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 XXth Century 
 Sheet Metal Worker 
 
 H, E, OS3SOJUME 
 
 THE AMERICAN ARTiSAN 
 
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XXth Century 
 Sheet Metal W^jrker 
 
 A Modern Treatise on Modern 
 Sheet Metal Work 
 
 BY 
 
 H. E. OSBORNE 
 
 THE AMERICAN ARTISAN 
 
 CHICAGO 
 
 1910 
 
^0 
 
 Entered according to Act of Congress in the Year 1908 
 
 by 
 
 H. E. Osborne 
 
 In the Office of the Librarian of Congress 
 
 at Washington, D. C. 
 
 CCI.A27S675 
 
TO 
 MY OLD TIME TEACHER 
 
 AND FRIEND 
 
 GRIFFETH L. JACKSON 
 
 THIS LITTLE BOOK 
 
 IS 
 
 AFFECTIONATELY 
 
 DEDICATED 
 
PREFACE 
 
 "Waste no time worrying over a mistake, but try 
 to correct it to the best of your ability, with as httle 
 loss of time and material as possible." — G. L. 
 Jackson. 
 
 And if this book shall prove to be of as- much help 
 to just one struggling' "tinker" as the above quotation 
 from my old teacher has been to me. then the time 
 spent in its preparation has been well spent. 
 
 I have endeavored to give in this work short, con- 
 cise explanations, which should be easily understood 
 by the young apprentice, and at the same time, suffi- 
 ciently scientific for the practical use of the journey- 
 man. Some of the items are of so simple a character 
 as to seem to be almost unnecessary, but I have re- 
 membered that even the most simple things have to be 
 learned. 
 
 H. E. Osborne. 
 
XXth Century 
 Sheet Metal Worker. 
 
 Having; a e^^^ii circle, to find the Bide of an equivalent square. 
 
 Multiply the diameter by the decimal .8862, or, mul- 
 tiply the circumference by the decimal .2821. Either 
 method gives the length of one side of an equivalent 
 square. 
 
 Having a gk'oi circle, to find tJic side of an in- 
 scribed square. 
 
 Multiply the diameter by the decimal .7071, or, mul- 
 tiply the circumference by the deciuidl .2251. 
 
 The first method may also be applied to find the 
 
 length of the chord of an arc of 90 degrees, a quad- 
 rant. Find the radius and multiply it by 2 and then 
 
2 XXTH CENTURY SHEET METAL WORKER. 
 
 by .7071. Because the side of an inscribed square is 
 the chord of the quadrant. 
 
 To i)iscribe a square in a circle. 
 
 Draw the two diameters BD and AC at right angles 
 to each other, and connect the extremities of the dia- 
 meters by straight lines drawn from A to B, B to C, 
 etc. 
 
 To find the radius of an arc. 
 
 To the square of the sine AC, add the square of the 
 
 versed sine CD, and divide the result by twice the 
 versed sine. 
 
 To make this plain, and dispense with the geomet- 
 rical terms. Square the length from A to C, and add 
 
 to it the square of the distance C to D and divide the 
 
XXTH CENTURY SHEET METAL WORKER. 3 
 result by twice C D. The quotient will be the length 
 of radius to produce the arc ABD. 
 
 To and the center from ivhich a given arc is pro- 
 duced. 
 
 Draw any two chords AB and CD, and bisect them, 
 and from the points thus found draw lines perpendi- 
 cular to the chords, and extending until they meet. 
 The point of meeting will be the center of the circle 
 of which the arc is a portion. 
 
 To describe a circle cutting any three points, ar- 
 ranged in any position other than a straight line. 
 
 Connect the points by straight lines; then lines 
 drawn perpendicular from the centers of these lines 
 will meet at the center of the required circle. 
 
 To find the length of an arc, zvhen the number of de- 
 grees it contains and the radius are knozvn. 
 
 Multiply the number of degrees by the decimal 
 .01745, and that product by the radius. 
 
 To find the area of a sector zvhen the number of de- 
 grees and radius arc knoion. 
 
4 XXTH CENTURY SHEET METAL WORKER. 
 
 Find the length of the arc by the preceding rule, and 
 multiply this length by one-half the radius. 
 
 To find the area of an oral or ellipse. 
 
 Multiply the two axes together, and their product 
 by the decimal .7854 and the result will be the required 
 area. 
 
 To find th« area of a clroalar ring. 
 
 1st. When the circumference and diameter are 
 both known, multiply the circumference by one-half 
 the radius (one-fourth the diameter), or multiply one- 
 half the circumference by one-half the diameter. 
 
 2d. When the diameter only is known, square the 
 diameter and multiply by the decimal .7854. 
 
 To find the area of a circular ring. 
 
 The space between two circles of unequal size., and 
 
 having a common center. Square the diameter of each 
 circle, and subtract the square of the lesser from the 
 square of the greater, and multiply the difference by 
 the decimal .7854. 
 
XXTH CKNTURY SHEET METAL WORKER. 
 To inscribe an equilateral triangle in a circle. 
 
 With any point (as A) as center, and radius equal 
 to radius of the circle, describe arc cutting the circum- 
 ference in B and then in C. Then bisect the arc B D 
 C, and connect the points B, C, and D. 
 
 To inscribe a hexagon in a circle. 
 
 Describe the eciuilateral triangle as before. Then 
 
XXTH CENTURY SHEET METAL WORKER. 
 
 bisect the arc C D in F, and the arc B D in G, and 
 drew AC, CF, FD, DG, GB, and BA. 
 
 Or it may be inscribed by applying the radius six 
 times around the circumference. This is the most 
 common method. 
 
 To inscribe a regular pentagon in a circle. 
 
 Draw the diameters AP and MN at right angles to 
 each other, and bisect the radius ON at E. From A 
 
 N 
 
 as center, and EA as radius, describe the arc SB. Join 
 the points A and B, and the hne AB being applied 
 five times around the circle will form the pentagon. 
 
 To draiv squares rvhose areas shall be proportionate 
 to the areas of given squares. 
 
 Fig. I. To draw a square % the area of a given 
 square. Bisect one side of the given square, and con- 
 struct a square upon half its length. 
 
 Fig. 2. To draw a square J/2 the area of a given 
 square. Draw diagonal lines from corner to corner 
 
XXTH CENTURY SHEET METAL WORKER. 
 
 Fig, !• Fig. 2, 
 
 of the given square, and construct a square upon 
 half the length of one of the diagonals. 
 
 Fig. 3. To draw a square twice the area of a given 
 
 Fig. 3. 
 
 square. Draw a diagonal line from corner to corner 
 of the square, and construct a square upon the diag- 
 onal. 
 
 This is simply the reverse of Fig. 2. 
 
 Fig. 4. To draw a square three times the area of 
 a given square. Extend the side of the given square 
 to a length equal to its diagonal, A to B, and from 
 
8 XXTll CENTURY SHEET METAL WORKER. 
 
 the extremity of the extension, draw a hne to the op- 
 posite corner of tiie square (B to C), upon which 
 construct a square. 
 
 Fig. I. To draw a square four times the area of a 
 given square. Construct a square on a Vme twice the 
 
 Fig. 4. 
 
 length of one side tlie given square. 
 
 Just the reverse of finding one of one-fourth the 
 area. 
 
 Fig. 5. To draw a square five times the area of a 
 given square. Extend one side of the square to twice 
 its original length, A to B, and from the extremity 
 of the extension draw a line to the opposite corner 
 of the square (B to C), upon which construct a 
 square. 
 
XXTii CENTL'RV SllKliT METAL WORKER. 9 
 
 Pig. 5. 
 
 To describe an i\i:^g-sliapC(i oz'al. 
 
 Describe a circle the size desired for the round 
 end of the figure, and draw two diameters at right 
 angles, as shown in cut. Then draw a straight line 
 from each end of one of the diameters through the ex- 
 tremity of the other diameter and extending indefi- 
 nitely. With each enfl of the first diameter for center, 
 and radius equal to the diameter, strike an arc from 
 tlie opposite end of the diameter just to the diagonal 
 line. Then with the intersection of the diagonal lines 
 with the other diameter for center, and radius to just 
 
10 XXTH CENTURY SHEET METAL WORKER. 
 
 meet the previous arcs, or side arcs, draw the small 
 end arc, which completes the fig;urc. 
 
 To draw an arc throngJi three points ■without locat- 
 ing the center. 
 
 Let A B and C be the points. Then with A and C 
 as centers, and radius from A to C make arcs from 
 A and C indefinitely towards D. Draw a straight line 
 
 from A through B intersecting the arc C D at F. And 
 another straight line from C through B intersecting 
 the arc A D at G. 
 
XXTH CENTURY SHEET METAL WORKER. n 
 
 Space the arcs between A and G. and between C and 
 F into the same number of equal spaces, continuing 
 one or two of the spaces beyond G and F towards D. 
 Connect the points marked on A D with the point C, 
 and the points marked on C D with the point A, and 
 draw a freehand line through the intersections of these 
 lines. 
 
 To draiv any number of concentric circles, the area 
 of each circular ring thus formed being equal to the 
 area of each of the others and to the circle in the center. 
 
 Draw a straight line A B. and space it into the num- 
 ber of equal spaces desired. Bisect A B and draw 
 
 upon it a semicircle, and draw a line perpendicular to 
 A B from each of the points to the circumference of 
 
12 XXTH CENTURY SHEET METAL WORKER. 
 
 the semicircle, as c, d, c, and f. Then with A as center 
 and rachus A c describe the inner circle. The next 
 with radius A d, &c., as shown in cut. 
 
 To draw a line from a gircii point in a straight line, 
 perpendicular to the gii'en line. 
 
 B 
 
 Let A be the given point, and R C the given line. 
 
 Place one point of the dividers at A and set off B 
 and C equal to each other. Tlien with B and C as 
 centers, and with radius greater than A B, describe 
 two arcs intersecting at D. Draw A D and it will be 
 perpendicular to the line B C. 
 
 Or, if the point A is near the end of the giz'en line. 
 
 Place one foot of the dividers at anv reasonable 
 
 point, as P. and extend the other foot to A. Then with 
 
XXTH CENTURY SHKET METAL WORKER. 13 
 
 P as center and radius from P to A, describe a semi- 
 circle, or a complete circle would be better, perhaps. 
 Through C. where the circle cuts the line B A, and the 
 point P, draw the line C P D. Then draw A D, and it 
 will be perpendicular to the line B A. 
 
 To draw from a i^ic'cii point outside a given straight 
 line, a perpendicular to that line. 
 
 Let A be the given point, and B D the given line. 
 Then from the point A as a center, and with a radius 
 greater than the distance from the line to A, describe 
 
14 XXTH CENTURY SHEET METAL WORKER. 
 
 an arc cutting the line B D in the points B and D ; then 
 mark the point E, equally distant from B and D, and 
 draw A E, and it will be perpendicular to B D. 
 
 Or if the point A is nearly opposite one end of the 
 given line. 
 
 Draw the line A C to any point on the line B D, as 
 C. Bisect A C at F. Then with F as center, and F 
 C or F A as radius, describe the semicircle C D A, and 
 draw A D and it will be perpendicular to B D. 
 
 Triangle 
 
 2nd posi- 
 tion. 
 
 Triepi 
 1st pQS 
 tion. 
 
XXTH CENTURY SHEET METAL WORKER. 15 
 
 To draiv a line to a gkrn p.oint, and pcrf^cndicidar 
 to a i^h'cn line, iisini^ only a rule and trianij^le. 
 
 Let AB be the given line, and C the given point. 
 
 Place the long edge of the triangle against the rule 
 v^ath the other long edge resting on the line AB. Then 
 holding the rule firmly, slide the triangle along until 
 the short side touches the point C. Then draw CD 
 and it will be perpendicular to the line AB. 
 
 Of course, only a right-angled triangle, as shown, 
 can be used. 
 
 With the same tools, to draiv a line to a given point, 
 and parallel to a gii'en line. 
 
 "" 'TrlangTe 
 
 I 2nd position, jy 
 
i6 XXTH CENTURY SHEET METAL WORKER. 
 
 Let C be the given point, and AB the given line. 
 
 Place the rule and triangle the same as in the pre- 
 vious example, and slide the triangle until the top 
 edge just reaches the point C. Then draw a line along 
 the top edge from C towards D, and it will be parallel 
 to the line AB. 
 
 To draiu a straight line equal to a given arc, an arc 
 equal to a gii'en straight line, or an arc of different 
 curvature equal to a gii'en arc. 
 
 1^ 
 
 Pig. 1. 
 
