William L. Ilgen

91. Tongs.—As tongs are among the most important tools and quite difficult to make, they will be taken up in this chapter on tool making.

The weakest places in a pair of tongs are where the shoulders or offsets are formed for the jaws and handles. These places should be reËnforced by fillets as large as the usefulness and appearance of the tongs will permit; they should never be made sharp and square, unless their construction demands it.

All tongs for general blacksmithing can be forged properly with the hand hammer and the use of such tools as the top fuller, the swages, and the round-edged set hammer. Some assistance with a light sledge will be necessary. The use of such tools as a square-edged set or the file for forming shoulders or fillets is very objectionable, especially in the hands of unskilled workmen. If the two parts do not seem to fit as they should, due to the fillets which are present, they will generally adjust themselves when they are riveted together, heated, and worked freely.

92. Heavy Flat Tongs.—Fig. 74. Fullering, forging, swaging, punching, and riveting. Material: 15 inches of ⁷/₈-inch square mild steel.

Mark the center of the 15-inch length with a hardy or cold chisel. Form two depressions ³/₈ inch deep, with a top fuller, one 2 inches from the end at a, the other 3 inches from the same end but on the opposite side. Form a third depression to the same depth, but at an angle of 45 degrees, starting from the bottom of the first one, and on the side indicated by the broken line, as at b. Draw the 2-inch end to 1 × ¹/₂ inch from a, tapering to 1 × ³/₈ inch at the end. This portion forms one jaw, as shown at c. Now flatten out about 2 inches of the metal from the beveled depression b toward the center mark, to ⁹/₁₆ inch thick, allowing the metal to spread as wide as possible. This should then be forged and formed into shape for the joint d, and the fuller again placed in the second depression to make the dimension there ⁵/₈ inch, as shown at d.

Fig. 74.—Steps in Making Heavy Flat Tongs.

Forge the other end in the same manner, exerting due care to have all dimensions correspond; cut the stock in two at the center. Draw out the heavy ends for the handles with the power hammer or with some assistance from a sledge. They should be roughly forged at first with an allowance for finishing as follows: Beginning at the joint, use the top and bottom swages on the outer edges through the greatest width, and swage to ⁵/₈ × ¹/₂ inch. This swaging should be continued toward the end to form the handle. By using the flatter during the swaging, the sides may be kept straight, smooth, and slightly tapering to a round section. Make the end ³/₈ inch in diameter for a length of 3 inches. Sketch F shows one side of a pair of tongs drawn and swaged.

Place the parts together to see if they fit properly; if they do not, make the necessary alterations. Use a top fuller to form a groove e about ¹/₈ inch deep, lengthwise on the inside of the jaws, and smooth the sides and edges with a flatter. Then punch a ³/₈-inch hole in the center of the joint, as shown in sketch F. This should be done on both parts.

Heat thoroughly the end of a ³/₈-inch rivet, 1³/₄ inches long, and with it rivet the two portions tightly together. Heat the tongs, make them work freely, and adjust them to hold ³/₈-inch flat iron, with the entire length of the jaws in contact and with the ends of the handles 1 inch apart. The jaws and handles should be adjusted so that a line extended lengthwise across the center of the rivet would pass midway between them.

93. Light Chain Tongs.—Fig. 75. Forging, swaging, punching, fullering, and riveting. Material: 13 inches of ³/₄-inch square mild steel.

Mark the center of this length with a hardy or cold chisel. Form a shoulder 1¹/₄ inches from the end, and draw this end to ⁷/₈ × ¹/₂ inch at the bottom of the shoulder, tapering to ³/₄ × ³/₈ inch at the end, as at a. Form a second shoulder at an angle of 45 degrees, starting from the bottom of the first one, by holding the work on the anvil, as shown at b. The blows should be directed a little toward the center mark, to flatten and spread the metal for forming the joint of the tongs. Form a third shoulder at c, 1 inch from and on the opposite side to the first and toward the center mark, the thickness here being ¹/₂ inch. Note that these shoulders should be made with overhanging blows and not by using the fuller. The metal between the shoulders c and a should now be forged into shape for the joint. Forge the other end in a similar manner, being careful to have all dimensions correspond; then cut the stock in two at the center.

