903 .8308 2% 9 6.491 2 9-16 Tables, Rules and Recipes. 99 Dia. in. Cir . Area in Side of Dia. in Cir. in Area in Area in inch, in inch sq. inch. = sq. inch. ft, . in. sq. inch. sq. ft. 3 in 9% 7.( )68 2% 10 in. 2 7% 78.540 .5497 3% »% 7. 669 2% ioy 8 2 7% 80.515 .5636 3V4 10% 8.295 2% ioy 4 2 8% 82.516 .5776 3% 10% s.940 3 in. 10% 2 8% 84.540 .5917 3y 2 11 9.62] 3y 8 ioy 2 2 8% 86.590 .6061 3% 11% 10.320 3y 4 10ft 10% 2 9% 88.664 .6206 3% 11% 11.044 3% 2 9% 90.762 .6353 3% 12% 11. 793 2 17-16 10% 2 10% 92.855 .6499 Dia. incl 4 in. 4% 4i/4 4% 41/2 4% 4% in Cir. in 1. ft. in. 1 oy 2 1 0% 1 1% 1 1% 1 2% 1 2% 1 2% Area in sq. inch. 12.566 13.364 14.186 15.033 15.904 16.800 L7.720 Area in sq. ft. .0879 .0935 .0003 .1052 .1113 .1176 .1240 11 in. 11% 11% 11% 11% 11% 11% 11% 2 2 2 2 3 3 3 3 10% 10% 11% 11% 0% 0% 0% 1% 95.033 97.205 99.402 101.623 103.869 106.139 108.434 110.753 .6652 .6874 .6958 .7143 .7290 .7429 .7590 .7752 4% 1 3% 18.665 .1306 12 in. 3 1% 113.097 .7916 5 in. 1 3% L9.63S .1374 12% 3 115.466 .8082 5% 1 4's 20.629 .1444 12% 3 2% 117.859 .8250 5% 1 4y, 21.647 .1515 12% L2% 12% 3 2% 120.276 .8419 5% 1 4% 22.690 .15.S.S 3 3% 122.718 .8590 5V 3 1 5% 23.758 .1 •;»;:•, 3 3% 125.185 .8762 5% 1 5% 24.850 .1739 12% 3 4 127.676 .8937 5% 1 6 25.967 .1817 12% 3 4% 130.192 .9113 5% 1 6% 27.108 .1897 13 in. 3 4% 132.732 .9291 6 in. 1 6% 28.274 .1070 13% 1314 3 5% 135.207 .0470 6% 1 7% 29.464 .2062 3 5% 137.886 .0642 »>', 1 7% .••.(MIT!) .2147 13% 3 6 140.500 .9835 6% 1 8 31.919 .2234 131/2 3 6% 143.139 1.0019 6% 1 8% 33.183 .2322 13% 3 6-Yt 145.802 1.0206 ti% 1 V S 34.471 .2412 13% 3 7% 148.489 1.0294 • »". 1 9% 3.-.. 784 .2504 13% 3 7% 151.201 1.0584 6% 1 9% 37.122 .2508 14 in. 3 7% 153.938 1.0775 7 in. 1 10 38.484 .2693 14% 3 8% 156.699 1.0968 7% 1 10% 39.871 .2791 14% 3 8% 159.485 1.1193 7% 1 10% 41.282 .2889 14% 3 9% 162.295 1.1360 7% 1 11% 42.718 .2900 14% 3 9% 165.130 1.1569 7% 1 11% 11% 44.178 .3092 14% 3 9% 167.989 1.1749 7% 1 45.663 .3196 14% 3 ioy 4 170.873 1.1961 7% 7% 2 0% 0% 47.173 47.707 .3299 .3409 14% 3 10% 173.782 1.2164 8 in 8% 2 2 1% 1% 50.265 51.848 .3518 .3629 15 in. 15% 3 3 11% 11% 176.715 170.672 1.2370 1.2577 si; 2 1% 53.456 .3741 15% 3 11% 182.654 1.2785 8% 2 2% 2% 55.088 .3856 15% 4 0% 185.661 1.2996 8V 2 2 56.745 .3972 15% 4 0% 188.692 1.3208 8% 2 a 58.426 .4089 15% 4 1 191.748 1.3422 8% 2 3% 60.132 .4209 15% 4 1% 194.828 1.3637 8% 2 3% 61.862 .4330 15% 4 1% 197.933 1.3855 in. 2 4% 63.617 .4453 16 in. 4 2% 201.062 1.4074 9% 2 4% 65.396 .4517 16% 4 2% 204.216 1.4295 9% 2 5 67.200 .4704 iey 4 4 3 207.394 1.4517 0% 2 5% 69.029 .4832 16% 4 3% 210.597 1.4741 'i!.', 2 5% 70.882 .4961 H£ 4 3% 213.825 1.4967 9% 2 6% 72.750 .5003 16% 4 217.077 1.5195 03; fi% 74.662 .5226 16% 4 4% 220.353 1.5424 9% 2 7 76.588 .5361 16% 4 5 223.654 1.5655 IOO 'fables, Rules and Recipes. I>ia. in Cii \ in Area in Area in Dla. In Cir. in Area in Area in Inch. ft. in. bq. Inch. Bq. ft. ft. in. ft. in. sq. Inch. 17 in. 4 226.980 1.5888 •J. «; 152.290 3.1418 17', 4 230.330 1.6123 2 0% 6 461.864 3.2075 17V4 4 G% 233.705 L.6359 L' 6 iti 136 3.2732 IT % 4 6% 237.104 1.6597 _ 6 181.106 3.3410 IT'... 4 .;: 240.528 ■J. l ♦; 190.875 3.4081 1 J% 4 243.977 1.7078 •> 1% 6 500.741 3.47 i 5 17% 4 7% 247.450 L.7321 2 6 M. 510.706 3 5468 17% 4 8% 250.947 1.7566 •J. i -. 6 520.769 3.6101 is in. 4 8% 254.469 1.7812 2 • > 6 530.930 3.6870 18% 4 8% 258.016 1 B061 2 6 10% 541.189 3.7583 18% 4 261.587 1.831 1 2 6 11', 551.547 :; 8302 1^'s 1 265 182 2 2% 7 562.002 3.9042 LS% 1 10% 1.8816 2 7 :.72. :.:.<; :; 9761 1 8% 4 10% 272.4 17 1.9071 2 3% T 1 * 583.208 4. <>:,( id 18% 4 10% 276.117 1 T 593.958 1.1241 L8% 4 11'. 279.811 - 7 604.807 L2 • 19 In. 1 11% 283.529 1 '..-IT •■ i 7 615.753 L2760 19% 5 287 272 1 9941 2 4% 7 626.798 1.3521 291 039 2 0371 2 7 637.941 I 1302 5 2.0637 •_> 7 6% 649.182 1 5083 19% 5 1', 298 648 2.090 t 2 7 7 660.521 5 1% 302. 189 2.1172 2 T 671 958 \ 6665 I 1 .", 2 2 1 l 1 ■: 2 5% 7 683. 194 I 7467 19% 5 310.245 2.1716 2 T 9% i B27 t 20 Id g 2% 31 1.160 2.1990 2 7 10% i 9081 20% 5 3% 318 099 2 2265 •j 7 i l 718.690 1.9 -'I 20% r, 322 063 2.2543 2 T l L% r.-.n 618 5 0731 r> i 326.051 •J 2822 2 B 0% 742.644 5.1573 5 330.064 2 3103 2 T S Tr.4.T«;;» 5 334 L01 2 7% - 20% 5 5% 338.163 2.3670 o 7', 8 779.313 5 Ml 'J 20% 5 5% 342.250 2.3956 2 791.732 21 in. 5 346 361 2 124 i 1! 8 B 4% 804.249 21% 5 350 197 2 1533 •« 8% 816.865 -1'. K :;:. 1 657 2.4824 2 8 6$ 5.7601 21% C 7% 358 841 2.51 IT •j - i B 6% 5 8491 21% 5 7% 363.051 2 5 1 1 2 2 B 855.300 21% 5 7 T - 367.284 2.5708 'J B 6.0291 21% 5 8% 371 543 2.6007 •i 8 881.415 6.1201 21% 5 375.826 2.6306 2 8 10 B94.619 6.2129 22 in. 5 9% 380.133 •_> 1ii 907.922 22% 5 9% 38 l. 165 2.6691 •_> - 11% 921.323 6.3981 22% 5 388.822 2.7016 ;_> 10% 9 934.822 6.491 1 5 10% 393 203 2.7224 •> 10% 9 1% 948.419 6.5863 22iZ 5 10% 397.608 2.7632 2 11 9 i T - 962.115 6.6815 22% 5 11 402 038 2.7980 •. 11% 9 975.908 6 7772 22% 5 1 1' . 106. 193 2.8054 •j 1 1% :» 3% 989 800 ■'" 7 . 5 Ll% 410.972 2.8658 •j 1 L% 4% 1003.79 6.9701 23 in. 6 0% 415.476 2.8903 3 <» 9 5 1017.87 T 0688 23% 6 0% 120.004 2 9100 3 0% 9 1032.06 7.1671 6 1 424.557 2.9518 3 0% 9 L046.35 7.2664 429.135 2.9937 3 9 7% 1060.73 7.3662 23% 6 433.737 3.0129 3 1 9 1075.21 T 1661 6 3.0261 3 1% 9 9 1089.79 7.5671 23% 6 2% 443.01 1 n.« »Tl2_i 3 1% 9 9% 1104.46 7.6691 23% 6 8 447.600 3.1081 3 9 10% 1110.24 7.7791 Tables, Rules and Recipes. ioi Da. in Cir. in Area in Area in ft sq. inch. sq. ft. 2% - ; » 3 3% i» ii* s 1134.12 7.st;si 6 7% 7% 7% 8% 9 9% to 10% 10% 10% 11 111, 111, Ll% 4 in 4', 10 -1>, L0 Ki :,', 10 :,'., L0 .-.■••■; 10 6% n 6% 11 l l 11 n l l 8 11 8% 11 9% ii i i 1 1 12 12 \-i 12 12 12 12 12 112 0% 12 0% 12 0% 12 1 12 T, 12 T, 12 t% 13 2 13 2% 13 -i, 13 2% 13 3 13 3% 13 3% 13 3% 13 0% 1 -, 2% 3% 4 4". 1149.09 1164.16 1179.32 l 194.59 1209.95 1225. 