 Space the given arc, Figure i, into 4 equal spaces 
 by the intermediate points i, 2, 3. Draw AC tangent 
 to the arc at A, and with A as center and radius A i 
 mark D (the chord of yi the arcj. Then with D as 
 center and radius D B strike the arc B E, and A K 
 will be the same length as A B. 
 
 Or, if the straight line be given, space it into 4 
 
XXTH CENTURY SHEET METAL WORKER. 17 
 
 equal spaces, and with the first point of division D as 
 center, strike the arc E B, and A B will equal A E. 
 
 Also, let A B be the given arc, and A F an arc of 
 unequal curvature. Space A B, as in the first proposi- 
 tion, and set off D on the straight line tangent to both 
 arcs at A, and with D as center and radius D B, draw 
 the arc B to F. Then A F will equal A B. 
 
 To develop, by the latter proposition, the pattern 
 for the envelope of a cone, the slant height and size 
 of base being known. 
 
 Fig. 2. 
 
 On any straight line, Fig. 2, set off the required 
 slant height C D, and with D as center and radius 
 C D, describe the indefinite arc X X. Set off from C, 
 
i8 XXTH CENTURY SHEET METAL WORKER. 
 
 on line A B, the radius of the desired base C to E, 
 and with E as center describe the complete circle. 
 Draw a radius E F perpendicular to A B and space 
 the quarter circle into 4 equal spaces. Erect a per- 
 pendicular at C which will be tangent to the circle 
 and to the long arc at that point, and on it set off 
 one of the 4 equal spaces of the quarter circle, marked 
 o. With o as center and radius o F describe the arc 
 from F to the long arc at G. Then C G equals C F, 
 or % the circumference of the base. 
 
 Now span the dividers from C to G, and step this 
 distance from G to H, and two steps from C to I, and 
 connect H and I with D. Allow edges for lock and 
 pattern is complete. 
 
 The Octagon. 
 
 To lay off an octagon ziithout a circle, or a cfttier, 
 and with no internal lines whatever. 
 
 Use the steel square, and after drawing a line the 
 length desired for one side of the octagon, place the 
 square on the line at 12 and 12, or 6 and 6, or any 
 convenient numbers, using the same figure on the 
 blade as on the tongue, and with one of these num- 
 bers just at the end of the line, draw the next side 
 along the blade of the square. Continue this process, 
 being caYeful to make the sides exactly the same length, 
 and to place the square so that the line last drawn 
 crosses it just at the figures selected. 
 
 The accompanying cut fully shows the manner of 
 using the square. Here A B is the first side drawn, 
 say 14 inches long, and the square is then placed on 
 A B as shown, with 8 and 8 on the line and the edge 
 of the blade (long side) at the end B of the line. Then 
 
XXTH CENTURY SHEET METAL WORKER. 19 
 draw B C 14 inches long, which would be just to 22 on 
 the blade. Swing the square around onto B C as 
 shown bv the dotted outline and draw the next side. 
 
 ' ' V S. 
 
 B ■/ / -V ^v. 
 
 k<- 
 
 The Octagon, 
 
 If the work is done accurately the resulting figure 
 will be a perfect octagon. 
 
 In the cut the square is shown a little off from the 
 line B C in order to show that line. But if the square 
 was placed so that the 8 inch mark just coincides with 
 end B of the line A B, then B C would just reach the 
 22 inch mark on the blade. 
 
 Of course anv size of octagon may be made in this 
 
20 XXTH CENTURY SHEET METAL WORKER. 
 
 manner, by using smaller numbers on the square for 
 drawing those with shorter sides. 
 
 Diam. 
 
 Area. 
 
 Cir. 
 
 Diam. 
 
 Area. 
 
 Cir. 
 
 i 
 
 0.0123 
 
 .3927 
 
 16 
 
 201.06 
 
 50.26 
 
 i 
 
 0.0491 
 
 .7854 
 
 
 213.82 
 
 51.83 
 
 1 
 
 0.1104 
 
 1.178 
 
 17 
 
 226.93 
 
 53.40 
 
 i 
 
 0.1963 
 
 1.571 
 
 
 240.53 
 
 54.98 
 
 f 
 
 0.3068 
 
 1.963 
 
 18 
 
 254.47 
 
 56.65 
 
 i 
 
 0.4418 
 
 2.356 
 
 
 268.80 
 
 58.12 
 
 i 
 
 0.6013 
 
 2.741 
 
 19 
 
 283 . 53 
 
 59.69 
 
 I 
 
 0.7854 
 
 3.142 
 
 
 29S . 65 
 
 61.26 
 
 i 
 
 O.9940 
 
 3.534 
 
 20 
 
 314.16 
 
 62.83 
 
 i 
 
 1.227 
 
 3.927 
 
 
 330.06 
 
 64 . 40 
 
 i 
 
 1.485 
 
 4.319 
 
 21 
 
 346.36 
 
 65.97 
 
 it 
 
 1.767 
 
 4.712 
 
 
 363.05 
 
 67.54 
 
 i 
 
 2.074 
 
 5.105 
 
 22 
 
 380.13 
 
 69.11 
 
 i 
 
 2.405 
 
 5.498 
 
 
 397.61 
 
 70.68 
 
 i 
 
 2.761 
 
 5.890 
 
 23 
 
 415.48 
 
 72.25 
 
 2 
 
 3.142 
 
 6.283 
 
 
 433.73 
 
 73.83 
 
 i 
 
 3.976 
 
 7.068 
 
 24 
 
 452 . 39 
 
 75.40 
 
 ^ 
 
 4.909 
 
 7.854 
 
 
 471.43 
 
 76.97 
 
 i 
 
 5.939 
 
 8.639 
 
 25 
 
 490 . 87 
 
 78.54 
 
 3 
 
 7.068 
 
 9.425 
 
 26 
 
 530 . 93 
 
 81.68 
 
 i 
 
 S.29^ 
 
 10.21 
 
 27 
 
 572.56 
 
 84.82 
 
 i 
 
 9.621 
 
 10.99 
 
 28 • 
 
 615.75 
 
 87. 9P 
 
 i 
 
 11.044 
 12.566 
 
 11.78 
 
 29 
 
 660.52 
 
 91.10 
 
 4 
 
 12.56 
 
 30 
 
 706 . 86 
 
 94.25 
 
 i 
 
 15.904 
 
 14.14 
 
 31 
 
 754 . 77 
 
 97.39 
 
 5 
 
 19.635 
 
 15.71 
 
 32 
 
 804 . 25 
 
 100.5 
 
 i 
 
 23.758 
 
 17.27 
 
 33 
 
 855 . 30 
 
 103.6 
 
 6 
 
 28.274 
 
 18.85 
 
 34 
 
 907.92 
 
 106.8 
 
 i 
 
 32,183 
 
 20.42 
 
 35 
 
 962 U 
 
 109.9 
 
 7 
 
 38.484 
 
 21.99 
 
 36 
 
 1017.9 
 
 113,1 
 
 i 
 
 44.179 
 
 23.56 
 
 37 
 
 1075.2 
 
 116.2 
 
 S 
 
 50 . 265 
 
 25.13 
 
 38 
 
 1134.1 
 
 119.4 
 
 i 
 
 56.745 
 
 26.70 
 
 39 
 
 1194.6 
 
 122.5. 
 
 9 
 
 63.617 
 
 28.27 
 
 40 
 
 1256.6 
 
 125.6 
 
 A 
 
 70.882 
 
 29.84 
 
 41 
 
 1320.2 
 
 128.8 
 
 i6 
 
 78.54 
 
 31.41 
 
 42 
 
 1385.4 
 
 131.9 
 
 i 
 
 86.59 
 
 32.98 
 
 43 
 
 1452.2 
 
 135.1 
 
 11 
 
 95.03 
 
 34.55 
 
 44. 
 
 1520.5 
 
 138.2 
 
 i^ 
 
 103.87 
 
 36.13 
 
 45 
 
 1590.4 
 
 141.4 
 
 12 
 
 113.10 
 
 37.70 
 
 46 
 
 1661.9 
 
 144.5 
 
 • i 
 
 122.72 
 
 39.27 
 
 47 
 
 1734.9 
 
 147.6 
 
 13 
 
 132.73 
 
 40.84 
 
 48 
 
 1809.6 
 
 150.8 
 
 * 
 
 143.14 
 
 42.41 
 
 49 
 
 1885.7 
 
 153.9 
 
 14 
 
 153.94 
 
 43.98 
 
 50 
 
 1963.5 
 
 157.1 
 
 if 
 
 165.13 
 
 45.55 
 
 51 
 
 2042.8 
 
 160.2 
 
 15' 
 
 176.71 
 
 47.12 
 
 52 
 
 2123.7 
 
 163.3 
 
 ^ 
 
 188.69 
 
 48.69 
 
 53 
 
 2206.2 
 
 166.5 
 
XXTH CENTURY SHEET METAL WORKER. 21 
 Diameters and Circumferences of Circles. 
 
 To find the circumference of any circle greater than 
 any given in the table, multiply by 2, 3, 4, 10 or any 
 number of times. For instance : 
 
 The circumference of 28 is 2 times that of 14. And 
 the circumference of 140 is 10 times that of 14. The 
 circumference of 14 is 43.98. and to find the circum- 
 ference of 140 multiply 43.98 by 10. which is done by 
 removing the decimal point one place to the right, 
 making 439.8. 
 A Short Method of Finding Circumferences Without Figures 
 
 Draw a line 12 inches long, as A B in Fig. i. Span 
 dividers to 3 13/16 inches, and with one point at B 
 
 strike an arc C D. Set ofi' on this arc from C, the 
 given diameter, as C E or C F. Then draw from B 
 through E or F, another line 12 inches long, and the 
 
22 XXTH CENTURY SHEET METAL WORKER. 
 
 distance from A to G will be the circumference of 
 the diameter C E, or from A to H will be the circum- 
 ference of the diameter C F. 
 
 This rule is good for all small circles up to yy^ 
 inches diameter which, being just 2 times 3 13/16, 
 
 12" 
 
 would make the arc C D a complete semi-circle, and 
 the line B G would be swung around to form a con- 
 tinuation of A B. thus making the distance from A to 
 G 24 inches, which is just a little more than the true 
 circumference of 7^, which is 23.955. 
 
 A very convenient way of applying this method is 
 
XXTH CENTURY SHEET METAL WORKER. 23 
 to mark across both legs of a two-foot folding rule, 
 3 13/16 inches from the center c f the rivet in the mid- 
 dle joint, which would be at 8 3/16 on one leg, and at 
 15 13/16 on the other. Then by opening the two end 
 joints of the rule and spreading the legs so that the 
 marked points at the inside edges will be just the dis- 
 tance apart of the given diameter, the inside corners 
 will be the distance apart equal to the required cir- 
 cumference. 
 
 Fig. 2 shows the application of the rule to the same 
 principle. B is the hinged joint, and the lines from 
 B to 12" are the inside edges of the legs of the rule. 
 It is here shown spread to 3>^ inches diameter, and 
 measures 11 inches circumference. 
 
 Some Remarkable Facts About Circles. 
 
 We are taught from our > outh up, that the diameter 
 of a circle multiplied by 3.1416 equals the circumfer- 
 ence, and that the square of the diameter multiplied 
 by .7854 equals the area. Some of the following facts, 
 however, have not been so generally taught: 
 
 That the diameter divided by .3183 equals the cir- 
 cumference. 
 
 That the circumference multiplied by .3183 equals 
 the diameter. 
 
 That one-half the circumference multiplied by one- 
 half the diameter equals the area. And that the square 
 of the circumference multiplied by .07958 equals the 
 area. 
 
 That the area of a circle is greater than that of an) 
 other plain figure bounded by an outline of equal 
 length. 
 
 That in any circle whose diameter is less than 4 
 
24 XXTH CENTURY SHEET METAL WORKER, 
 the area is less than the circumference ; i. e., the num- 
 ber of square units of area is less than the number of 
 lineal units of the circumference. 
 
 That if the diameter is 4 the circumference and 
 area are represented by the same number, each being 
 12.5664, while in all circles whose diameters are more 
 than 4 the areas exceed the circumferences, and the 
 proportions of one to the other advance by a regular 
 ratio, or progression, as will be seen by the following 
 table: 
 
 Diameter. Table. 
 
 .1 area equals circnm. divided by 40. 
 .4 area equals circum. divided by 10. 
 .5 area equals circum. divided by 8. 
 
 1 area equals circum. divided by 4. 
 
 2 area equals circum. divided by 2. 
 
 3 area equals circum. divided by i^. 
 