Draw out the heavy ends for the handles with a power hammer or with some assistance from a sledge. Roughly forge them from ¹/₂ × ⁷/₁₆ at c, down to ⁵/₁₆ inch round, 3 inches from the end. Finish the edges by using the top and bottom swages. By using the flatter on the sides during the swaging, the handle may be kept straight, smooth, and slightly tapered to where it terminates into round. Sketch F in Fig. 74 shows the handle drawn out and swaged.

Place the two parts together to see if they fit properly; if they do not, make the necessary alterations. Taking each piece separately, perform the following operations: Fuller a groove ¹/₈ inch deep, lengthwise on the inside of the jaw, and another crosswise about ¹/₄ inch from the end as shown at A, Fig. 76. Then punch a ⁵/₁₆-inch hole in the center of the joint. A ⁵/₁₆-inch rivet 1¹/₂ inches long should be obtained, its end should be thoroughly heated, and the two parts riveted tightly together. Heat the tongs and make them work freely; adjust them to hold ³/₁₆-inch flat iron with the full length of the jaws in contact, also to hold ³/₈-inch round material in the cross groove when the handles are 1 inch apart. They should be adjusted, so that if a line were extended lengthwise through the center of the rivet, it would pass midway between the jaws and handles. When complete these tongs will appear as in Fig. 76.

94. Lathe Tools.—A complete description of lathe tools would require too much space in this book, therefore only six common ones will be explained; by applying the knowledge received from making these, the operator should be able to forge many others. These with the other tool steel exercises should supply sufficient practice in forging, hardening, and tempering tool steel.

If these tools are to be put into practical use, a good quality of tool steel should be provided, cut about 8 inches long for each one, and great care should be taken in the heating, forging, and tempering. If, however, they are to be made for practice alone, then much shorter pieces may be conveniently used, also an inferior grade of steel; mild or soft steel would be sufficiently good to provide the needed practice in heating, forging, and tempering. Even though the material is inferior, the operations should receive the most careful attention.

The material may be 1 × ¹/₂-inch, ⁷/₈ × ³/₈-inch, or any suitable stock size.

95. Brass Tool.—Fig. 77. Forging, hardening, and tempering. Material: 6 to 8 inches of ¹/₂ × 1-inch tool steel.

Starting about ³/₄ inch from one end, draw to a uniform taper on both sides and on one edge only, so that the metal is ¹/₄ inch thick and ¹/₂ inch wide at the end. The lower or beveled edge also should be drawn thinner than the upper to provide the necessary clearance amounting to about 5 degrees on each side, as shown in the sectional view. The end should be cut off at an angle of 70 degrees and ground semicircular in form with the necessary clearance.

Heat about 2 inches of this end and harden in the manner described for the cold chisel, but in this case the color for tempering is a very pale yellow.

96. Cutting-off or Parting Tool.—Fig. 78. Fullering, forging, hardening, and tempering. Material: 7 inches of ¹/₂ × 1-inch tool steel.

With a top fuller form a depression across one side ⁵/₈ inch from the end, fullering the metal to ³/₁₆ inch thick. Draw this end down to 1 × ³/₁₆ inch. The thickness of the metal where it was fullered should also be decreased to ¹/₈ inch, gradually increasing to ³/₁₆ inch at the end, taking extreme care to have sufficient clearance from front to back and from top to bottom. The cutting edge is generally allowed to project about ¹/₈ inch above the stock; the end is trimmed off at an angle of 75 to 80 degrees and ground, as shown in Fig. 78, after which it is hardened and tempered to a pale yellow.

97. Heavy Boring Tool.—Fig. 79. Drawing, bending, hardening, and tempering. Material: 7 inches of ¹/₂ × 1-inch tool steel.