12 1240.98 5% 1256.64 6 & 121 I', 1288 25 1304.20 1320.25 1336.40 1352.65 1369.00 9% 11% 11% 0% i ; -", 3 6% 7 10% 10% Ll% .i'.. i* 4% ;;'' 6% 7'.. 9% 9% io4i 11% 0% 1 l 7 - 2y 2 t A 5% ey 3 1385.4 1 1 101.98 l 118.62 1 135 36 1452.20 1 169.1 l l isf.. 17 1503 30 1530.53 1555.28 1572.81 1590. 13 1608.15 1625.97 1643.89 1661.90 1680.02 1698 23 1716.54 1734.94 1753. 15 1772.05 1790.76 1809.56 1828.46 1847.45 1866.55 1885.74 1905.03 1924.42 1943.91 1963.50 1983.18 2002.96 2022.84 2042.82 2062.90 2083.07 2103.35 7.9791 8.0846 8.1891 8.2951 8.4026 8.5091 8.6171 8.7269 8.8361 8.9462 9.0561 9.1686 9 21 12 9.3936 9.5061 9.6212 9.7364 9.8518 9.9671 10.084 10.202 10.320 L0 139 10.559 10.679 10.800 10.922 1 1.04 1 11.167 11.291 11.415 11.534 1 1.666 l 1 793 l 1.920 12.048 12.176 12.305 12.435 12.566 12.697 12.829 12.962 13.095 13.229 13.304 13.499 13.635 13.772 13.909 14.047 14.186 14.325 14.465 14.G06 Dia. in ft. in. 4 4 4 4 4 l 4 4 Cir. in ft. in. 4 13 4', 13 8% 41, 13 8% 4% 13 9% .» 13 10% 5% 13 11% 5% 1 1 14 0% 6 14 IB* <'-', 14 6% 14 3% 14 4 7 14 '■| 7% 14 5% '•'1 8 8% 8% 9 9% 9% 9% 10 10% 111'-.. 10% 1 1 11% 11% 11% 0% 111.. 0% 1 1% 1% 1% 2% 3 3% 3% 3% 4 4i, 4% 4% 5 5% 5% 5% 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 6 7% 14 7% i i m 14 9% 14 10% 11 11 II 11% 15 i»'s 15 1% 2% 2% :: : , 1% 5% 6% 6% 7- ; , 15 9% 15 I" 15 10% 15 11% 16 0% 16 l', 16 1% i»; i<; i<; io% 16 11% 2% :;i, 5% 6% 7% 8% 9 9% 17 17 17 17 0% 0% 1% 2% Area in sq. inch. 2123.72 2144.19 2164.75 2185.42 2206.18 2227.05 2248.01 2269.06 2290.22 231 1.48 2332.83 2354.28 2::7:>.s:; 2397.48 2410.22 2441.07 2463.01 2485.05 2507.19 2529.42 2551.76 2574.19 2596.72 2619.35 2642.08 2664.91 2687.83 2710.85 2733.97 2757.19 2780.51 2803.92 2827 14 2851.05 2874.76 2898.56 2922.47 2946.47 2970.57 2994.77 3019.07 .••.in::. 4 7 3067.96 3092.56 31 17.25 3142.04 3166.92 3191.91 3216.99 3242.17 32 07. 40 3292.83 3318.31 3343.88 3369.56 3395.33 Area in sy. ft. 14.748 14.890 15.033 15.176 15.320 15.465 15.611 15.757 15.904 16.051 1 0.200 16.349 16.498 16.649 16.800 16.951 17.104 17.256 17,111 17.565 17.720 17.876 18.033 18.189 18.347 18.506 18.665 18.825 18.965 19.1 17 19.309 19.471 19.635 10. 7! IS 19.963 20.128 20.294 211.401 20 629 20.797 20.965 21.135 21.305 21.476 21.647 21.819 21.992 22.100 22.333 22.515 22.021 22.S00 23.043 23.221 23.330 23.578 102 Tables, Rules and Recipes. Dia. in Cir . in Area in Area in Dia. in Cir . in Area in Area in ft. in. ft. iu. sq. Inch. sq. ft. it. in. ft. in. sq. inch. sq. ft. 5 6 17 3% 3421.20 23.758 1; 4 19 10% 4536.47 31.50.i 5 G& 17 4% 3447.16 23.938 G 4V 4 19 11% 4566.36 31.710 5 6% 17 4% ::47:;.j:; 24.119 6 4% 20 0V 4 4596.35 31.910 5 6% 17 5% 3499.39 24.301 6 4% 1*0 1% 1626.44 3J.114 5 7 17 6% 3525.26 24.483 6 5 20 l T s 4656.63 32.337 5 7% 17 7% 3552.01 24.666 t; 5% 20 2% 4686.92 32.548 5 7% 17 8 3578.47 24.850 6 5% 20 3% 1717.30 32.759 5 7% 17 s% 3605.03 25.034 6 20 "I 1 ! 4747.70 32.970 5 s 17 9% 3631.68 25.220 <; 6 20 ."» 4778.37 33.183 5 8% 17 10% 3658.44 25. 4 6 6% 20 5% 1809.05 33.396 5 8% 17 11% 3685.29 2 5 . 5 '• ' 2 6 6% 20 6% 4839.83 33.619 5 8% 17 ll T / 8 3712.24 25.779 6 6% 20 7% 4870.70 33.824 5 9 is 0% 3739.28 25.964 <; 7 20 8% 4901.68 34.039 5 9% IN 1% 3766.43 26.155 G i^ 20 1932.75 34.255 5 !•'., IS 2% 3793.67 26.344 6 t ' ■. 20 '•'•, 4963.92 34. 17 1 T> 9% IS 3% 3821.02 26.534 c. 7% •Jo 10% 1995.19 34.688 5 10 18 3% 3848 If. 26.725 6 s 20 11% 5026.26 34.906 5 10Vi is 3875.99 26.916 6 - •Jl 0% 5058.02 :\:,.\\::< 5 10% 18 5% 3903.63 27.108 (i M.. 21 0% 5089.58 35.34 1 5 10% 18 6% 3931.36 27.301 6 &% 21 lg 5121.24 35.564 5 11 18 7 3959. n\ 27.494 6 9 •Jl 5153.00 35 784 r> 11', 18 3987.13 27.688 6 9% 21 3% 5184.86 36.006 5 11% 18 4015.16 27.883 6 9% 21 1 5216.82 36.227 5 11% 18 4043.28 28.078 6 9% Jl l', 5248.87 36.450 6 18 10% 1071.51 28.274 6 10 21 5281.02 :w;.<;7 i 6 0% 18 10% 4099.83 28 47 1 6 10% 21 5313.27 36 897 6 0% is 11% 4128.25 28.663 6 10% 21 7% 5345 82 37.122 6 0% 19 0% 4156.77 28.866 1; 10% 21 7% 5378.07 37.347 6 1 19 l'i H85.39 29 Ofi I 6 11 21 5410.62 37.573 ♦; 1% 19 2% 4214.11 29.264 6 11% 21 9% 54 13.26 37.700 6 1% 19 2% 1242 92 29.466 6 11% 21 10% 5476.00 38.027 G 3% lit 3% 4271.83 29.665 6 1 1"'. 21 11 5508.84 38.256 6 • > 10 4% 4300 85 29.867 6 t; 21 i 10 19 5% 6 4329.95 4359.16 30.069 30.271 6 2% 19 6% 1388. »7 30.475 R 3 19 7% \ H7.87 30.619 6 6 3% 10 19 9% 4447. :i7 447C. 07 30.884 31.090 6 3% 19 9% 450G.G7 31.296 Tables, Rules and Recipes. 103 Dia. in ft. in. 7 7 1 7 2 7 6 7 7 7 8 7 9 7 10 7 11 1 2 3 4 5 6 7 8 9 10 11 1 2 :•. I 5 6 7 8 9 10 9 11 10 10 111 10 1() 10 10 10 10 10 10 10 10 11 Circum. in ft. in. 21 11% 22 3 22 6% .,•> '•"» 23 0% 23 2% 23 6% 23 11 2 1 U6 2 1 4'. 24 7 '4 24 10% 25 L% 25 1% 25 7% 25 1 1 26 2% 26 •»'. 26 26 llVs 27 •J 7 5% 27 g :> 0% 28 3% 28 6% 28 9% 29 0% 29 ::■'•, 29 7 29 10% 30 1% 30 t% 30 7% 30 11% 31 1% 31 5 31 8% ::i 11% 32 32 5% 32 8% 32 11% 33 2% 33 6% 33 9% 34 0% 34 3y 2 Area in feet. 38.4846 39.4060 40.3388 41.2825 42.23U7 4:;. 2022 44.17^7 45.1656 46.1638 47.1730 48.1926 49.2236 50.2656 51.6178 52.3816 53.4562 54.5412 55.6377 56.7451 57.8628 58 9920 60.1321 61.2826 62.4 1 15 63.6174 64.8006 65.9951 67.2007 68.4166 69.6440 70.8823 72.1309 73.3910 74.6620 75.9433 77.2362 78.5400 79.8540 81.1795 82.5190 83.8627 85.2211 86.5903 87.9697 80.366S 90.7627 92.1749 93.5986 Dia. in ft. in. Circum. in ft I 1 I I 1 1 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 1 3 13 13 13 13 1 3 13 13 13 13 13 1:1 11 10 11 11 12 in 12 11 8 1(1 11 1 1 14 1 I 14 14 14 1 1 11 14 14 9 14 10 14 11 34 34 35 35 35 in. 6% 9% 0% 4V 8 7% 3.") 10% 36 1% 30 4% 36 7% 36 10% 37 2% 37 5% 37 8% .",7 11% 38 2% 38 38 39 39 39 39 40 40 40 5% 3% 6% 91. , 0% 3% 6% 40 10 41 1% 41 4% 41 7M; 4 1 10% 42 1% 42 4% 4 2 8 42 11% 43 214 43 5% 43 8% 43 11% 44 2% H 41 6 9% 45 01/, 45 3% 45 45 46 46 46 6% 9% CVS 4 7Vs 46 11% Area in feet. 95.0334 96.4783 97.9347 99.4021 ltto.8797 102.3689 103. 