 4 area equals circum.. 
 
 5 area equals circum. multiplied by l54- 
 
 6 area equals circum. multiplied by ij^. 
 
 7 area equals circum. multiplied by i^. 
 
 8 area equals circum. multiplied by 2. 
 10 area equals circum. multiplied by 2^. 
 12 area equals circum. multiplied by 3. 
 14 area equals circum. multiplied by 3^. 
 16 area equals circum. multiplied by 4. 
 18 area equals circum. multiplied by 4^2. 
 20 area equals circum. multiplied by 5. 
 24 area equals circum. multiplied by 6. 
 28 area equals circum. multiplied by 7. 
 32 area equals circum. multiplied by 8. 
 36 area equals circum. multiplied by g. 
 40 area equals circum. multiplied by 10. 
 44 area equals circum. multiplied by 11. 
 48 area equals circum. multiplied by 12. 
 
XXTH CENTURY SHEET METAL WORKER. 25 
 To use the table: Find the circumference by ref- 
 erence to the table of diameters and circumferences 
 given in another chapter, or by any rule, and divide or 
 multiply by the number given in this table opposite 
 the chosen diameter. For example: Diam. 2, the 
 circum. of which is 6.2832, which divide by 2 and the 
 area is found to be 3.1416. Again, diam. 12, circum. 
 of which is 37.6991, which this table shows is to be 
 multiphed by 3. 37-6991 X3=ii3-0973- the required 
 area. 
 
 The ratio of increase of the multipliers continues 
 the same indefinitely, increasing ,^ for each unit of 
 increase of diameter, so that this table may be used 
 for finding the area of circles of other diameters than 
 those given. If the diameter is 9 multiply the circum. 
 by ^Ya. If 49 multiply by 12^4. If 50. by I2>4. H 
 51, by 12^, and if 52, by 13. The multiplier con- 
 tinuing to increase one unit for each 4 units of di- 
 ameter. Hence, to find the area of a circle whose 
 diam. is 400, multiply the circumference by 100. Thus, 
 diam. 400, circum. 1256.64X100=125664. 
 
 In other words, multiply the circumference by one- 
 fourth the diameter to find the area of any circle. 
 Scale of Hundredths. 
 It frequently happens in making particularly accur- 
 ate measurements that it is desired to measure a cer- 
 tain number of hundredths of an inch. And some- 
 times the required number is such that considerable 
 time, and much figuring would be necessary, to re- 
 duce it to a common fraction. 
 
 A scale of hundredths is a great convenience in 
 
26 XXTH CENTURY SHEET METAL WORKER. 
 
 such cases, and if the shop square does not contain 
 one, it may be made very accurately, by any one, with 
 a few minutes careful work. 
 
 Near one end of a strip of tin, lay off a square inch, 
 and space horizontally into ten equal spaces by paral- 
 lel lines, and it is a good plan to continue these lines 
 several inches along the tin. 
 
 Space it the other way into equal spaces, and draw 
 parallel lines having a slant of one space. That is, 
 draw the first line from one corner of the square to 
 the first space mark on opposite side, thus forming e 
 triangle with one inch perpendicular, and one-tenth 
 inch base. Draw the remainder of the lines exactly 
 parallel to the first, and you will have a similar tri- 
 angle at the opposite side only reversed. 
 
 To use the scale extend dividers the required num- 
 ber of whole inches and place both points on the re- 
 quired line, .01, .02, etc., according to the number of 
 hundredths to be added, with one point exactly on line 
 A B. Then hold the other point firmly and extend 
 the one resting on line A B to the intersection of the 
 diagonal line with the one on which the dividers rest. 
 
XXTH CENTURY SHEET METAL WORKER. 2- 
 
 For example, to find 2.06", extend the dividers two 
 inches, and place one point on the intersection of the 
 line .06 with the line A B, and holding the other point 
 on line .06, extend the point on A B to the intersection 
 of the first diasfonal line. 
 
 With this scale any number of hundredths may be 
 readily found. To find 1.99" extend dividers from 
 X to X. Or for 1.92, from v to v, etc. 
 
28 XXTH CENTURY SHEET METAL WORKER. 
 Measuring Degrees on the Steel Square. 
 
 It sometimes happens that it is desirable to find a 
 certain number 'of degrees when there is no protractor 
 at hand. In such cases the steel square and the fol- 
 lowing table will be found to answer the purpose with 
 a reasonable degree of accuracy. 
 
 Table. 
 
 No. I No. 2 
 
 Inches. Deg. Deg. 
 
 1-2 45 45 
 
 lo i/i6 40 50 
 
 8 13/32 ;. -35 55 
 
 6 15/16 30 60 
 
 5 19/32 25 65 
 
 5 22'{. (,r/2 
 
 AVs 20 70 
 
 3 7/32 15 75 
 
 2 3/32 10 80 
 
 I 1/16 5 85 
 
 o o 90 
 
 EXPL.\N.\TI0N OF T.^BLE. 
 
 A line drawn from 12" on the blade to 12" on the 
 tongue is 45° to either edge of the square. And a 
 line drawn from 12" on either edge to any number in 
 the column of inches, on the other edge, will be, at 
 the 12". the number of degrees indicated in the column 
 of degrees marked "No. i." And where it intersects 
 the outer edge of the other arm of the square, it will 
 be the number of degrees indicated in the column 
 marked "No. 2." 
 
 As the cut shows, the angles given in column No. I 
 of Degrees are those at C, and the ones given in 
 column No. 2 are those between A and B. 
 
XXTII CF.NTURY SHI'.F.T METAT. WORKER. 29 
 Chimney Tops. 
 
 An article of very general use throughout the coun- 
 try, and yet one which seems to be quite difficult for 
 many tinners to quickly draw patterns for, is the gal- 
 vanized iron chimney top base. Really this is a tran- 
 sition piece, being an article hav a square or rec- 
 tangular base, and round top. 
 
 The pattern for this article may e so quickly drawn 
 that it is better to lay it off on the sheet to be used, 
 and if made in two pieces, one only need be drawn, 
 and the other cut by it. 
 
 For the purpose of explaining the process we will 
 take definite dimensions, say I3"xi7" with 4* perpen- 
 dicular base, and tapered to fit a f pipe, the height to 
 be just what will cut from 30-inch iron. The seams to 
 he in the middle of the narrow sides. 
 
 At a distance of 17 inches from one end of the 
 ^ect scribe at right angles across it, a line, as A B, 
 letting the line extend indefinitely to A on the floor 
 or bench after reaching the edge of the iron. This 
 line is the center "\t« t tl' c half pattein. Set off from 
 center line at B W2 to E, and the same distance to 
 F. Then with the square scribe up from F to D 4^*, 
 and from E to C 4^^", and connect C and D. 
 
 From the center line at K set off a little less than ^ 
 the circumference of top each way to G and H. For 
 7* pipe about 5 inches each way, making 10 inches for 
 the chord G H. For other sizes of top use about the 
 same proportion — 10 to 22, or 5 to 11 — which would 
 be about 85^ for 6-inch pipe, and about 11^ for 8- 
 inch. 
 
30 XXTH CENTURY SHEET METAL WORKER. 
 
 Next place the blade of square at G and 6J/2 inches 
 on the tongue at C, as shown in drawing, and scribe 
 from G to I, and from I to C, then slide the square 
 down 4^ inches, keeping the blade to the line G I, 
 and mark from J to E 63/2 inches, and connect E and 
 
 C. Continue the line J G to A where it intersects 
 with the center line. Mark the other side the same 
 from H around to D, etc., and continue the line from 
 H to A. 
 
XXTH CENTURY SHKKT MI'TAL WORKER. 31 
 
 With A as center and radius A G strike the arc G 
 H. Tlien draw lines from D to H, and from D to K, 
 also from C to G and C to K. Lay off the allowance 
 for lock along- each edge as shown by dotted lines, and 
 cut out. 
 
 The top should be cut on the arc G K H so the 
 bends can be the more easily made on the lines C K 
 and D K. Notch in from F to D and from E to C, 
 leaving an allowance to rivet. Mark the other half 
 by this, being careful to prick the points K, C, and D. 
 Fold the bottom edge y\ inch over flat, and then 
 straight out, to make a good stiff edge at bottom. 
 
 Fig. 1. 
 
32 XXTH CENTURY SHEET METAL WORKER. 
 
 Now fold the edg^e locks, one out and the other in, 
 the same as for stove pipe, and then brake over stake, 
 or in the brake if you have one, on the lines G C, K C, 
 H D and K D, forming about square at C and D, and 
 running out to round at top end G K H. Lock the 
 two halves together and groove down the seams, after 
 which bend on lines I C, C D, etc., to bring the 4-inch 
 base strip to perpendicular, and rivet the corners. 
 
 Chimney Saddles. 
 
 The chimney saddle is a very important article, and 
 is much better than a plain flashing behind the chim- 
 ney, because being sloped both ways, it allows the 
 water to all run off quickly, while the flashing usually 
 remains wet for some time, and soon rusts through. 
 
 Fig. 2. 
 
 Fig. I shows the saddle in place behind a chimney 
 on a 1/3 pitch shingled roof. A, B, C, D and E being 
 a side elevation. 
 
 To develop the pattern, draw X X, Fig 2, the pitch 
 of roof, A E the perpendicular line of chimney, B C 
 
XXTH CENTURY SHEET METAL WORKER. 33 
 
 the width desired for high point of saddle, and E the 
 width of ends at low point. 
 
 Suppose, for example, the roof is 1/3 pitch, and the 
 chimney is 26 inches wide, and the saddle to be 6 
 inches wide at high point. Make B C. at right angles 
 to A E, and 6 inches long. And E, i inch long, par- 
 allel to B C. 
 
 Next cut a piece of galvanized iron 16x28 inches 
 and lay it off as shown in Fig. 3. A to B is 4 inches, 
 [') to C 6 inches and C to D 6 inches. Cut straight in 
 from A to B, and from D to C. Then bend at right 
 angles on line E E, and to about 1/3 pitch on lines C 
 E and C E. Bend at B C until the line B C is as high 
 
 Pig. 3. 
 
 above the ends at E as the distance B E in Fig. 2. 
 Rest it on the bench in this position and solder a gore 
 over the V-shaped opening A B. Turn the wide side 
 E D E down flat on bench and solder a gore over the 
 opening D C. These gores should also l)c riveted to 
 prevent the solder breaking, and they should both be 
 
34 XXTII CENTURY SHEET .METAL WORKER. 
 
 put on the inner side, as they will not leak quite so 
 badlv in case the solder does become broken. 
 
 Fig, 4, 
 
 Fig. 4 shows the completed article with the riveted 
 gores. 
 
 Gutter and Gutter Aliters— Octagon and Half Round. 
 
 In Figures i and 2 are shown square miter patterns 
 for octagon and half round gutter, the inside and out- 
 "^ide of miter of each, and each taking the same width 
 of stock, in this case Q inches. 
 
 In Fig. 1 the dimensions are as follows, tht^ugh these 
 
XXTIl CENTURY SHEET METAL WORKER. 35 
 may be varied at will: o to i. I2 in.; i to 2. -ji in..; 
 2 to 3, }i in. ; 3 to 4, i in. ; 4 to 5, i in. ; 5 to 6, 2/2 
 in. ; 6 to 7, I in. ; 7 to 8, i>^ in. 
 
 This takes jnst inches width of stock, and is a 
 
 Pig. 1. 
 
 very convenient size of gutter to make, as a 3()-inch 
 sheet of iron will cut 4 pieces without waste. 
 
 To develop the pattern, draw profile as shown, then 
 draw a stretch-out 9 inches from o to 8, and any de- 
 sired len.Qth. Space the stretch-out 0123. etc.. the 
 same measurements as o i 2 3, etc., in profile. Draw 
 
36 XXTH CENTURY SHEET METAL WORKER. 
 
 lines from the points of bend in profile to intersect 
 the space lines in stretch-out as shown, and connect 
 these intersections by straight lines. 
 
 Cut on the miter line, and prick both end? of each 
 
 piece on the space lines, ai 
 complete, by which any nu 
 
 d the two patterns are 
 nber of pieces may be 
 
 marked and pricked for bending. In cutting out by 
 these patterns one piece of each pair should be cut a 
 half inch longer and notched in at each point of bend, 
 to form a lap, as a much stronger job is made by so 
 doing, than by butting them together. 
 
 For marking the long pieces which are to have no 
 
XXTH CENTURY SHEET METAL WORKER. i7 
 miters cut on them, a narrow strip of iron may be 
 prick marked i 2 3, etc., and cut 9 inches long. Prick 
 each end of the piece by this pattern, and it is then 
 ready to form up in the brake. 
 