8601 105.3794 106.9013 108.4342 109.9772 111.5319 113.0976 1 1 1.6732 116.2007 117.8590 119.4674 121.0876 122.7187 124.350:' 126.0127 127.6765 129.3504 131.0369 132.7326 134.4391 136.1574 137.8867 139.6260 1 11.3771 143.1301 144.0111 1 16.6949 148.4896 150.2043 152.1109 153.9484 155.7758 157.6250 159.4852 161.3553 163.2373 165.1303 167.0331 168.9479 170.8735 172.8091 174.7565 io4 Tables, Rules and Recipes. I)ia . in Circum. in Dia in «'ircum. in ft. in. ft. in. Area in feet. ft. in. ft. in. Area in feet. L5 47 1', 176.7150 17 <> 1% 226.9806 15 1 47 I ft 178.6832 IT 1 53 B 229.2105 15 2 47 7 ; , 180.6624 IT 'J, 53 11% 231.4625 15 :: 47 10% 182.6545 1 7 3 54 233.7055 10 i 184.6555 IT 4 54 235.9682 L5 5 4^ 186.6684 1 7 ."> 54 M.. 238.2430 15 6 18 188 6923 IT •; 54 11% 240.5287 L5 7 18 1 1 •_ 190.7260 1 T T .... - T . 242.8241 15 8 19 2% 192.7716 IT 8 55 6 245.1316 15 g 49 ■<■■, 194.8282 1 T 9 :. :. '••'* 247.4500 15 io 19 8% 196.8946 IT 10 249.7781 i:> n 50 «' 198.9730 IT 1 1 56 ••••'-■ 252.1184 16 50 3% 201.0624 is 56 254.4696 16 i 50 <••'. 203.1615 L8 1 56 256.8303 16 2 50 205.2726 is •• 5 1 0% 259.2033 16 3 51 0% 207.3946 18 3 .">T 1 261.5872 16 1 51 209.526 1 18 l 57 7% 263.9807 16 - r.1 »;i., 211.6703 is 5 57 1" , 266.3864 16 »; :.1 10 " 213.8251 is 6 58 268.8031 it; 7 52 1% 215.9896 18 T 271.2293 16 8 52 »', 218.1662 is s 273.6678 11; 9 52 220.3537 is 9 58 1095 276.1171 16 10 52 111'.. 222 5510 18 10 59 2 278.5761 IS li 53 224 7603 is 11 281.0472 WEIGHT PER FOOT OF LEAD PIPE. Inside AAA A A A B C > E diam- B •ook- •]\. I X. Foun- eter. Ivn. strong. Si i • Mm. Me< liuni. I. ght. light. tain. Ins. Lb. « >. . Lb. Lb Oz. Lb. LI . Oz. Lb. LI.. Oz. 1 L2 1 8 1 1 1 ii ii L2 ii in 1 7 7-16 1 ii ii 13 ', 3 6 2 ii 1 12 1 1 1 n 12 ii % 3 - • > 12 • > s 2 (1 1 8 1 (1 12 % 1 12 :; B 3 II • > t 1 12 1 \ 1 <» 1 6 4 12 1 ;; 1 • > s 2 1 8 1% <; 12 .i L2 t 12 3 12 :; II '2 8 2 n 1 ' . 8 8 7 8 6 s .~i ii I 4 :; s 3 o l& 10 ii s 8 7 II r. r» ii 4 o 11 12 9 U 8 7 u 1 12 e i - — >-. » > - - ' a -r. ^> = ~ —i — : i -J T ^r uS ITS LS LS Lrt O P5 Tf 00 Ifl 1< ' J C '.O OS 3 t— CO iS i- o r I O '.O rH ".O — < \0 T i i - CO :t — -r iS is CO so id id its ooioiaus •o ~ oo — i .c ~ r~ 'X lQ t— Of< is t~ O '-O i- y. n .- OSCO00N ri I- CO x5c0 0»-*0 krf t-i »ci t>i eo oi-^5 50 COCOCOCOOCDcOCOt-» S^s&ft^c&S £;£&£&§*£ ^^as^jft&s 5 ^sft&jft&s- .-ir-t-rHT-n-^coso :-. -r sfi 90 OfjOiO so 3 — x -txr ~~ * ko co co co co ro co co co lS ^ i— r- — VO eoeoeoec '■-■ •2 ;&*$&£ .':-/ .= -'--./ j i -'-j -s^m^s^ 3» i-4 o' CO t-"oCO f," O o o — ' — ' ■ 1 .d-V::'-'.^',-' .= _ / -T: / J , .: / ::'*,/ .E-'-T::^^^ to IM : — n 1- — - "■ ■ ". - 1 - x ..,-: 1 :■ r. ~ -^ -r ;: Z = Tl "J 70 CO is •_•:, — so >q r-; ■* i- ^ t— ~. tA eo «o SS - 55 " * S S S S s .= J-"::' J'.-'::".' E-^: 7 -' 7 ^- 7 .= -' -":/ - ' ■■' -"-' .= ^ ^ »' ~ ''^^ '"V § £ Is § = JS- i-hnt;z .:-m- S 1 - X — ' I - '■£> t - O — y_ : I I - — ■_ — I - - /. :::; — — — -r -r -r iSiriiSiSin is 00 co 00 in «o otc 1 1 - ■ - — , - X — T 1 :-.-_: 7 1 : 1 X — = 1 - -r — /- ■ - 1 = _' _V- .2^^^^^^^^ - ^-1 v: — -. -j . n 1 - OS m 0C — r. r r c_ <3 • ^ h ,-: c i c i z i .-•-:':-' —' — 1 -',-' •-' , ^ i - A >5 OS O j-h t-j c -| co t>J J£5 l ^ ^ !^ S 5§ a* . " T d — . r-l : 1 CO ■* C1 r,:: of Tin: 1ai-.lt:: To find the capacity of any cylindrical measure, from 1 inch diameter to 30 indies, take the inside diameter of the meas- ure in inches, and multiply the area in the table which corresponds tc the diameter by the depth in Inches, and divide the products if gill* are required, by 7.2135 ; if pints, by 28.875 ; if quarts, by 57.75 ; and if gal- lons, by 231. If bushels are required (say in a tierce or ban'el, after tn- mean diameter is obtained), multiply as above, and divide the product by 2150.42 : the quotient is trie number of bushels. Calling the diameteis feet the areas are feet.— then, if a ship's water tank, steam boiler etc., is 5y s . or anv number of feet and parts of feet in diameter nnd the area in the table which corresponds in inches, multiply it by the lengtn in feet, and multiply this result bv the number of gallons in a cubic foot (7.4805), and the product is the answer in gallons. In any case where there are more figures in the divisor than in the dividend, add ciphers. 106 Tables, Rules and Recipes. CAPACITY OF CANS ONE IXCH DEEP. USE OF THE TABLE. Required the contents of a vessel, diameter 6 7-10 Inches, depth 10 inches. By the table o vessel l Inch deep and 6 MO Inches diameter contains .15 (hundredths) gallon, then 15 X 10 = L50, or l gallon and 2 quarts. Required the contents of a can, diameter L9 8-10 inches, depth 30 Inches By the table a vessel l Inch deep and 198-10 Inches diameter con- tains l gallon and .33 (hundredths), then 1.33 x 30 = 39.90, or nearly 40 gallons. Required the depth of a can whose diameter is 12 2-10 Inches, to contain 16 gallons. By the table a vessel 1 inch deep and 12 2-10 inches diameter contains .50 (hundredths) gallon, then 16 ■*- .50 = 32 inches, the depth required. DIam . eter. Vio Vio Vio Vio V.o Vio Vio 3 .03 .03 .03 .03 .03 Ji4 .04 .05 4 ■ .06 .05 .06 .07 .oT .67 .08 5 .08 .MS .08 .10 .10 .11 .11 .11 6 .12 .12 .12 .13 .13 .14 .14 .15 .16 .16 7 ,16 .17 .17 .18 .is .19 .19 .20 .21 8 .21 .22 .... .23 .23 .24 .26 .26 .26 9 .27 .28 .30 .30 .31 .31 .32 .33 10 .34 .34 .36 .36 .37 .39 .10 11 .n .41 .43 .44 .41 .46 .46 .47 is 12 .is .49 .50 .:,1 .52 .53 .64 .55 13 .57 .58 .59 .60 .61 .63 .64 .65 14 .66 .67 .68 .69 .70 .71 .72 .74 .75 15 .76 .77 .78 .80 .si .82 .83 .84 16 .ST .88 .89 .90 .91 .92 .94 .95 .97 17 .98 .99 1.005 1.017 1.028 L040 1.061 L063 1.076 1.086 18 1.10] 1.113 l . 1 26 1.150 L162 l.lTo 1.187 1.200 1.211 19 1 ' ,-, 7 L240 1.253 1.266 1.279 1.292 L317 1.330 L343 20 L360 1.373 1.386 L400 1.414 MI'S 1.441 1 . 166 1 ITS 1 . 182 21 L499 1.513 1.527 1.542 1.556 1.570 1.600 1.612 1 630 '"2 1.646 L660 1.675 1.696 1.706 1.720 1.735 1.760 l 770 L780 23 L.798 1.814 L845 1.861 is;,; L892 L908 1.923 1.940 24 1.958 1.974 1.991 2.007 2.023 2.040 2.072 2.105 25 2.125 2.142 2.159 2.176 2.193 2.12H 2.227 '.'.211 2.261 2.280 26 2.298 2.316 2.333 2.361 2.369 2.404 2.446 2.460 27 2.478 2. 196 2.515 2.552 2.570 2.607 2.643 28 2 665 2.684 2.703 2 722 2.741 2.764 2.800 2.820 29 2.859 2.879 2 898 2.918 2.977 2.997 3.017 3.036 30 3.060 3.080 3.100 3.121 3.141 3.162 3.182 3.202 3.223 3.246 ::i 3.267 3.288 3.309 3.330 3.351 3.393 3.414 3.436 3.457 32 3.481 3.503 3.524 3.543 3.568 3.590 3.612 3.633 3.655 3.589 33 3.702 3.725 3.747 3.773 3.814 3.860 3.882 3.904 34 3.930 3.953 3.976 1.003 4.022 4.046 4.070 i.o«.i2 1.115 4 llo 35 4.165 4.188 4.212 4.236 1.260 1.284 4.307 4.331 1.366 4.380 36 4.406 4.430 4.465 4.483 4.503 4.528 1.553 L577 4.602 4.626 37 4.654 4.679 4.704 1.730 1.755 4.780 4.805 4.834 4.855 4.880 38 4.909 4.935 4.961 4.987 5.012 5.038 6.064 5.090 5.120 5.142 39 5.171 5.197 5.224 5.250 5.304 5.330 5.357 5.383 5.410 40 5.440 5.467 6.491 5.548 5.576 5.603 5.630 5.657 5.684 Tables, Rules and Recipes. 107 RULES FOR CALCULATING CIRCUM- FERENCES. 1st. Multiply the given diameter by 22, and divide the product by 7 ; or 2d, divide 22 by 7 and multiply the di- ameter by the quotient ; or 3d, multiply the diameter by 3.1416; or 4th, multiply the diameter by 3 and add 1 inch for every 7 of the diameter, or about y% inch for every 1. For example: If the given diameter be 15 inches, by the first rule the circumference would be 47 1-7 inches ; by the second, 47 1-7 inches ; by the third, 47.1240 inches; by the fourth, 47J/8 inches; by the table. XJ X A inches. It will be seen that the result is not just the same by the several rules, yet either is near enough for general use and prac- tice. WEIGHT OF WATER. 1 cubic inch is equal to .0361 7 pound. 12 cubic inches is equal to .434 pound. 1 cubic fool is equal to pounds. 1 cubic fool is equal to 7.50 I T .S. gallons. 1.8 cubic feel isequalto 112.00 pounds. 3f>.84 cubic feet is equal to 2240.00 pounds. 1 cylindrical inch is equal to .02842 pound. 12 cylindrical inches isequalto .341 pound. cylindrical foot isequalto 49.10 pounds. 1 cylindrical foot isequalto <;.0() U.S. gallon' 2.282 cylindrical feet isequalto 112.00 pounds. 4r>.<;4 cylindrical feet isequal to 2240.00 pounds. 13.43 United States gallons. ..isequalto 111'. <><> pounds. 268.8 United States gallons ... is equal to 2240.00 pounds. Center of pressure is at two-thirds depth from surface. TO FIND NUMBER OF BARRELS IN CISTERNS. The following table shows the number of barrels (31^ gallons) contained in cisterns of various diameters, from 5 to 30 feet, and of depths ranging from 5 to 20 feet io8 Tables, Rules and Recipes. To use the table, find the required depth in the side column, and then follow along the line to the column which has the required diameter at the top. Thus, with a cistern 6 feet deep and 16 feet in diameter, we find 6 in the second line, and then follow along until column 16 is reached, when we find that the contents is 286.5 barrels. NUMBER OF BARRELS (31^ GALLONS) IN CISTERNS AND TANKS. Diameter in feet. Depth in feet. 5 6 7 8 9 10 11 12 13 5 23.3 33.6 4:,. 7 59.7 75.5 93.2 112.8 134.3 157.6 6 28.0 40.3 54.8 71.7 90.6 111.9 135.4 161.1 189.1 7 32.7 47.0 04.0 83.6 105.7 130.6 158.0 188.0 220.6 8 37.3 53.7 73.1 95.5 120.9 149.2 180.5 214.8 252.1 9 42.0 60.4 82.2 107.4 136.0 107.9 203.1 241.7 283.7 10 46.7 07.1 91.4 119.4 151.1 186.5 225.7 268.6 315.2 11 51.3 73.9 100.5 13L3 166.2 2i»5.1 248.2 295.4 346.7 12 56.0 80.6 109.7 143.2 181.3 223.8 270.8 322.3 378.2 13 Gii.7 L55.2 196.1 242.4 293.4 349.1 4U9.7 14 65.3 94.0 127.9 167.1 211.5 261.1 315.9 376.0 441.3 15 70.0 L00.7 137.1 179.0 226.6 289.8 338.5 402.8 472.8 16 74.7 107.4 146.2 191.0 241.7 298.4 361.1 429.7 504.3 17 79.3 114.1 155.4 202.9 250.S 317.0 383.6 456.6 535.8 18 84.0 120.9 164.5 214.8 272.0 335.7 406.2 483.4 567.3 19 88.7 127.6 17::. 226.8 287.0 354.3 428.8 510.3 598.0 20 93.3 134.3 182.8 238.7 302.1 373.0 451.3 537.1 630.4 Diamet er in feet. Depth in feet ;. 14 15 16 17 18 19 20 21 22 5 182.8 209.8 238.7 269.5 302.1 336.6 373.0 411.2 451.3 6 219.3 251.8 286 5 323.4 362.0 404.0 447.6 493.5 541.6 7 255.9 293.7 J!34 2 377.3 423.0 471.3 522.2 575.7 631.9 3 292.4 335.7 382.0 431.2 483.4 538.f 596.8 658.0 722.1 9 329.0 377.7 429.7 485.1 543.S 605.9 671.4 740.2 812.4 10 365.5 419.6 477.4 539.0 604.3 673.3 746.0 822.5 902.7 11 402.1 461.6 592.9 667.7 740.6 820.6 904.7 992.9 12 438.6 503.5 572.9 616.8 725.1 807.9 895.2 987.0 1083.2 475.2 545.5 620.7 700.7 785.5 875.2 969.8 1069.2 1173.5 14 511.8 587.5 668.2 754.6 846.6 942.6 1044.4 1151.5 1263.7 15 548.3 029.4 716.2 808.5 906.0 1009.9 1119.0 1233.7 1354.0 16 584.9 071.4 77::. 9 862.4 966.8 1077.2 1193.6 1315.9 1444.3 17 621.4 713.4 811.6 916.3 1027.2 1144.6 1268.2 1398.2 1534.5 IS 658.0 755.3 859.4 97(1.2 1087.7 1211.9 1342.8 1480.4 1624.8 19 694.5 797.3 907.1 1024.1 1148.1 1279.2 1417.4 1562.7 1715.1 20 731.1 839.3 954.9 1078.0 1208.5 1346.5 1492.0 1644.9 1805.3 Tables, Rules and Recipes. 109 Diameter in feet. Depth in feet . 23 24 25 26 27 28 29 30 5 493.3 537.1 582.8 630.4 679.8 731.1 784.2 6 644.5 699.4 756.5 M5.X 877.3 941.1 1007.1 7 690.6 752.0 815.9 882.5, 951.7 1023.5 1097.9 1175.0 8 789.3 859.4 932.5 1008.6 1087.7 1169.7 1254. X 1342.8 9 887.9 966.8 1049.1 1134.7 L223.6 1316.0 1411.6 1510.7 10 986.6 1074.2 1165.6 1260.8 1359.6 1162.2 156S.2 1678.5 11 Ins:,.:: 1181.7 1282.2 1386.8 1495.6 1608.7 1723.0 1846.4 12 1183.9 1289.1 1398.7 1512.9 1631.5 1754.fi 1882.2 2014.2 i.; 1282.6 1396.5 1515.3 1639.0 1767.5 1900.8 2039.0 2182.0 11 1381.2 1503.9 1631.9 1765.1 1903.4 2047.1 2195.9 2343.9 15 1479.9 Mil. 4 1748.4 1891.1 2039.4 2193.3 2352.7 2517.8 it; L578.5 1S65.0 20172 2175.4 2339.5 2509.6 2685.6 17 1677.2 1826.2 1981.6 2143.3 2S11.3 2485.7 2666. 