 In forming up, put the 0123 edge of piece into 
 the brake to the third dot (dot 3). Bend square up. 
 Reverse and put the same edge in, the other side up, 
 to dot 2, and bend square up. Pull back to dot i, 
 and also bend square, this finishes the bead. Turn it 
 around and put in to dot 4, and bend up to 45°, pull 
 back to 5 and bend to 45°, then 6 and 7 each 45°. 
 
 It is a good plan to cut a. stay the exact shape of 
 profile, and form the gutter to the shape of the stay, 
 as nearly as possible. 
 
 In Fig. 2 is shown a very similar development of 
 the half round gutter miter. The bead pattern is a 
 complete two-piece elbow pattern, and the half round 
 part is just half of an elbow pattern, and each part 
 may be laid out by any method of elbow with which 
 the workman is familiar. 
 
 The bead in Fig. 2 is shown somewhat out of pro* 
 portion, but the principle of development is the sami 
 regardless of the size. 
 
 Box Gutter. 
 
 I used to dread a job of box gutter. It seemed to be 
 a hard matter for me to put it in properly, and not 
 spend too much time on the job. 
 
 For the benefit of others who may be troubled in 
 the same manner, I will describe my present method. 
 And, by the way, I rather like the work. 
 
 We will suppose we have a box gutter job which is 
 
38 XXTH CENTURY SHEET METAL WORKER. 
 
 to finish over the edge of crown mould with a bead, 
 which is a common style of finish at the present time. 
 Make up the bead in 28-inch lengths (or in 20-inch 
 if you have only a 20-inch header in the shop), and of 
 sufficient width to cover the flat or slightly sloped sur- 
 face between the gutter and outer edge of cornice, and 
 a ^-inch allowance to turn up to lock the edge of 
 gutter to. For instance, if the deck strip is 2^ inches, 
 and you have a 30-inch header which turns a ^-inch 
 bead, cut the tin in 5-inch strips, and cut in with the 
 snips }i of an inch deep in each end of each piece, 2 
 inches from one edge, as shown at A, Fig. i. Notch 
 
 Box Gutter Fig. 1. 
 
 r 
 
 ^ ---- ---A ? 
 
 the other two corners, being careful to take off corner 
 enough to allow for a 34 -inch fold across the end and 
 along the side also. 
 
 Next fold both ends the same as for valley, i. e., in 
 opposite directions, one up and one down, turning 
 clear down so as to lock them together, and fold the 
 edge C D up square, or a little more. Then straighten 
 out the 2 inches of end folds which was previously cut, 
 
XXTH CENTURY SHEET xMETAL WORKER. 39 
 as shown by dotted lines B A at each end of cut Y in 
 Fig. I. Hammer these ends down pretty flat with the 
 mallet, so they will slip into the header readily. Then 
 bead the edge B B, turning the bead on the side oppo- 
 site to the bend of edge C D. 
 
 An end section of the finished- piece is shown in Fig. 
 2, which clearly shows the bead turned down, the op- 
 posite edge turned up, and the up fold of one end, 
 but does not show the down fold of the other end. 
 
 Get out enough of these pieces to cover the deck 
 strip, and enough valley (14-inch is wide enough for 
 
 o 
 
 Pig. 2. 
 
 most ordinary gutters) being careful that it is well 
 soldered. 
 
 Put on the bead first, by putting one in place, then 
 slip the bead of the next over that, and pushing them 
 together far enough to let the fold A C catch over the 
 fold A D, and then pulling back till they lock together. 
 
 Nail close to the fold C D, so the heads will be cov- 
 ered when it is hammered down, and put an occasional 
 slim nail through the bead into the edge of crown 
 mould as shown at A in Fig. 3. 
 
 When the bead is all in place, measure from bottom 
 of gutter at B to a point about J4 inch above the turned 
 up edge at C, Fig. 3. Take this measure at the low 
 point of gutter, and again at the high point, and trans- 
 fer these measurements to the edge of the strip of 
 valley, and bend up with tongs or straight edge and 
 mallet. Then measure the width of gutter B to D, at 
 
40 XXTH CENTURY SHEET METAL WORKER. 
 
 both ends, as the width often varies as well as the 
 depth, and bend square up. 
 
 Next set the tin into the gutter and get into it with 
 one knee, or one foot, to hold it down, and start the 
 edge C over with tongs or plyers, and hammer it down 
 to an angle, and then clinch it tight with cleating tongs 
 
 Fig. 3. 
 
 or plyers, and finish down flat with the mallet. 
 
 Then, still keeping the weight in the gutter, bend 
 the back at E down onto the roof boards, and put in 
 an occasional nail if the roof is to be shingled, but if 
 it is to be tinned, turn up the back edge at F and blind 
 nail, thus leaving it ready to lock the roofing on. 
 
 This same method of bead finish may also be used 
 without gutter, if so desired. I have often put on 
 porch roofs with this kind of finish. Using, however, 
 full sheets instead of the narrow strips. 
 
 Slit each end of the sheets, and, after folding the 
 two ends and one side, straighten out the narrow part 
 of the end folds, just as described, and turn the bead 
 the same as shown on the narrow strips. 
 
XXTll CEX'IURV SIIF.ET METAL WORKER. 41 
 
 In connection with the box c;ntter it might be well to 
 mention my way of making the ends. Tinners differ 
 in their manner of doing things, and I do not claim 
 to have the only right way. But I mention these mat- 
 ters, hoping to help some workman who has met with 
 the same difificulties that have hindered me so many 
 times. 
 
 I usually cut the tin enough longer than the gutter 
 to equal the greatest depth of both ends, and a little 
 to spare. Then slash straight in at the ends, at each 
 bend, B, D and E, about as far as the height of D E. 
 Bend C B and D E in towards each other, and the 
 bottom, BD, up. ^^rim off the surplus tin and solder 
 the edges well. 
 
 An end may be cut to fit and soldered in, but in most 
 cases this is no advantage, and takes much longer. 
 And in these days of competition, time is quite an 
 object, and the workman who can do things quickly 
 and well, stands a better show than the one who does 
 them ever so well, but works slowly. 
 
 Tlie ElUpse or Oval. 
 
 A perfectly true ellipse can not be drawn with the 
 dividers and two radii. But there are several methods 
 of drawing them in this manner, which so nearly 
 approximates the true ellipse as to answer the purpose 
 for most tin shop work. 
 
 A very accurate method, however, is by the string 
 and nail process. Fig. i is drawn in this manner. 
 
 Draw A B the length of the major axis and bi- 
 secting it at right angles draw C D the length of the 
 minor axis. With C or D as center and one-half the 
 
42 XXTH CENTURY SHEET METAL WORKER. 
 
 major axis as radius, mark the points E and F on the 
 major axis. Drive nails at E. F and C, and tie a 
 string tightly around the three nails. Remove the nail 
 at C and with a pencil or scriber draw the ellipse, 
 keeping the string tight. 
 
 / 
 
 -. \ 
 
 / 
 
 "~\ 
 
 1 
 
 / 
 
 
 / 
 
 / 
 
 
 / 
 
 f 
 
 / 
 
 V ' 
 
 / 
 
 
 / 
 
 
 / 
 
 
 / 1 
 
 
 / / 
 
 
 / 
 
 
 / 
 
 \ « 
 
 p / 
 
 Fig. 1. 
 
 If the pencil is held in an upright position and the 
 string is not allowed to slip up or down on it, and does 
 not stretch more in some directions than in others, the 
 result will be a perfect ellipse. In fact, it is in strict 
 accord with the scientific definition of an ellipse — "A 
 
XXTH CKNTURY SHEET METAL WORKER. 43 
 figure bounded 1 y a curved line, every point of which 
 is equally distant from two points within, called foci." 
 
 In this figure, E and F are the foci, and the distance 
 from any point in the curve to F plus the distance from 
 
44 XXTH CENTURY SHRET METAL WORKER. 
 
 the same point to E is the same as the combined dis- 
 tances from these two ])oints to any other point in the 
 curve, and is just equal to the lenj::^th of the major 
 axis. 
 
 In Fig". 2 is shown a very near approximate to an 
 elHpse, composed of arcs of circles, having three dif- 
 ferent radii and eight centers, hence it is called the 
 "eight centered oval." 
 
 To draw an oval by this method, draw A B the 
 length of major axis, and bisect it at right angles by 
 C D indefinitely. Mark points O P on C D the length 
 of minor axis. 
 
 Now to determine the radii to be used, draw X Y 
 and X Z, Fig. 3, forming any convenient angle at X. 
 With X as center and radius equal to half the short 
 axis strike the arc V W. With same center and radius 
 half the long axis draw the arc S T. Connect W and 
 S, and parallel to W S draw \' U and R T. Then 
 X U w^ill be the radius to use for the arcs at the ex- 
 tremities of the major axis, and X R will be the radius 
 for the side arcs at the extremities of the minor axis. 
 For the radius of the arcs to connect the side arcs 
 with the end arcs take the length of the semi-minor 
 axis plus half the difference between the semi-axes, 
 which is (in Fig. 3) the distance X V plus half the 
 distance V S, hence X O. 
 
 On A B of Fig. 2 set oft" -\ E and B F, each equal 
 to X U. And .\ G and B H each equal to X O. Lay 
 off from O to D and from P to C, each equal to X R 
 and from O to J and P to I each equal to X O. 
 
 With C as center and radius C I draw the arc i 2, 
 
XXTH CENTURY SHEET METAL WORKER. 45 
 and with D as center and same radius draw the arc 3 
 4. With E and F as centers and radius E G or F H 
 strike the arcs through G and H intersecting the arcs 
 I 2 and 3 4 at the points i 3 and 2 4. Draw a hne 
 
 FiG. 4. • 
 
 through E from i to 5 equal in length to X Q, and 
 from 3 to 6 same length, and the same through F 
 from 2 to 7 and from 4 to 8. 
 
 From C through i and 2 draw lines the length of 
 X R, and from D through 3 and 4 same length, end- 
 ing at 9, 10, II and 12. 
 
46 XXTH CENTURY SHEET METAL WORKER. 
 
 With C as center and radius C P (or X R) draw 
 the arc 9 10, and with D as center and same radius 
 draw II 12. With E and F as centers and radius E A 
 (or X U ) draw 5 6 and 7 8. Then with i, 2, 3 and 4 
 
 B 
 Pig, 5. 
 
 respectively as centers and radius I to 5 (or X Q) 
 draw the four connecting arcs 5 to 9, 7 to 10, 8 to 12 
 and 6 to II. This completes the eight centered ellipse, 
 which is a very near approach to the shape of that in 
 Fig. I, constructed with the string and nails. 
 
 Figures 4 and 5 are of the four centered kind, using 
 
XXTH CENTURY SHEET METAL WORKER. 47 
 only two radii. Eitlier of these will answer very well 
 for small articles. ¥\g. 4 is, however, slightly nearer 
 to the perfect ellipse than Fig. 5. 
 
 To draw Fig. 4 make A B the length of major axis, 
 and bisect it with the indefinite line C D at right 
 angles to it on which mark x x length of minor axis. 
 From A set off the length of required minor axis, 
 marked E, and divide E B into 4 equal spaces. With 
 3 of these spaces, (which is ^ the difference of the 
 two axes) as radius, and F as center, mark G and H 
 and describe circles with radius A M or B G. Take 
 the distance from F to the nearest ei\s:;e of one of the 
 circles and set off from x x marking the points I and 
 J. From I and J draw lines through H and G re- 
 spectively, as J to I and 2. and I to 3 and 4. 
 
 With I and J as centers and radius I to opposite x 
 draw the arc 3 4. And with J as center and same 
 radius strike the arc i 2, completing the figure. 
 
 For Fig. 5, draw A 15 and C D, the length and 
 width desired. From A set off the width, A to E, 
 then E B is the difference of the axis. Take half this 
 difference, which is E V, for radius, and with G as 
 center strike the arc H I. Draw the chord H I and 
 bisect it at J. With I as center and radius I J draw 
 the arc J K. With G as center and radius G K mark 
 L, M and N. Draw lines from L and N both ways 
 through K and M, and use K, L, M and N respec- 
 tively for the centers from which to draw the four 
 arcs to form the oval. 
 
 These four figures are all drawn to the same dimen- 
 sions, i.e, the same lengths of axes, and the different 
 
48 XXTH CENTURY SHEET METAL WORKER. 
 
 degrees of variation from the nearest perfect form 
 (Fig. i) are readily detected. 
 