1 2853.5 18 1775.9 1933.6 2098.1 2269.4 2447.3 2631.9 2823.3 3021.3 19 1874.5 2041.1 2214.7 2395.4 277S.1 29S0.1 3189.2 20 1973.2 2148.5 2321.2 2521.5 2719.2 2924.4 3137.0 3357.0 For tanks that are tapering the diameter may be measured four- tenths from large end. TABLE SHOW IXC THE PRESSURE 01- WATER PER SQUARE INCH, DUE TO DIFFERENT HEADS, FROM 1 TO 250 FEET. Head. Pressure in lbs. Head. Pressure in lbs. Head. Pressure in lbs. 1 .4335 J9 8.237 37 16.04 2 .8670 20 8X70 38 16.47 3 1.300 21 9.104 39 16.91 4 1.734 22 9.537 40 17.34 5 2.167 23 9.971 50 21.67 6 2.601 24 10.40 100 43.35 7 3.035 25 10.84 110 47.68 8 3.408 26 11.27 120 52.02 9 3.902 27 11.70 130 56.36 10 4.335 28 12.14 140 60.69 11 4.768 29 12.57 150 65.03 12 5.202 30 13.00 160 69.36 13 5.636 31 13.44 170 73.70 14 6.069 32 13.87 180 78.03 15 C.503 33 14.S1 190 82.36 16 6.936 34 14.74 200 86.70 17 7.370 35 15.17 225 97.41 18 7.803 36 15.60 250 108.37 MEASURES OF CAPACITY AND WEIGHT. Measures of Weight. — Avoirdupois. — 16 drams equal 1 ounce; 16 ounces 1 pound; 112 pounds 1 hundred- weight ; 20 hundredweights 1 ton. Troy. — 24 grains 1 pennyweight; 20 pennyweights 1 ounce; 12 ounces 1 pound. Apothecaries'. — 20 grains equal 1 scruple ; 3 scruples i dram; 8 drams i ounce; 12 ounces 1 pound. no Tables, Rules and Recipes. Measures of Capacity (Dry). — 2150.42 cubic inches equal 1 United States (or Winchester) bushel; the di- mensions of which are iSy 2 inches diameter inside, 19^2 inches outside and 8 inches deep ; 2747.70 cubic inches equal 1 heaped bushel, the cone of which must not be less than 6 inches high. Measures of Capacity (Liquids). — 231 cubic inches equal 1 United States standard gallon ; 2JJ.2J<\ cubic inches equal 1 Imperial (British) gallon; 31^ United States gallons equal 1 barrel ; 42 gallons equal 1 tierce ; 63 gallons equal 1 hogshead ; 84 gallons equal 1 puncheon ; 126 gallons equal 1 pipe; 252 gallons equal 1 tun. French Measures of Frequent Reference, Com- pared with U. S. Measures. — Meter, 3.28 feet ; Deci- meter (1-10 meter), 3.94 inches; Centimeter, .4 inch; Millimeter, .04 inch; Hectoliter, 26.42 gallons; Liter, 2. n pints ; Kilogram, 2.2 pounds. Weights of Various Substances. — Pounds Avoir- dupois. — 1 cubic foot of bricks weighs 124 pounds; 1 do. of sand or loose earth, 95 ; 1 do. of cork, 15 ; 1 do. of gran- ite, 170; 1 do. of cast iron, 450; 1 do. of wrought iron, 485; 1 do. of steel, 490; 1 do. of copper, 555; 1 do. lead, 709; 1 do. brass, 520; t do. tin, 459; 1 do. white pine, 30; 1 do. oak, 48 ; 1 do. sea water, 64.08 ; 1 do. fresh. 62.35 ; 1 do. air, 0765. Tables, Rules and Recipes. in CAPACITY OF CYLINDERS IN IMPERIAL GALLONS This table gives the number of Imperial gallons (277.274 inches) in cylindrical vessels from 1 to 72 inches in depth and from 4 to 72 inches in diameter. Diameter in Inches. Depth. 10 lin. .0453 .0708 .102 .1388 .1814 . 2295 .2833 2 .0906 .1416 .204 . 2776 .3628 .4590 .5666 3 .1359 .2124 .306 .4104 .5442 .6885 .8499 4 .1812 .2832 .408 .5552 .7256 .9180 1.1332 5 .2265 . 3540 .510 .6940 .9070 1.1475 1.4165 6 .2718 .4248 .612 .8328 1 . 0884 1.3770 1 . 6998 7 .3171 .4956 .714 .9716 1.1698 1 . 6065 1.9831 8 .3624 .5664 .816 1.1104 1.4512 1 . 8360 2 . 2664 9 .4077 .6372 .918 1.2492 1 . 6326 2.0655 2 . 5497 10 .4530 .7080 1.020 1 . 3880 1.8140 2 . 2950 2 . 8330 11 .4983 .7788 1.122 1 . 5268 1 . 9954 2.5245 3.1163 12 .5436 .8496 1.224 1 . 6656 2.1768 2.7540 3 . 3996 13 . 5889 . 9204 1.326 1 8044 2 . 3582 2.9835 3 . 6829 14 .6342 .9912 1.428 1.9432 2 . 3396 3.2130 3 . 9662 15 .6795 1.0620 1 . 530 2 . 0820 2.7210 3.4425 4.2495 16 .7248 1.1328 1.632 2 . 2208 2.9024 3.6720 4.5328 17 .7701 1 . 2036 1 . 734 2 . 3596 3.0838 3.9015 4.8161 18 .8154 1.2744 1 .836 2 . 4984 3.2652 4.1310 5 . 0994 19 .8607 1.3452 1.938 2.6372 3.4466 4 . 3605 5.3827 20 .9060 1.4160 2.040 2.7760 3 . 6280 4 . 5900 5.6660 21 .9513 1 . 4868 2.142 2.9148 3 . 5094 4.8195 5.9493 22 .9966 1 . 5576 2.244 3.0536 3 . 9908 5 . 0490 6.2326 23 1.0419 1 . 6284 2.346 3.1924 4.1722 5.2785 6.5159 24 1.0872 1 . 6992 2.448 3.3312 4 . 3536 5.5080 6.7992 25 1.1325 1 . 7700 2.550 3 . 4700 4 . 5350 5.7375 7 . 0825 26 1.1778 1 . 8408 2.652 3 . 6088 4.7164 5.9670 7.3658 27 1.2231 i '.tut; 2.754 3.7476 4 . 8978 6.1965 7.6491 28 1 . 2684 1 . 9824 2 . 856 3 . 8864 4 . 6792 6.4260 7.9324 29 1.3137 2.0532 2.95S 4 . 0252 5 . 2606 6.6555 8 . 3057 30 1 . 3590 2.1240 3.060 4.1640 5.4420 6 . 8850 8.4990 31 1.4043 2.1948 3.162 4 . 3028 5.6234 7.1145 8.7823 32 1.4496 2.2656 3 . 264 4.4416 5 . 8048 7 . 3440 9 . 0656 33 1.4949 2 . 3364 3 . 366 4 . 5804 5.9862 7 . 5735 9 . 3489 34 1 . 5402 2.4072 3.468 4.7192 6.1676 7 . 8030 9.6322 35 1 . 5855 2.4780 3.570 4 . 8580 6 . 3490 8.0325 9.9155 36 1 . 6308 2 . 5488 3.672 4 . 9968 6.5304 8.2620 10.1988 40 1.8120 2 . 8320 4.080 5.5520 7 . 2560 9 . 1800 11.3320 44 1.9932 3.1152 4.489 6.1072 7.9816 10.0980 12.4652 48 2.1744 3 . 3984 4.896 6.6624 8.7072 11.0160 13 . 5984 54 2.4462 3.8232 5.508 7.4952 9.7956 12.3930 15.2982 60 2.7180 4 . 2480 6.120 8.3280 10 . 8840 13.7700 16.9980 72 3.2616 5.0976 7.344 9.9936 13.0608 16.5240 20.3976 112 Tables, Rules and Recipes. CAPACITY OF CYLINDERS IN IMPERIAL GALLONS— Continued Diameter in Inches. Depth. 11 12 13 14 15 16 lin. .3428 .4080 .4788 .5553 .6375 .7253 2 .6856 .8160 .9576 1.1106 1 . 2750 1.4506 3 1 . 0284 1.2240 1.4364 1 . 6659 2.0125 2.1759 4 1.3712 1 . 6320 1.9152 2.2212 2 . 5500 2.9012 5 1.7140 2 . 0400 2 . 3940 2.7765 3.1875 3.6265 6 2 . 0568 2.4480 2 . 8728 3.3318 3 . 8250 4.3518 7 2.3996 2.8560 3.3516 3.8871 4.3625 5.0771 8 2 . 7424 3.2640 3 . 8304 4.4424 5.1000 5.8024 9 3 . 0852 3.6720 4.3092 4.9977 5.7375 6.5277 10 3.4280 4.0800 4.7880 5.5530 6.3750 7.2530 11 3.7708 4.4880 5.2668 6.1083 7.0125 7.9783 12 4.1136 4 . 8960 5.7456 6.6636 7.6500 8.7036 13 4.4564 5 . 3040 6.2244 7.2189 8.2875 9.4289 14 4.7992 5.7120 6.7032 7.7742 8.7250 10.1542 15 5.1420 6.1200 7.1820 8.3295 9.5625 10.8795 16 5.4848 6.5280 7 . 6608 8.8848 10.2000 11.6048 17 5.8276 6.9360 8.1396 9.4401 10.8375 12.3301 18 6.1704 7.3440 8.6184 9.9954 11.4750 13.0554 19 6.5132 7.7520 9.0972 10.5507 12.1125 13.7807 20 6.8560 8.1600 9.5760 11.1060 12.7500 14 . 5060 21 7.1988 8.5680 10.0548 11.6613 13.0875 15.2313 22 7.5416 8.9760 10.5336 12.2166 14.0250 15.9566 23 7 . 8844 9 . 3840 11.0124 12.7719 14.6625 16.6819 24 8.2272 9.7920 11.4912 13.3272 15.3000 17.4072 25 8.5700 10.2000 11.9700 13.8825 15.9375 18.1325 26 8.9128 10.6080 12.4488 14.4378 16.5750 18.8578 27 9.2556 11.0160 12.9276 14.9931 17.2125 19.5831 28 9 . 5984 11.4240 13.4064 15.5484 17.4500 20.3084 29 9.9412 11.8320 13.8852 16.1037 18.4875 21.0337 30 10.2840 12.2400 14.3640 16.6590 20.1250 21.7590 31 10.6268 12.6480 14 . 8428 17.2143 19.7625 22.4843 32 10.9696 13.0560 15.3216 17.7696 20.4000 23.2096 33 11.3124 13.4640 15.8004 18.3249 21.0375 23.9349 34 11.6552 13.8720 16.2792 18.8802 21.6750 24 . 6602 35 11.9980 14.2800 16.7580 19.4355 21.8125 25.3855 36 12.3408 14.6880 17.2368 19.9908 22 . 9500 26.1108 40 13.7120 16.3200 19.1520 22.2120 25.5000 29.0120 44 15.0832 17.9520 21.0672 24.4332 28.0500 31.9132 48 16.4544 19.5840 22 . 9824 26.6544 30.6000 34.8144 54 18.5112 22 . 0320 25.8552 29.9862 34.4250 39.1702 60 20.5680 24.4800 28.7280 33.3180 38.2500 43.5180 72 24.6816 29.3760 34.4736 39.9816 45.9000 52.2216 Tables, Rules and Recipes. "3 CAPACITY OF CYLINDERS IN IMPERIAL GALLONS— Continued Diameter in Inches. Depth. 17 18 19 20 21 24 lin. .8188 .9180 1.0228 1.1333 1.2495 1 . 632 2 1.6376 1 . 8360 2.0456 2.2666 2 . 4990 3.264 3 2.4564 2 . 7540 3.0684 3 . 3999 3 . 7485 4.986 4 3.2752 3.6720 4.0912 4 . 5332 4.9980 6.528 5 4.0940 4 . 5900 5.1140 5.6665 6.2475 8.160 6 4.9128 5.5080 6.1368 6.7998 7.4970 9.792 7 5.7316 6 . 4260 7.1596 7.9331 8.7465 11.424 8 6 . 5504 7.3440 8.1824 9.0664 9.9960 13.056 9 7.3692 8.2620 9.2052 10.1997 11.2455 14 . 688 10 8.1880 9 . 1800 10.2280 11.3330 12.4950 16.320 11 9.0068 10.0980 11.2518 12.4663 13.7445 17.952 12 9 . 8256 11.0160 12.2736 13.5996 14.9940 19 . 584 13 10.6444 11.9340 13.2964 14 . 7329 16.2435 21.216 14 11.4632 12.8520 14.3192 15.8662 17.4930 22.848 15 12.2820 13.7700 15.3420 16.9995 18.7425 24.480 16 13.1008 14 . 6880 16.3648 18.1328 19.9920 26.112 17 13.9196 15.6060 17.3876 19.2661 21.2415 27.744 18 14 . 7384 16.5240 18.4104 20.3994 22.4910 29.376 19 15.5572 17.4420 19.4332 21.5327 23 . 7405 31.008 20 16.3760 18.3600 20.4560 22.6660 24 . 9900 32.640 21 17.1948 19 . 2780 21.4788 23 . 7993 26 . 2395 34 . 272 22 18.0136 20.1960 22 . 5036 24.9326 27 . 4890 35 . 904 23 18.8324 21.1140 23.5244 26.0659 28.7385 37.536 24 19.6512 22 . 0320 24 . 5472 27.1992 29 . 9880 39.168 25 20.4700 22.9500 25.5700 28.3325 31.2375 40.800 26 21.2888 23 . 8680 26 . 5928 29.4658 32.4870 42.432 27 22.1076 24.7860 27.6156 30.5991 33.7365 44 . 064 28 22.9264 25.7040 28.6384 31.7324 34.9860 45.696 29 23.7452 26.6220 29.6612 32 . 8657 36.2355 47.328 30 24.5640 27 . 5400 30.6840 33.9990 37.4S50 48.960 31 25.3828 28.4580 31.7068 35.1323 38.7345 50.592 32 26.2016 29 . 3760 32.7296 36.2656 39.9840 52 . 224 33 27 . 0204 30.2940 33.7554 37.3989 41.2335 53.856 34 27.8392 31.2120 34 . 7752 38.5322 42.4830 55.488 35 28.6580 32 . 1300 35.7980 39 . 6655 43.7325 57.120 36 29.4768 33 . 0480 36 . 8208 40.7988 44.9820 58.752 40 32.7520 36.7200 40.9120 45.3320 49.9800 65.280 44 36.0272 40.3920 45.0072 49 . 8652 54.9780 71.808 48 39 . 3024 44 . 0640 45.0944 54 . 6384 59.9760 78.336 54 44.2152 49 . 5720 55.2312 61.1982 67.4730 88.128 60 49 . 1280 55.0800 61.3680 67.9980 74.9700 97.920 72 58.9536 66.0960 73.6416 81.5976 89.9640 117.504 ii4 Tables, Rules and Recipes. CAPACITY OF CYLINDERS IN IMPERIAL GALLONS— Continued Diameter in Inches. Depth. 30 36 40 48 DO 72 lin. 2.55 3.672 4.5333 6.528 10.2 14 . 688 2 5.10 7.344 9 . 0666 13.056 20.4 29.376 3 7.65 11.016 13.5999 19 . 584 30.6 44 . 064 4 10.20 14.688 18.1332 26.112 40.8 58.752 5 12.75 18.360 22.6665 32 . 640 51.0 73 . 440 6 15.30 22.032 27.1998 39.168 61.2 88.128 7 17.85 25.704 31.7331 45.696 71.4 102.816 8 20.40 29.376 36.2664 52 . 224 81.6 117.504 9 22.95 33 . 048 40.7997 58.752 91.8 132.192 10 25.50 36.720 45.3330 65.280 102.0 146.880 11 28.05 40.392 49.8663 71.808 112.2 161.568 12 30.60 44 . 064 54 . 3996 78.336 122.4 176.256 13 33.15 47.736 58.9329 84 . 864 132.6 190.944 14 35.70 51.408 63 . 4662 91.382 142.8 205 . 632 15 38.25 55.080 67.9995 97.920 153.0 220.320 16 40.80 58.752 72 . 5328 104.448 163.2 235 . 008 17 43.35 62.424 77.0661 110.976 173.4 249 . 696 18 45.90 66.096 81.5994 117.504 183.6 264 . 384 19 48.45 69 . 768 86.1327 124.032 193.8 279.072 20 51.00 73.440 90.6660 130.560 204.0 293.760 21 53.55 77.112 95.1999 137.088 214.2 308.448 22 56.10 80.784 99.7326 143.616 224.4 323.136 23 58.65 84.456 104 . 2659 150.144 234.6 337.824 24 61.20 88.128 108.7992 156.672 244 . 8 352.512 25 63.75 91.800 113.3325 163.200 255.0 367 . 200 26 66.30 95.472 117.8658 169.728 265.2 381.888 27 68.85 99 . 144 122.3991 176.256 275.4 396 . 576 28 71.40 102.816 126.9324 182 . 784 285.6 411.264 29 73.95 106.488 131.4657 189.312 295.8 425.952 30 76.50 110.160 135.9990 195.840 306.0 440.640 31 79.05 113.832 140.5326 202.368 316.2 455.328 32 81.60 117.504 145.0656 208.896 326.4 470.016 33 84.15 121.176 149.5989 215.424 336.6 484 . 704 34 86*. 70 124.848 154.1322 221.952 346.8 499 . 392 35 89.25 128.520 158.6655 228 . 480 357.0 514 . 080 36 91.80 132.192 163.1988 235.008 367.2 528.768 40 102 . 00 146.880 181.3320 261.120 408.0 587.520 44 112.20 161.568 199.4652 287 . 232 448.8 646.272 48 122.40 176.256 217.5984 313.344 489.6 705.024 54 137.70 198.288 244 . 2982 352.512 550.0 793.152 60 153 . 00 220.320 271.9980 391.680 612.0 881.280 72 183.60 264 . 384 326.3976 470.016 734.4 1057 . 536 Tables, Rules and Recipes. 