 Oval Flaring: Pan. 
 
 Having described several methods of drawing ellip- 
 tical and oval figures, and knowing that many work- 
 men have their own rules for drawing the oval, I will 
 omit that part here, and give an easy short rule for 
 pattern for the body of flaring oval pans. 
 
 Around the corner of the square draw indefinitely 
 ABC. Fig. I. From B mark D the perpendicular 
 depth of pan desired. From D draw D E parallel to 
 A B, and make the distance from D to E the same 
 as the radius I x of the side arc of the oval, Fig. 4. On A 
 B mark F as far from B as the side radius plus the 
 required flare of one side of pan, i. e., make B F just 
 once the flare longer than D E. Then draw from F 
 a line through E, continued to intersect B C at C. The 
 distance from C to E is the radius of curvature of the 
 bottom of the portion of the body to fit a side arc (as 
 I X 2) of the oval. 
 
 Next, on D E mark e, the length of end radius of 
 oval (A H of Fig. 4). and from B mark f the same 
 distance plus the flare, and draw fee, which will be 
 parallel to F E C, and gives the radii for end portion 
 of body. 
 
 Now draw a center line G H^ Fig. 2. and with H as 
 center and radius C E of Fig. i. describe the arc I J 
 equal in length to i x 2 of the oval, measured with a 
 bent strip or by stepping with dividers. With same 
 center and radius C F draw the arc K L limited by 
 lines drawn from H through I and J. Then K I J L 
 
XXTH CENTURY SHEET METAL WORKER. 49 
 is the pattern for one side of pan. No-.v we will sup- 
 pose the body is to be made in two pieces, with the 
 
 Fig,, 1. 
 
 seams at the ends. To complete the pattern we must 
 add half the end pattern to each end of K I J L. Set 
 
so XXTH CENTURY SHEET METAL WORKER, 
 off from K and L. towards H, the distance c f of Fig. 
 I, here marked h h and with these points as centers 
 and radius c e draw tlie arcs I i and J j each equal in 
 length to one-half the end arc of oval^ as A i or A 4 
 of Fig. 4. From h and h draw lines through i and j 
 
 to k and 1. With same centers and radius c f draw 
 arcs K k and L 1. Add allowance for wire, burr and 
 locks, and the pattern is complete for one-half the 
 body. 
 
 If the body is to be in four pieces, make lock allow- 
 
XXTH CENTURY SHEET METAL WORKER. 51 
 
 ance at K I and L J, and draw the two end halves 
 in one piece, and add locks to both ends of it. 
 
 Figs. I and 2 are drawn to a smaller scale than the 
 ovals in the other chapter, and the measurements do 
 not exactly correspond with them. For this reason 
 F'\g. 4 is here reproduced of a size and shape suitable 
 to illustrate Figs, i and 2 of this chapter. 
 
 0-- 
 
 — i) 
 
 Fig. 4. 
 
 Above all things do not use C D and c D of Fig. i 
 for radii, as is often done by some, they are not the 
 correct radii, being only the perpendiculars of the 
 triangles the hypothenuse of which are the true radii. 
 
 Pan Corners. 
 
 There are several ways of cutting a pan corner so 
 that the folded corner will come up true under the 
 wire. And there are many workmen who only guess 
 at it, and make a poor corner in consequence. 
 
 In this chapter I will mention three methods, by 
 
52 XXTH CENTURY SHEET METAL WORKER. 
 
 any one of which the corner may be so quickly laid out 
 that it would not be profitable to use guess work, and 
 thev are all accurate methods. 
 
 Fig. 1. 
 
 The first is the: one I most often use, although I do 
 not know that it is any better or quicker than either 
 of the others. 
 
 On a perfectly square corner of the sheet to be 
 used, lay off the allowance for wire ABC Fig. i. 
 Parallel to these lines and far enough in from them 
 for the slant depth of the pan, make D E F. From 
 the points G and E set off towards B the desired flare, 
 one-half the difference between the size of the top and 
 bottom. Draw lines from the points thus found at H 
 and I, to J. 
 
 Next place the handle of a bevel against the edge 
 of sheet, and adjust the blade until it coincides with 
 
XXTH CENTURY SHEET METAL WORKER. 53 
 
 the line H J. Then swing the bevel around till the 
 handle is on H J as shown in Fig. 2, with the inner 
 angle of blade and handle at H, and scribe along the 
 blade from H to the center line J B. Reverse the 
 
 FiS. 2. 
 
 bevel, placing the handle on line I J, and scribe from 
 I to the same point on center line as before. 
 
 Cut across the wire allowance at any desired angle, 
 or square in to H and I, then through on the lines 
 drawn, being careful to cut accurately when the piece 
 may be used for a pattern by which to cut the other 
 three corners, when you have them located. To do 
 this measure from H along line A B the distance re- 
 quired for width of top, inside of wire. And from I 
 along line B C the length of top, inside of wire. Then 
 place the little corner pattern on with one of its 
 straight edges coinciding with the edge of the iron, 
 
54 XXTH CENTURY SHEET METAL WORKER, 
 and the point H or I at the point found by measure. 
 Mark the cut line and along the farther edge of pat- 
 tern which will give the point at which to square off 
 the sheet. Square from both the corners thus found, 
 which will locate the fourth corner. 
 
 
 1 
 
 3 
 
 
 ^" 
 
 T/ 
 
 *• 
 
 
 Vo^^r' 
 
 T- 
 
 K0 
 
 ? 
 
 Q 
 
 r^ 
 
 
 "P 
 
 0^ 
 
 
 ^J 
 
 Jf 
 
 Fig. 3, 
 
 J 
 
 K 
 
 D 
 
 
 The second method is by means of rule or square, 
 and dividers. 
 
 Lay off A B C, D E and F G, and locate H and I 
 the same as described in the first method. Then with 
 dividers set at J, Fig. 3, strike a long arc, or semi- 
 circle. Span dividers from intersection of arc with 
 line B J to intersection with line H J and swing 
 around to point X. Draw a line from J to X and the 
 point where this line intersects the line of wire allow- 
 ance is the right height from J for the center line B J, 
 
XXTH CENTURY SHEET METAL WORKER. 55 
 because the line J X is in the position B J will occupy 
 when folded around against end of pan. 
 
 Span dividers from J to o and swing around and 
 mark B J at o'. 
 
 Scribe from H to o' and from I to o', and cut out, 
 
 E 
 
 Si 
 
 Nb 1/ 
 
 n 
 
 
 \^^\ 
 
 \f 
 
 
 Ik 
 
 Pig, 4, 
 D 
 
 p 
 
 cutting wire allowance at any desired angle, thus com- 
 pleting the corner. 
 
 The third method is on nearly the same principle 
 as the first, except that the angles are found by means 
 of the dividers instead of a bevel. 
 
 After laying ofif A B C, D E and F G, and locat- 
 ing H and I as before, span dividers from H to a point 
 nearly, but not quite to B. on line A B, and strike on 
 arc downward as shown in Fig. 4. With dividers un- 
 
56 XXTH CENTURY SHEET METAL WORKER. 
 
 changed set one foot at J and strike an arc cutting 
 H J and G J at K and L. 
 
 Then span dividers from K to L, and starting at M 
 step off twice that distance (two steps) to N. Draw 
 by the straight edge from H to N, and from I to the 
 point of intersection with B J, and cut out as before. 
 
 In the first method we obtained the angle of H J 
 by means of the bevel and by applying this angle again 
 we produced the line H N (or the line corresponding 
 to H N) at twice that angle with the line A B, and 
 in this case, by stepping twice the distance K to L on 
 an equal arc, we produce H N at just twice the angle 
 of H J. 
 
 As before stated, the corner may be cut out and 
 used as a pattern for the other three corners, but in 
 practice I prefer to lay out all the corners first except 
 the lines of cut, and then complete one, and use the 
 piece for pattern for the others. Because the lineJ 
 H J, B J and I J are needed as guides for making the 
 bends when forming up. 
 
 A Deflected Snap Bottom. 
 
 A snap bottom may often be used on small articles 
 of tinware, instead of a double seamed bottom, and 
 given a deflection in the "setting down machine." 
 Cups, dippers, small basins and other small vessels 
 may be made in this manner, quickly and neatly. 
 
 Burr the bottom of body out nearly as much as for 
 a double steam, and perhaps just slightly wider. Not 
 too wide, however. 
 
 Cut and burr the bottom so it will po on pretty snug, 
 and run it in the setting down machine, holding the 
 
XXTH CENTURY SHEET METAL WORKER. 57 
 article up enough to begin to just start a deflect in the 
 bottom, and continue to raise gradually until the seam 
 is at an angle of about 45 degrees, as shown in the sec- 
 tion of bottom underneath the cup, in drawing. 
 
 With very little practice, and a good setting down 
 
 Section of Bottom. 
 
 —4 
 
 machine, this can be done very quickly, and makes a 
 neat job. 
 
 A double seamed bottom can also be deflected in 
 the setting down machine, if it is a very small seam, 
 and pretty smoothly finished, and not too tight. If the 
 
58 XXTH CENTURY SHEET METAL WORKER. 
 
 seam is small enough to allow of starting it between 
 the wheels of the machine, and care is used in handling 
 the work, quite a neat looking deflect may be made. 
 
 Farnac* Pipe Boot by Trlsngulation. 
 
 As triangulation is a more simple and accurate 
 method of obtaining patterns for some of the more 
 irregular and complicated shapes, this second chap- 
 ter is given for the benefit of those unfamiliar with the 
 process. And I believe, if the reader will carefully 
 study this and the chapter on the "Transition Piece," 
 he will be able to develop the pattern for almost any 
 desired article, by this very useful and simple process. 
 
 Figure i is a perspective view of a common shape 
 
 Fig. 1. 
 
 of boot for furnace pipe, and is a transition piece, or 
 more strictly speaking, the body between the straight 
 collars is a transition piece, and is the portion for 
 which we will develop the pattern. 
 
 This boot is to fit a round pipe at one end lo inches 
 in diameter, and to fit a "riser" or wall pipe at the 
 other 2x14 inches. 
 
 In practice it is unnecessary to draw the perspec- 
 tive. And even the elevations may be omitted, if the 
 workman has the idea, or the picture of the article in 
 his mind, and the work done entirely with the plan 
 
XXTH CENTURY SHEET METAE WORKER. SO 
 
 shown at the bottom of Fig-. 2. the circle and the 
 parallelogram. 
 
 Space the circle into any desired nnmher of eqnal 
 parts, here 10 are used. Construct a diagram of tri- 
 angles as shown at the right of "side elevation." Make 
 
 Pig. ' 2. 
 
 the j)erpen(Iicular E P> equal to the vertical height of 
 the body of the article, and the base exactly at right 
 angles to it, and of indefinite length. With the divid- 
 ers measure each of the distances from the corner D 
 
6o XXTH CENTURY SHEET METAL WORKER. 
 
 to E, I. 2, 3, 4 and 5 and set each one as found, off 
 to the right from E on tlie base Hne of the diagram of 
 triangles, marking each one for future references. 
 Then take the distances from X to 5, 6, 7, 8, 9 and 
 10. being careful to number each one. 
 
 Now to develop the pattern, draw the right angle 
 BED, making B E equal to the vertical height (BE 
 of the diagram of triangles) and E D equal to E D of 
 the plan (one-half the length of one side of the par- 
 allelogram) and with one pair of dividers take the 
 distance from B to i on the D of T and place one 
 foot at D on pattern, and with another pair of dividers 
 set to one of the spaces on circle place one foot of 
 these at B on pattern describe a short arc to intersect 
 an arc made by the other spanned from D, thus lo- 
 cating the point i of the irregular curve of pattern. 
 Keep the one pair of dividers set the length of one 
 of the spaces and continue in rotation, setting the other 
 pair from B to 2 on the D of T and span from D to 
 meet the space dividers at 2, and continue the meas- 
 urements thus until 5 is located on the curve line of 
 pattern. Then take the distance from 5-X from B 
 on the D of T and span downward from 5 on the pat- 
 tern and meet it with a measurement from D equal 
 to D X on the plan (the width of the parallelogram)- 
 Then proceed with the remaining distances the same 
 as with the first quarter of the circle, except we span 
 from X instead of D to locate 6, 7, 8, 9 and 10. 
 
 It was necessary for us to take the measurement 
 from 5 to X as well as from 5 to D on plan and trans- 
 
XXTH CENTURY SHEET METAL WORKER. 6i 
 fcr it to the D of T in order to locate the point X of 
 the pattern. 
 
 Now to locate the point G of pattern take the dis- 
 tance lo to G shown in "end elevation" and span it 
 downward from lO on pattern and meet it with the 
 
 Fig. 3. 
 
 distance X G of plan (half the length of parallelo- 
 gram) spanned out from X. Connect the points thus 
 found by straight lines from D to X, from X to G and 
 from G to lo, and by drawing a free hand curve 
 through B, 1,2, 3, 4, 5, 6 7, 8. 9 and 10, which com- 
 pletes one-half the pattern. The other half may be 
 drawn in the same manner, or by cutting out this 
 half and scribing around it. 
 
 The end elevation was referred to once in the above 
 description, and a measurement from that elevation 
 was used in locating G on the pattern, but we could 
 have located it without the end elevation, by measur- 
 ing across from 10 to G on the plan and transferring 
 the distance to the base line of the D of T, then 
 from that point to B is equal to 10 G of the eleva- 
 tion, and of the pattern as well. 
 
62 XXTH CENTURY SHEET ^lETAL WORKER. 
 
 Of course, an allowance must be made all around 
 this pattern, to lock the ends of pattern together, and 
 to lock the collars on. 
 
 Tee on a Tapered Pipe. 
 
 For convenience in describing we will use definite 
 dimensions- — viz.: A tapered pipe (frustrum of a 
 cone) 8 inches in diameter at base, 3 inches at top and 
 8 inches i)erpendicular height, about S^i inches slant 
 height, intersected by a straight pipe 2 inches in 
 diameter, at an angle of 30 degrees to the axis of the 
 tapered pipe. 
 
 To develop the patterns for the above descril^ed 
 article : 
 
 Draw a center line A B and with C on this line as 
 center construct the plan of the tapered pipe, C(jn- 
 sisting of a circle of 3 inches diameter surrounded by 
 a concentric circle 8 inches in diameter. Then draw 
 an 8-inch diameter through C at right angles to A B, 
 and from the ends of this diameter extend dotted linos 
 upward any convenient distance to the points D and 
 E. Connect D and E by a straight line parallel to 
 the diameter drawn in plan, and at right angles to 
 A B, thus forming the base of an elevation of the 
 article. 
 
 On the center line 8 inches above the point X. 
 where it intersects the base line D E, mark Y. and 
 through L draw G F 3 inches long, being careful to 
 make it just i>^ inches each side of Y and parallel to 
 D E. Connect E F and D G and continue the lines 
 until they meet on the center line at A. 
 
 Next draw the 2-inch pipe projecting from the side 
 
XXTH CENTURY SHEET METAL WORKER. 63 
 
 F F of elevation and at an angle of 30 degrees to the 
 center line A B, represented by the straight lines 
 H I J K. This completes the elevation. 
 
 Now drop dotted lines from H and K down to the 
 
 transverse diameter of plan, and using for center a 
 point midway between these lines on this diameter, 
 describe a 2-inch circle and space it into any number 
 of equal spaces, here 12. From center C draw radial 
 lines through tliese space points just to the outer 
 circle (base of tapered pipe), and from tliose inter- 
 sections above and including- the diameter line, draw 
 
64 XXTH CENTURY SHEET METAL WORKER. 
 
 parallel dotted lines upward to D E, and radial lines 
 from A to meet these on D E. 
 
 Find the center of the line I J representing the up- 
 per end of the 2-inch pipe, and draw a semi-circle 
 upon it as shown, and space it into six equal spaces, 
 and from these points draw parallel lines to intersect 
 each in turn of the radial lines, and draw a free hand 
 curve through the points of intersection, which gives 
 us the true elevation view of the shape of the base of 
 the small pipe, shown by the heavy curve line H to K. 
 
 To develop the pattern for this pipe draw the 
 stretchout ^Nl X O P equal to 12 of the spaces on the 
 semi-circle I J and space it into 12 equal spaces as 
 shown and placed exactly parallel with the pipe. Then 
 draw lines at right angles to the pipe and stretchout, 
 from the points of intersection on curve H K to inter- 
 sect with the space lines on stretchout, and through 
 these points of intersection draw the curve the same 
 as in making an elbow pattern. 
 
 To develop the pattern for the tapered pipe, set the 
 dividers at A and with radius A D draw the arc O R 
 and with radius A G the arc S T. Step off one-quar- 
 ter of the large circle in plan into any desired number 
 of equal spaces and, if only half the pattern is desired 
 in a piece as here shown, step twice the number 
 found in the quarter circle on the arc O R, and con- 
 nect R T and O S by drawing radial lines towards A. 
 This will then be the pattern for half the tapered pipe. 
 If, however, it is desired to make the pattern in one 
 piece, step off four times the number of spaces found 
 
XXTH CENTURY SHEET METAL WORKER. 65 
 in the quarter circle of plan, onto the continued arc 
 OR. 
 
 To cut the opening in this pattern for the small pipe 
 to fit, draw the radial line A U wherever desired — 
 here shown in the middle of the half pattern — and 
 from it space off each way the spaces obtained in plan 
 
 by drawing the radial lines through the space points 
 in small circle to the circumference of tlie base. The 
 line A U of pattern is the same line as C L' in plan, 
 hence we space on O R each way from U the same 
 distances as shown in plan each side of U. Then 
 draw radial lines from A to all these points on O R. 
 Next draw parallel lines across the elevation from the 
 
66 XXTH CENTURY SHEET METAL WORKER. 
 
 intersecting points on curve H K at right angles to 
 A B and intersecting the side D G and with the di- 
 viders draw curves from the points where the hori- 
 zontal Hues meet D G, using A as center to intersect 
 the radial lines drawn from A to O R, and through 
 the points of intersection draw the irregular egg 
 shaped oval which will be the shape of the opening. 
 
 All locks and laps must be allowed outside of the 
 pattern lines. 
 
 To develop patterns for the same article by trian- 
 gulation. 
 
 Draw plan and elevation the 'same in outline as for 
 projection, and the semi-circle T J on end of small 
 pipe and space it the same as in the previous example. 
 Drop dotted lines from the points H and K to the 
 transverse diameter of plan and space the portion be- 
 tween them into 6 equal spaces, and with C as center 
 draw short concentric arcs through these space marks. 
 Draw a dotted outline of the small pipe projecting as 
 far as the point I in elevation and on its diameter 
 X Y dfaw a semi-circle spacing it the same as the one 
 in elevation. 
 
 Draw lines from the semi-circle X Y to intersect the 
 arcs and through the points of intersection draw the 
 irregular curve as shown, which represents the top 
 view of the small pipe intersecting the tapering pipe. 
 
 Now through the intersections above the diameter 
 draw 3 radial lines to the large circumference of plan 
 and project lines from these points up to base line 
 D E of elevation, and draw radial lines from A to 
 meet them. Draw parallel lines from the semi-circle 
 
XXTII CENTURY SHEET METAL WORKER. 67 
 I J to intersect the radial lines and mark the curve 
 HK. 
 
 Space one quarter of the large circle of plan into 
 6 equal spaces, and make lines towards the center C 
 and just to the small circumference, thus spacing the 
 small circle into the same number of equal spaces as 
 the large one. Number the points on the inner circle 
 
 1 to 7. and those on the outer circle 8 to 14. Draw a 
 diagonal line from i to 13 and set off its length on 
 base line of elevation as shown from 14 to 13, then the 
 distance from the center of the line F G and i. to the 
 point marked 13 on the base line, will be the true 
 length of the diagonal line i to 13. And the side 
 G D or F E is the true length of i to 14. 2 to 13, etc. 
 
 Now draw one side of pattern T R. the length of 
 D G and mark one end i and the other 14. With a 
 pair of dividers spanned to the length of the line i to 
 13 in elevation set one point at i at the top end of 
 the line T R. and with a second pair of dividers 
 spanned one of the spaces of the large circle of plan, 
 measure out from 14 at the lower end of the line T R 
 and mark a short arc across one made by the dividers 
 reaching from i, thus locating 13. Next take the dis- 
 tance D G of elevation and with one foot of dividers 
 at the newly found point 13 measure upward and 
 locate 2 just the distance of one of the spaces of small 
 circle out from i. It is a great convenience to have 
 a third pair of dividers and keep them set to this dis- 
 tance. And as i to 13, and D to G happen, in this 
 instance, to be the same length, they can be used with- 
 out change for both measurements. Now mark from 
 
 2 to 12 measuring out from 13 with the dividers which 
 
68 XXTH CENTURY SHEET METAL WORKER. 
 
 are set to the large circle spaces. Then from 12 to 3 
 measuring out with those set to the short spaces, and 
 so on until one-half, or if so desired, the whole pat- 
 tern is completed. 
 
 To get the opening for small pipe mark down on 
 center line of pattern tl.^ distance from F to K (eleva- 
 tion) and up from 8 the distance from E to H, and 
 locate the center * where the side lines of pattern 
 would cross, and using center * draw short arcs 
 through the points marked. (T\y the way, if the work 
 has been correctly done, the distance from O or R 
 to * will be the same as from D or E to A of eleva- 
 tion.) Next measure from point F to each in turn 
 of the intersection points in curve between K and H 
 and transfer them to the center line of pattern, meas- 
 uring down from 7 each time, and draw an arc through 
 each using * as center. Now take the distance from 
 the center line, or rather the transverse diameter of 
 plan, to the intersection point on each of the arcs and 
 transfer each measurement to the corresponding arc 
 on pattern, and through these points draw the curve 
 for the opening. 
 
 For pattern for small pipe, draw AI N the length 
 required for circumference of pipe, in this case about 
 6 5/16 inches, and M P and N O each equal to J K of 
 elevation. Space M N into 12 equal spaces and draw 
 the center line V W equal to H I, then draw lines 
 from the space points parallel to V W of indefinite 
 length but not longer than V W, and measure the 
 distance from each of the points on the straight line 
 I J to each corresponding point on the curved line H 
 K and transfer each in turn to each side of the pattern. 
 
XXTH CENTURY SHEET METAL WORKER. 69 
 
 These measurements may be verified by a diagonal 
 measurement from each point as found, back to the 
 last preceding" point as sliown by the diagonal dotted 
 lines on both pattern and elevation. 
 
 Fruit Jar Filler. 
 
 A very convenient and ready selling fruit jar filler 
 and dipper combined is here shown. 
 
 The article is made in two pieces, which are shown 
 
 in Figs. I and 2. Fig. i is the dipper portion, and 
 should be raised slightly with the hammer. The edge 
 A, of Fig. I, is to be double-seamed to the edge B, of 
 
 Fig. 2, between the points marked e and e. The edges 
 C and D are locked together forming the top side of 
 
70 XXTH CENTURY SHEET METAL WORKER. 
 
 the funnel portion. And those edges marked a a a a 
 are simply hemmed and flattened down in the burring 
 machine. A wire makes the edge too thick to dip into 
 the fruit. 
 
 Fig. 3 shows the finished article, with the exception 
 of the handle, which may be a dipper handle, soldered 
 and well bossed, or a large saucepan handle riveted 
 and soldered at the point marked E. 
 
 This dipper and filler, when once tried, becomes a 
 favorite with the ladies of the house, and will sell 
 readily when its many uses become known in a neigh- 
 borhood. 
 
 Elbozi's, angles, tecs, roof saddles, chimney thiinhles, 
 etc., all cut ill the same manner. 
 
 We will first consider a square two-piece elbow, 
 and a very convenient method of cutting it. By a 
 square elbow I mean one of 90 degrees 
 
 Lay cut the blank of sufficient length to make a 
 pipe of the desired size, 18^8 inches for 6-inch pipe, or 
 22 inches for 7-inch. Then allow as much on each 
 side as will be required for locks, or lap if to rivet. 
 
 We will now suppose we are to cut a 7-inch 90- 
 degree elbow in two pieces. We will take a piece of 
 sheet iron about 23 x 14 inches arid mark tlie lines 
 XY and OZ 22 inches apart and parallel. This will 
 
XXTH CENTURY SHEET METAL WORKER. 71 
 leave a half -inch for lock on each edge if we have 
 previously cut it 27, inches long. 
 