115 TABLE OF EFFECTS UPON BODIES BY HEAT. Degrees F. Cast iron thoroughly melts at 2,228 Gold melts at 1.9J3 Silver melts at M*J Copper melts at 1070 Brass melts at • vm Zinc melts at ■ u -' Lead melts at tns Bismuth melts at ^6 Tin melts at 444 Tin and lead, equal parts, melt at 4is Tin 2 parts, bismuth 5 and lead 3. melt at u» PRACTICAL RECEIPTS. SOLDERS. SOLDER FOR GOLD. Gold, 6 pennyweights ; silver, 1 pennyweight ; copper, 2 pennyweights. SOLDER FOR SILVER, FOR THE USE OF JEWELERS. Fine silver, 19 pennyweights; copper, 1 pennyweight; sheet brass, 10 pennyweights. WHITE SOLDER FOR SILVER. Silver, 1 ounce ; tin, 1 ounce. WHITE SOLDER FOR RAISED BRITANNIA WARE. Tin, 100 pounds; copper, 3 ounces; to make it free, add lead, 3 ounces. BEST SOFT SOLDER FOR CAST BRITANNIA WARE. Tin, 8 pounds ; lead, 5 pounds. YELLOW SOLDER FOB BRASS OR COPPER. Copper, 1 pound ; zinc, 1 pouna. n6 Tables, Rules and Recipes. YELLOW SOLDER FOR BRASS OR COPPER. (Stronger than the last.) Copper, $2 pounds; zinc, 29 pounds ; tin, 1 pound. SOLDER FOR COPPER. Copper, 10 pounds ; zinc, 9 pounds. BLACK SOLDER. Copper, 2 pounds ; zinc, 3 pounds ; tin, 2 ounces. BLACK SOLDER. Sheet brass, 20 pounds ; tin, 6 pounds ; zinc, 1 pound. SILVER SOLDER FOR PLATED METAL. Fine silver, 1 ounce; brass, 10 pennyweights. plumbers' solder. Lead, 2 ; tin, 1 part. tinmen's solder. Lead, 1 ; tin, 1 part. PEWTERERS' SOLDER. Tin, 2; lead, 1 part. HARD SOLDER. Copper, 2 ; zinc, 1 part. SOLDER FOR STEEL JOINTS. Silver, 19 pennyweights; copper, 1 pennyweight; brass, 2 pennyweights. Melt under a coat of charcoal dust. SOFT GOLD SOLDER Is composed of 4 parts gold, 1 of silver and 1 of copper. It can be made softer by adding brass, but the solder be- comes more liable to oxidize. Tables, Rules and Recipes. 117 CEMENT FOR MENDING EARTHEN AND GLASS WARE. I. Heat the article to be mended a little above boiling water heat, then apply a thin coating of gum shellac on both surfaces of the broken vessel, and when cold it will be as strong as it was originally. 2. Dissolve gum shellac in alcohol, apply the solution and bind the parts firmly together until the cement is perfectly dry. CEMENT FOR STONE WARE. Another cement in which an analogous substance, the curd of milk, is employed, is made by boiling slices of skim milk cheese into a gluey consistence in a great quan- tity of water, and then incorporating it with quicklime on a slab with a muller, or in a marble mortar. When this compound is applied warm to broken edges of stone ware, it unites them very firmly after it is cold. IROX RUST CEMENT Is made from 50 to 100 parts of iron borings, pounded and sifted, mixed with 1 part of sal ammoniac, and when it is to be applied, moistened with as much water as will give it a pasty consistency. Another composition of the same kind is made by mixing 4 parts of fine borings or filings of iron, 2 parts of potters' clay and 1 part of pounded pot- sherds, and making them into a paste with salt and water. CEMENT FOR IRON TUBES, BOILERS, ETC. Finely powdered iron, 66 parts; sal ammoniac, 1 part; water, a sufficient quantity to form a paste. CEMENT FOR IVORY, MOTHER OF PEARL, ETC. Dissolve 1 part of isinglass and 2 of white glue in 30 of water, strain and evaporate to 6 parts. Add 1-30 part it8 Tables, Rules and Recipes. of gum mastic, dissolve in l / 2 part of alcohol and I part of white zinc. When required for use warm and shake up. CEMENT FOR HOLES IN CASTINGS. The best cement for this purpose is made by mixing I part of sulphur in powder, 2 parts of sal ammoniac and 80 parts of clean powdered iron turnings. Sufficient water must be added to make it into a thick paste, which should be pressed into the holes or seams which are to be filled up. The ingredients composing this cement should be kept separate and not mixed until required for use. It is to be applied cold, and the casting should not be used for two or three days afterward. CEMENT FOR COPPERSMITHS AND ENGINEERS. Boiled linseed oil and red lead mixed together into a putty is often used by coppersmiths and engineers to se- cure joints. The washers of leather or cloth are smeared with this mixture in a pasty state. A CHEAP CEMENT. Melted brimstone, either alone or mixed with rosin and brick dust, forms a tolerably good and very cheap cement. plumbers' cement Consists of black rosin, 1 part ; brick dust, 2 parts ; well incorporated by a melting heat. cement for bottle corks. The bituminous or black cement for bottle corks con- sists of pitch hardened by the addition of rosin and brick dust. Tables, Rules and Recipes. no CHINA CEMENT. Take the curd of milk, dried and powdered, 10 ounces ; quicklime, 1 ounce ; camphor, 2 drams. Mix and keep in closely stopped bottles. When used, a portion is to be mixed with a little water into a paste, to be applied quickly CEMENT FOR LEATHER. A mixture of India rubber and shellac varnish makes a very adhesive leather cement. A strong- solution of common isinglass, with a little diluted alcohol added to it, makes an excellent cement for leather. MARBLE CEMENT. Take plaster of paris and soak it in a saturated solu- tion of alum, then bake the two in an oven, the same as gypsum is baked to make it plaster of paris ; after which they are ground to powder. It is then used as wanted, being mixed up with water like plaster and applied. It sets into a very hard composition capable of taking a very high polish. It may be mixed with various coloring min- erals to produce a cement of any color capable of imitating marble: CEMENT FOR MARBLE WORKERS AND COPPERSMITHS. White of an t throat for any size pipe from 3 to 62 inches and for any number of pieces with laps ■ r shows md area of all sizes of pipe, from s to 6a inches inclu- Full instru irding the use of the Chart are given in a 1 which is supplied with it. : numerous diagrams makes