 On the line XY, about 3 i'.iches clown from X mark 
 A: 3>< inches from A mark C, a' id 7 inches from A 
 mark B. In the same manner, and at the same dis- 
 tances mark on line OZ the points D, F and E. A and 
 P,. and D and E are each 7 inches apart on their re- 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 £ 
 
 A 
 
 1 
 
 Ur^ 
 
 
 
 
 
 
 -^ 
 
 X 
 
 
 
 / 
 
 r' 
 
 
 \ 
 
 
 
 ^' 
 
 5- 
 
 C 
 
 
 1.\ 
 
 \ 
 
 ^ 
 
 
 
 
 
 \ 
 
 /, 
 
 3 
 
 :i 
 
 
 — d- 
 
 4)^ 
 
 /I 
 
 <^ 
 
 
 
 
 
 / 
 
 \ 
 
 ^a 
 
 
 
 — -^ 
 
 A 
 
 
 
 \ 
 
 
 
 y 
 
 
 
 ^ 
 
 
 B 
 
 ^i^XX 1 • 1 1^=^ 
 
 F=^=-4 1 1 1 H 
 
 r-^"*" ' 
 
 E 
 
 Elbows Fig. !• 
 
 spective lines XY and QZ. This is tlie correct dis- 
 tance, because the rise or backset of a 7-inch elbow 
 is 7 inches, or just equal to the diameter of the pipe. 
 This is the same in any other size, that is, the rise 
 for any size of 90-degree two-piece elbow is just the 
 diameter of the pipe. 
 
 Now span the dividers 3J^ inches, the radius of the 
 pipe, and with one foot at C, describe the semi-circle 
 A to B. And with one foot at F describe one from 
 
72 XXTH CENTURY SHEET METAL WORKER. 
 
 D to E. Next draw the center line from C to F, 
 and with the dividers unchanged place one foot at 3 
 where the center line crosses the semi-circle, and 
 mark short arcs at i and 5. From A. same span, 
 mark 2, and from B mark 4. Proceed the same at the 
 other end of pattern, thus dividing each semi-circle 
 into 6 equal spaces. 
 
 Draw parallel lines from XY to OZ rnrough these 
 
 Elbows Fig. 2, 
 
 points, dividing the pattern into 6 unequal spaces, as 
 chown in Fig. i of Elbows. 
 
 Snace any one of the parallel lines, or the bottom 
 edge of sheet into 12 equal spaces, and draw lines 
 from the points perpendicularly, crossing the hori- 
 zontal lines as shown, and draw a freehand line 
 through the alternate points of intersection, from B 
 to 5, to 8, to 7, to 10, to 5 and ending at E. This 
 
XXTH CENTURY SHEET METAL WORKER. 72> 
 line is clearly shown by the heavy curved line in 
 Fig. I. 
 
 Cut on this line, and we have the two pieces A and 
 B shown in Fig. 2, which, when formed up and locked 
 will make a two-piece 90-degree elbow with one seam 
 in the throat, and one on top. 
 
 B 
 
 Elbows Fig, 3» 
 
 To make a roof saddle for the side of a half-pitch 
 roof, cut on same line. 
 
 But if for comb of roof, cut from B to 8, then down 
 to 9, up to 10 and down to E, and use the lower piece 
 shown by B of Fig. 3. The other piece resulting from 
 this cut is a tee pattern, but without allowance for lap. 
 
74 XXTH CENTURY SHEET METAL WORKER. 
 
 which may be added as desired, as shown bv dotted 
 lines in A of Fig'. 3. It is, however, tlie true intersec- 
 tion Hne of the Tee. 
 
 A Fig. 3 is also the pattern for a stove-pipe thimlile 
 to fit in a corner. And the other piece, B, is a thimble 
 to fit the projecting corner of a chimney. 
 
 Thus far we have only been working with angles 
 of 90 degrees. To make patterns for other angles it 
 is only required to get the rise of the miter line, and 
 span the dividers to equal one-half of it, after which 
 the process is the same. The semi-circles must be 
 of a diameter equal to the required rise. 
 
 To Find the Rise of Miter Line for 90 Degree Elbow of 
 Any Number of Pieces. 
 
 An easy manner of finding the rise of miter line for 
 90 degree elbows of an\- number of pieces, is as fol- 
 lows: 
 
 Draw a square having each side equal to the diame- 
 ter of the pipe, as shown by A, B, C and D of Figs. 
 I, 3 and 5 of Miters. Draw the diagonal line from 
 A to C, and with the dividers set the length of one 
 side of the square, and one foot at C, draw a quadrant 
 from B to D, and divide one half of it into i less equal 
 spaces than the number of pieces desired in the elbow. 
 Miters, Fig. i, shows method of getting the miter line 
 for a three piece elbow. Fig. 3 a four piece, and Fig. 
 5 a five piece. And Figs. 2, 4 and 6 show the pattern 
 developed. 
 
 In all cases the spacing on the quadrant must be 
 done accurately, and the miter line extended through 
 
XXTH CKNTURY SHEET METAL WORKER. 75 
 the point to the side of the square, and the true rise of 
 the miter hne is the distance from B to the point 
 where the miter Hne cuts the side of square, marked 
 E in Fig. r. 
 
 To prove that this mnhod gets the true rise, it is 
 only necessary to refer to Fig. 7, which shows the out- 
 
 I 
 
 m 
 
 Fig. 2. 
 
 Fig. 3. 
 
 Fig, 4. 
 
 ^ifi« 5« Fig. 6. 
 
 Hne of the long, or outer, side of a three piece elbow 
 drawn within the square, and drawn to a larger scale. 
 This drawing also clearly shows the reason for spac- 
 ing half the quadrant into one less than the number of 
 pieces desired. .\ three piece elbow only has two 
 miter lines. A four piece, three, etc. 
 
76 XXTH CENTURY SHEET METAL WORKER. 
 
 The foregoing methods may also be appliKl to the 
 cutting of patterns for angles of an}' shape ai well as 
 90 degrees. It is only necessary to find th? rise of the 
 
 Pig. 7. 
 miter line, and draw the pattern as described by using 
 semi-circles whose diameter is the rise required. 
 Elbows of Less Than 90 Degrees, Called Angles. 
 
 As before stated, these patterns may be obtained in 
 the same manner as those we have been studying, after 
 we obtain the rise of the miter line. 
 
 We will now suppose we have found the required 
 pitch of an angle to fit a certain place, by setting a 
 bevel, or with two pieces of iron riveted together, or 
 with two pieces of lath or shingle, as H and I of 
 Fig. I. 
 
 Draw AB and BC along the two blades of HI, and 
 bisect the angle thus formed. This may be done by 
 spanning the dividers an equal distance each way from 
 
XXTH CENTURY SHEET METAL WORKER. 17 
 
 B and marking points as A and C, then with these 
 points as centers and radius greater than A to B, strike 
 
 rig. 2 
 
 the intersecting arcs at D. Draw BF indefinitely 
 through the intersection, and on this Hue locate a 
 
78 XXTH CENTURY SHEET METAL WORKER. 
 
 point F just the diameter of the pipe distant from the 
 nearest point on AB, which may be done by spanning 
 the dividers to the diameter of pipe and striking the 
 arc AC. Then draw EF at right angles to AB by 
 means of one of the elementary rules for drawing a 
 line from a given point to a given line, perpendicu- 
 lar to the given line. 
 
 When E is accurately located, BF will be the miter 
 
 Fifi. 3. 
 
 line, and the distance E to B is the required rise, and 
 hence is the diameter of the semi-circles from which 
 we develop the pattern. In other words, span the di- 
 viders one-half the distance E to B for the radius, 
 and proceed as in the development of elbows as before 
 given. 
 
 The angle shown in Fig. i, the complete elevation of 
 which is shown in Fig. 2, is 45°. But it is not neces- 
 sary that we should know the number of degrees. 
 
 If, however, the required degrees are known, and 
 we have a protractor, the process is even more simple. 
 
 Draw AD, Fig. 3, equal in length to the diameter 
 
XXTH CENTURY SHEET METAL WORKER. 79 
 
 of pipe, and by the protractor, draw DB at one-half 
 the required angle. 
 
 For instance, for a 30° angle, we draw DB at an 
 angle of 15° to AD. Then one-half the distance A to 
 B is the radius for our semi-circles. 
 
 Pig, 4. 
 
 The elevation of the finished 30° angle is shown in 
 
 Fig. 4. 
 
 To Draw Pattern for Any Regalar Tapering or Flaring Article 
 
 The method here described will apply in drafting 
 patterns for any of the round flaring and tapered arti- 
 cles made in a tin shop, whether basins, pans, coffee 
 pots or "Sibley stoves." Provided the bottom and top 
 are parallel, and the sides a regular taper. 
 
 Draw an elevation of the article, full size, as A, B, 
 
8o XXTH CENTURY SHEET METAL WORKER. 
 
 C, D, of Fig. I, and extend the side lines until they 
 meet, as at E. Then with E as center, and E D as 
 radius, describe an arc cutting D and C, and if the 
 pattern is to be in one piece, continue indefinitely to 
 F. And with the same center, and radius E to A, 
 
 Pig. !• 
 
 strike an arc through A and B and extending in- 
 definitely to G. 
 
 Next draw a circle the size the large end of the 
 finished article is to be, as Fig. 2, and divide it into 
 quarters, as shown. (Or if more convenient, draw 
 only a quarter circle.) Space the quarter circle into 
 
XXTH CENTURY SHEET METAL WORKER. 8i 
 
 4, 5, or 6 spaces, or any convenient number, (here 5) 
 as D to X, Fi,q-. 2, and step these onto the Hne D F, 
 as shown from D to X in Fig. i. Then span dividers 
 from D to X and step off three more times, 2, 3, F, 
 thus locating- the point F, and making the arc D F 
 almost equal in length to the circumference in Fig. 2. 
 
 Draw an arc outside of, and parallel to D C F, as 
 an allowance for burr or wire, according to whether 
 the large end is to be the top or bottom of the finished 
 
 Fig* 2. 
 
 job. And another arc inside of, and parallel to A B G. 
 Also, allow edges for lock or lap. parallel to A D, and 
 G F, as shown by dotted lines in Fig. i. 
 
 If it is desired to make the pattern in two pieces, use 
 only twice the distance D X as shown at 2 in Fig. i. 
 And if it is to be in three pieces get one-third the 
 circle, Fig. 2, by stepping twice the radius, as O to P, 
 and divide this into a number of equal spaces (here 7), 
 which step on arc D F of Fig. i, from D to Y. 
 
 It is a mistake sometimes made by tinners, to step 
 6 times the radius of the required circle, on D F, to 
 locate F, as this will make the pattern too short. While 
 
82 XXTH CENTURY SHEET METAL WORKER. 
 
 6 times the radius just measures around inside its own 
 circumference, yet it will not measure the same length 
 of line when applied to the arc of a circle of a differ- 
 ent size. This is illustrated in Fig. 3, where the circle 
 shown is the same size as that in Fig. 2, and the radius 
 
 Pig. 3. 
 
 is shown stepped around it in six steps. Also, D F is 
 made the same as DF in Fig. i, and the six steps 
 shown only reaching to f, showing how much too 
 short the pattern would be if measured in this manner. 
 Even the method I have described is a little short 
 of the true length but will be found near enough for 
 most cases. If greater accuracy is desired I would 
 recommend cutting a narrow strip of light sheet metal 
 just the required length, and bending it to the proper 
 curve, measure from D to locate F. 
 
XXTH CENTl'RV SHEET METAL WORKER. 83 
 
 Some Convenient DimensioBi of Tinware. 
 
 In the following dimensions the locks, burrs, wire 
 locks, etc.. have all been allowed. That is for small 
 neat seams. Don't put a pint cup together with a 
 "stove pipe lock." 
 
 There are two regular sizes of No. 8 wash boilers. 
 The No. 8-18, and the small No. 8. 
 
 For the No. 8-18 cut 3 pieces 14 x 19, or i piece 
 56 X 14. 
 
 For the No. 8 small cut 3 pieces 13^ x 18, or i 
 piece 53-^ I3K'- 
 
 For No. 9 boiler cut 3 pieces 14 x 20, or i piece 
 59 X 14- 
 
 Covered Buckets. 
 
 2 quart . . .• 2 pieces 10 x 5^ 
 
 3 quart . 2 pieces 10^ x 6 
 
 4 quart 2 pieces 12 x 7 
 
 6 quart 2 pieces 12^ x 8>^ 
 
 8 quart 2 pieces 13^ x 9^ 
 
 Flaring Pails. (Net Sizes ) 
 
 2 quart, 6yi in. diam. top, 43^ diam. hot., 4 deep 
 4 quart, 7>4 in. diam. top, 5 diam. bot., 5 '4 deep 
 6 quart, 9I4 in. diam. top, 5>4 diam. bot., 6y2 deep 
 8 quart, io'< in. diam. top, 6 diam. bot., 7J/< deep 
 10 quart, UV2 in. diam. top, 7 diam. bot., 8 deep 
 14 quart, 13 in. diam. top, 9 diam. bot., 9 deep 
 
 Pans. (Net Sizes.) 
 