imple and • Many valuable tables giving the of various materials arc also include 1, together with much pi ■1 heating an 1 ventilating work. A lew of the principal articles are: Circumference including laps for all sizes of pipes from 3" to 62". Areas of all sizes of pipes from .V to §2". Length of throat of 4, 5, 6 piece elbows all radius from .V to 62". Deductions from s nail ends from No. 26 to gauge steel. Tapering joints of all sizes. Length of throat for 8, 10, 12, 15, 16, 18, 20, 24 piece elbow. Elbows of less than 90 decrees. Mitre lines for 4, 5, 6, 8, 10, 12, 15, 16, 18, 20, 24, piece elbows. Laying out elbows. Weight of galvanized pipe per lineal foot No. 26, 2 1, 22, 20 gauge. Weight of galvanized elbows of an\ radius. Weight of galvanized ducts from !"X )" to 1 1 ' 5 " X 1 1 ' 5" in three gauges. Weight of black and galvanized steel per square foot. The Booklet is bound in durable linen with a pocket in the inside front cover for the Chart. It is small enough to go in the hip-pocket. It was made for you — send for it and profit. Price Complete, 75 cents Postpaid. DAVID WILLIAMS COMPANY 239 West 39th Street, ----- New York THE NEW Metal Worker Pattern Book A TREATISE ON PATTERN CUTTING AS APPLIED TO ALL BRANCHES OF SHEET METAL WORK By GEO. W. KITTREDGE [| covers the subject so thoroughly and accurately that it is called "The Bible of the Sheet Metal Worker." Every detail of the work is taken up systematically from the selection of the instruments, through linear drawing, geometrical drawing and the principles of pattern cutting to the problems in laying out which range from the simple elbow work to the very diffi- cult problems where triangulation is thoroughly explained. Features which make the work exceptionally popular are the chapters on drawing and geometrical problems, which explain these usually difficult and discouraging subjects so clearly that no one can fail to understand them. ... As a book for home study it has no equal. The Principal Contents Terms and Definitions — 15 Pages— Explaining the various terms employed by Draftsmen, Architects and Mechanics. Drawing Instruments and Mate- rials— 13 Pages — Describing the tools and materials used by Draftsmen. Linear Drawing— 6 Pages— Explaining the principles of geometrical drawings as applied to the wants of the pattern cutter. Geometrical Problems — 35 Pages — Containing 85 problems of most frequent occurrence and sup- plementing the previous chapter. Principles of Pattern Cutting — 25 Pages — Explaining the theory of pattern cutting as applied to all classes of work. Pattern Problems (3 Sections) — 325 Pages — 1. Miter Cutting. 2. Flaring Work. 3. Triangulation. A collection of practical examples of work daily encountered by Cornice Workers and Tinners and of frequent occurrence with Builders. 438 Pages. 10X13 inches. 744 Illustrations. Cloth. Price $5.00 Delivered. DAVID WILLIAMS COMPANY 239 West 39th Street, - New York TO HANG UP IN THE SHOP THE METAL WORKER SHOP CARDS Presenting a Series of Useful Tables Convenient for Reference Every shop needs a set of these cards for they give the information you want the minute it is needed. They arc printed on heavy manila of best quality 10JX14 inches in size and are eyeletted for hanging right handy to the work. If you have ever figured the time lost in looking up the size sheet required for a tank or cylinder of givi or in getting the area of a circle. nothing more need be said in favor of the cards. No. i -The Quantity of Tin Required for Roofs (Flat and Standing Seam) With Rules for Calculating Roof No. J -The Diameters. Areas and Circumferences of Circles. Advancing by eighths, from 1 inch to 54] inches. With full Direc- tions for Use; also Tables of Conversion of Inches and Eighths into Decimals of a Foot, and n of Vulgar Fractions into Decimals; also Rules relating to the Circle. No. S —Capacity of Cylinders in United States Gallons; with Direc- tions for" Use and a schedule of Decimal Equivalents Of the Fractional Parts of a Gallon. PRICE 25 CENTS EACH. PER SET, *U) < / \ 7 V MENSURATION FOR SHEET METAL WORKERS AS APPLIED IN WORKING ORDINARY PROBLEMS IN SHOP PRACTICE With 71 Figures By WILLIAM NBUBBCKBR This new book contains an easily applied explanation of the principles of mensuration (the art of measurements), showing its practical application in solving the great number of prob- lems that arise in finding the areas, dimensions, or capaci- ties of the different sizes and shapes ol sheet metal products turned out from the shop. A very handy aid in computing the measurements of material by correct methods, and invaluable to the mechanic, shop foreman, and apprentice. 51 Pages. Cloth Covers. 50 Cents, Postpaid DAVID WILLIAMS COMPANY 239 West 39th Street, - New York METAL WORKER You want the news of your trade in a clear and interesting form with a lot of particulars about new tools, machinery and apparatus, so written that you would rather read it than your daily paper. You desire to be posted regarding the latest ideas on the design and installation of heating and plumbing systems, to know about the best ideas in pattern cutting and you desire to know the solution of the problems of the cornice maker, the plumber and the stove-man. A knowledge of what the other man is doing is a mighty good business asset, and the advice of the best brains and talent of trained experts in your line is at your command. For nearly forty years METAL WORKER has been the recognized authority and technical adviser of the sheet metal, plumbing and heating, steam-fitting, ventilating, tool and machinery trade. METAL WORKER comes from the press every week at a cost to you of only $2.00 a year. Any issue you miss may contain just the particular article that will be of greatest value to your business. M ETAL WORKER 139 WEST :59TH STREET, NEW YORK CITY IR 2 1912