 2 quart, 9 in. top, 6 in. bot., 3^)4 i"- fleep 
 6 quart, 12^ in. top, 9 in. bot., 4 in. deep 
 
84 XXTH CENTURY SHEET METAL WORKER. 
 
 10 quart. 14 in. top, 11 in. bot., 4^4 iii- deep 
 
 14 quart, I5>:| in. top, 10 in. bot., 6 in. deep 
 
 16 quart, 18 in. top, n iii. bot., 6^/ in. deep 
 
 20 quart, 19^^ in. top, 13 in. bot., 8 in. deep 
 
 Cans. (Cut to Bent Advantage.) 
 
 To Hold. Size to Cut Sheet. 
 
 1 gallon 7 X 21 inches 
 
 2 gallons 10 X 25 inches 
 
 3 gallons 103/2 X 30 inches 
 
 4 gallons . 12 X 32 inches 
 
 5 gallons 12 X 36 inches 
 
 6 gallons 13 x 40 inches 
 
 8 gallons 14 x 42 inches 
 
 10 gallons 16 X 46 inches 
 
 15 gallons 20 X48 inches 
 
 20 gallons 20 X 57 inches 
 
 25 gallons 22 X 60 inches 
 
 40 gallons .26 X 70 inches 
 
 50 gallons 26 X 76 inches 
 
 75 gallons 30 X 86 inches 
 
 fr>o gallons 36 X 96 inches 
 
 To find the contents of cylindrical vessels. 
 
 Multiply the square of the diameter in inches by the 
 height in inches, and this product by the decimal .0034. 
 The result will be the gallons, and decimal fraction of 
 a gallon. 
 
 This is a shorter method than finding the cubic 
 inches and dividing by 231, and the result is exactly 
 the same. 
 
XXTH CENTURY SHEET METAL WORKER. 85 
 Practical Suggestions. 
 
 To Clean Water Backs When Filled Up With Lime 
 or Alkali. 
 
 Pour slowly into the casting, muriatic (hydro- 
 chloric) acid. 
 
 This must be done carefully, as it will boil over and 
 waste the acid unless care is taken. 
 
 When the lime has all been removed, wash thor- 
 oughly, and replace. 
 
 To Cut Heavy Iron With the Stock Shears. 
 
 When very heav\- iron is to be cut by hand, it will 
 often be found a great help to turn the shears wrong 
 side up and slip a piece of i-inch gas pipe, or larger if 
 necessary, onto the tang, thus making a long leverage, 
 and the pipe stands so nearly perpendicular that the 
 workman can stand almost erect, and yet has a good 
 leverage on the work. 
 
 To Lock the Edges of a Pitched Cover, or Can Top. 
 
 Often when making a cover or can top with only 
 a slight pitch, it is desirable to lock the seam, but dif- 
 ficult to do so in the folder. Try sli])ping each edge 
 in the slot of the rod of gutter header, and turning 
 the rod just enough to break the aV^c up a little more 
 than sciuare, when the seam may be grooved down 
 ver}' nicely. 
 
 Teiitporarx Handles for Soldering Coppers. 
 
 These may l)e (|uickly made by wrapping around 
 the shank several thicknesses of asbestos paper. Draw 
 it snug with a wire, and it will be found to answer 
 the purpose very well, 
 
86 XXTH CENTURY SHEET METAL WORKER. 
 
 To Tin Black Iron Rivets, or Other Small Articles. 
 
 Put them in a bowl of raw acid (hydrochloric) until 
 the black scale is well eaten off. Rinse with water 
 and place in "killed" acid ; i. e., acid which has had 
 all the zinc it will eat, and then without rinsing, drop 
 into a pot of melted solder. Remove with a strainer. 
 
'V^/^T T cannot afford to place your 
 
 ^ ^^ vJ order for Stoves or Ranges 
 
 of any kind without writing to the 
 
 MONITOR STOVE 
 AND RANGE CO. 
 
 CINCINNATI 
 FOR THEIR NEW CATALOG 
 
 Makers of the 
 
 MONITOR RADIATOR 
 
 The Greatest and Best Hard Coal 
 Base Burner 
 
 Stoves and Ranges for all kinds of fuel 
 
 MIONITOR 
 
 STOVES & RANGES 
 
The Sheet Metal Worker With Ambition 
 To Get Ahead Needs 
 
 THE AMERICAN ARTISAN 
 
 AND HARDWARE RECORD 
 In His Business 
 
 PUBLISHED EVERY SATURDAY 
 
 Slieet metal workers, tinners and roofers wlio knf)\v, 
 consider it the most authoritative and valuable pul)li<a- 
 tion devoted to their interests — 
 
 IT IS AND WILL CONTINUE TO BE 
 
 Each issue contains one or more tinshop proljlems 
 prepared and edited by experts. 
 
 Each issue contains a fund of practical and instructi\e 
 articles relating to the sheet metal industry. 
 
 Subscribers are always at liberty to submit tinshop 
 problems which puzzle them. In fact when we say that 
 no publication even attempts to prepare as interesting or 
 valuable a department for the sheet metal worker, we 
 speak the truth. If you want the most news, tlie freshest 
 news, the most instructive illustrated articles by the best 
 authorities on Sheet Metal Work, Cornice Work, Tin 
 Roofing. Furnace Installation, etc., 
 
 THE AMERICAN ARTISAN 
 is your trade paper. 
 
 Subscribe To=day and Take Advantage of Our Special Offer 
 Subscription Price, $2.00 A Year, 52 Issues. 
 
 DANIEL STERN, 
 
 Publisher and Proprietor, 
 
 355 Dearborn St., CHICAGO 
 
Books by Mail 
 
 D*TTCDMc''\'^ position to supply Teclinical BOOKS and 
 PATTERNS ot all characters, at lowest prices 
 « .**."«,''';*' ii'^l^i^'^'^ ^''C' most staiuianl works on Sheet 
 >1etal Work, Heating and Ventilation, Plumbing and Drain= 
 age. Advertising and the Workshop. 
 
 Some Books and Patterns for the 
 Sheet Metal Worker 
 
 100 TINNERS' PATTERNS -Full sized patterns tor 
 complete hne ot tniware— on lieavy manila i)aper ready 
 tor use— nowhere can so complete a set be obtained a't 
 the very Iom- price of ^1 ^^^ 
 
 Gray's PERFECT ELBOW PATTERNS — absolutelv 
 on'^'r^% ro'J'' -°" <^0 Pattt-rns 2, 8. 4, T, pieces) $1.50 
 20 to 40" (SO patterns 5, 6, 7, 8 pieces) | so 
 
 C'oinplete set of 1" to 4()" (2 to S pieces, 160 patterns) 
 with angle chart 3 qq 
 
 (hay's PERFECT SKYLIGHT PATTERNS -for sinHe 
 pitch, hip and gal)le skyliglits. "" 
 
 24" bar::;: ;:;::: ::::;;:::::: '^aH 
 
 . CORNICE WORK /VlANUAL-240 pages (]S4'engn; v- 
 mg.s) of important information for cornice worker $3.50 
 
 TIN, SHEET IRON and COPPER PLATE WORKER 
 ''•X,,^^- •^- '^'""'' ''qiially valual)le for beginner and 
 skilled artisan S;^ SO 
 
 TINNERS' HELPER and PATTERN BOOK by II K 
 Vosburgh — valuable rules, diagrams and tabl(\s— p,„ke1 
 edition «1 00 
 
 SHEET METAL WORKERS' QUIDE-with rulcs.md 
 ihagrams for describing most useful patterns ordinarily 
 used— al.so chapter on Sheet Metal Work, soldering and 
 geometry «q ^q 
 
 MANUAL OF RECEIPTS-' 241 pages', 1718 usefulre- 
 
 ceipts tor the worksliop $3 SO 
 
 Send for our complete list and prices. 
 We prepay express on all orders. 
 No books exchanged. 
 
 DANIFI ^TFPIM 353-357 Dearborn St. 
 1-^.n.l lULiLi O I ILiIxl^ CHICAGO, ILLINOIS 
 
29 \^IQ 
 
 100 TINNERS' PATTERNS 
 
 THE AMERICAN ARTISAN FULL SIZE PATTERNS 
 
 Comprise patterns for a full line of tinware, in numerous sizes, square and round 
 elbows, cut-offs, etc. These full size patterns, numbering upward 100, are printed 
 on inanila paper, from which they are readily transferred fo heavy sheets and 
 cut out ready for use. The list contains the following patterns; 
 Tea Steeper Fourteeii-quart Milk Pail Breast 
 
 Two-pint Tea Pot Two-inch Four-piece Round Elbow 
 Three-pint Tea Pot Three-inch Four-piece Round Elbow 
 Four-pint Tea Pot Four-inch Four-piece Round Elbow 
 Five-pint Tea Pot Five-inch Four-piece Round Elbow 
 One-quart Coffee Pot Five-and-a-half-inch Round Elbow 
 
 Two-quart Coffee Pot Six-and-a-half-inch Round Elbow 
 
 Three-quart Coffee Pot Seven-and-a-half-inch Round Elbow 
 Small Grocers' Scoop 
 Medium Grocers' Scoop 
 Large Grocers' Scoop 
 
 Four-quart Coffee Pot 
 Five-quart Coffee Pot 
 No. 1 Coffee Boiler 
 No. 2 Coffee Boiler 
 No. 3 Coffee Boiler 
 Lamp Filler 
 One-Pint Dipper 
 One-quart Dipper 
 Two-quart Dipper 
 Four-quart Flaring Pail 
 Six-quart Flaring Pail 
 Eight-quart Flaring I'ail 
 Ten-quart Flaring Pail 
 Twelve-quart Flaring Pail 
 Fourteen-quart Flaring Pai 
 Ten-quart Dish Pan 
 Twelve-quart Dish Pan 
 Fourteen-quart Dish Pan 
 Sixteen-quart Dish Pai\ 
 Dinner Bucket 
 I'^ive-inch T-Joint 
 Six-inch T-Joint 
 Eave Trough Mitre .Joint 
 "Snap" 2-inch Conductor Elbow 
 Cullender 
 Two-inch Square Elbow 
 Two-and-a-half inch Square Elbow 
 Three-and-a-half-inch Square Elbow 
 Four-and-a-half-inch Square Elliow 
 Five-and-a-half-inch Square Elbow 
 Six-and-a-half-inch Square Elbow 
 Seven-and-a-half-inch Square Elbow 
 One-pint Funnel 
 Two-pint Funnel 
 Three-jiint Funnel 
 Four-pint Funnel 
 Small Milk Strainer 
 f^arge Milk Strainer 
 Ten-(iuavt Milk Pail Breast 
 
 Apple Corer 
 Oval Foot Bath 
 Oval Pudding Pan 
 Half-gallon Can Breast 
 One-gallon Can Breast 
 Two-gallon Can Breast 
 Three-gallon Can Breast 
 Half-i)int Measure 
 One-pint Measiue 
 One-quart Measure 
 Half-gallon Measure 
 One-i)int Basin 
 T wo-pint Basin 
 Three-pint Basin 
 Four-T)int Pan 
 Six-quart pan 
 Ten-(iuart Pan 
 Small Cuke Pan 
 Medium Cake I'an 
 Large Cake Pan 
 Small Wash Basin 
 Large Wash Basin 
 Sprinkler Breast 
 Four-gallon Churn 
 Five-gallon Churn 
 Small Dust Pan 
 Large Dust Pan 
 Five Sizes Funnel Patrns. 
 Oval Dinner Bucket 
 Rain Water Cut-off 
 No. 7 Boiler Cover 
 No. 8 Boiler Cover 
 No. 9 Boiler Cover 
 No. 7 Boiler Bottoms 
 No. 8 Boiler Bottoms 
 No. 9 Boiler Bottoms 
 
 THE AMERICAN ARTISAN full size patterns are a great convenience, and in no 
 
 other way can they be obtained at so small a cost. Price, sent postpaid for the 
 
 FULL SET OF 100 PATTERNS $1.00 
 
 355 DEARBORN ST. 
 CHICAGO, ILL. 
 
 DANIEL STERN, 
 
REGISTERS and 
 
 VENTILATORS 
 
 » 
 
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 CAST IRON 
 
 or 
 
 SEMI-STEEL 
 
 or 
 
 WROUGHT 
 STEEL 
 
 500,000 in Stock 
 
 lY MFG. CO. 
 
 One copy del. to Cat. Div. ) boston 
 
 9tr:: 29 1910