Draw about 2¹/₂ inches tapering to ¹/₂ inch square at the end; the taper on the top edge should be only ¹/₈ inch, while that on the bottom should be ³/₈ inch, as shown at a. With the metal resting flat on the anvil and the top edge to the left, bend down ³/₄ inch of the end to an angle of about 80 degrees, then forge down the corners from the point back to the heel, to a slight octagonal form, as shown in Fig. 79. Grind the projecting end of the angle semicircular with a clearance of 15 degrees, then harden and temper to a pale yellow.

98. Light Boring or Threading Tool.—Fullering, drawing, hardening, and tempering. Material: 5 inches of ¹/₂ × 1-inch tool steel.

Using a top fuller, form a depression ⁷/₁₆ inch deep on one edge and 2 inches from the end. Draw this metal slightly tapering to ⁷/₁₆ inch square at the end, keeping it straight on the top. With the metal resting flat on the anvil and the straight edge to the left, bend down ³/₄ inch of the end to an angle of 80 degrees, then forge the corners between the angle and where the depression was formed to a slight octagonal form.

For a boring tool, grind the projecting end of the angle semicircular in form, with sufficient clearance for boring a hole of the desired size; for a threading tool grind it to the proper angle of the thread with sufficient clearance, then harden and temper it to a pale yellow.

99. Diamond Point Tool.—Fig. 80. Forging, hardening, and tempering. Material: 7 inches of ¹/₂ × 1-inch tool steel.

Using a top fuller, form a depression ³/₈ inch deep on one edge ³/₄ inch from the end, as at a. Then holding the depression over a round edge of the anvil and delivering blows on the end, as indicated at b, forge the ³/₄-inch end into a square form, at an angle of 70 degrees to the lower edge of the stock, as shown at c. By resting the inner corners of this end on the face of the anvil and delivering blows on the opposite outside corners, as shown in Fig. 81, its form should be changed to ⁷/₁₆ inch square, projecting diagonally from the stock, as shown at a, Fig. 82.

By using a sharp, hot cutter and cutting entirely from the right inside surface (a, Fig. 82), and by holding the point over the edge of the anvil, so that the operation will have a shearing effect, the excess metal which extends more than ³/₈ inch above the upper line of the stock may be removed. For a right-hand tool the point should be set ¹/₈ inch to the left, as shown at b, the two outside surfaces being ground smooth and forming an acute angle; the inside portion of the end on the side indicated by a should be ground somewhat shorter, producing a diamond-shaped appearance. Harden and temper to a very pale yellow.

Reverse the operations of cutting, setting, and grinding for a left-hand tool.

100. Right Side Tool.—Fig. 83. Forging, offsetting, hardening, and tempering. Material: 7 inches of ¹/₂ × 1-inch tool steel.

Heat and cut off about ⁵/₈ inch of one corner, as at a, Fig. 83, and form a depression with the top fuller 1¹/₂ inches from the end on the side indicated at b, ¹/₄ inch deep at the upper edge, leaving the metal full thickness at the lower edge. Then the metal should be roughly spread out from the upper edge of the stock by holding the fuller lengthwise, as shown at C, leaving the lower edge the full thickness, and smoothed with a flatter, drawing the upper edge to ¹/₈ inch in thickness. The above operations could be done with a hand hammer, but not without considerable hard work.

Trim this end to the form shown in Fig. 84, by using a sharp, hot cutter and cutting entirely from the side indicated by d. When this has been done correctly remove all metal extending more than ¹/₄ inch above the upper edge of the stock. When this has been forged to the correct shape, heat and place the tool so that the fullered shoulder is just beyond the edge of the anvil, then form the offset with a round-edged set hammer, as shown in Fig. 85. Grind the upper edge parallel with the stock but at a slight angle, to produce a cutting edge, and grind the face side straight and smooth. In cooling this tool for hardening it should be placed in the water, as shown in Fig. 86, to insure hardening the whole cutting edge. Leave sufficient heat in the heel or bottom of the tool to draw the temper uniformly to a pale yellow.

101. Forging Tools.—The following forging tools are somewhat smaller than those used in general smith work, but they are perfectly serviceable and sufficiently heavy for manual training or considerable ordinary work. The material for their construction should be tool steel of 0.80 to 0.90 per cent carbon, 1¹/₄ inches square, unless otherwise specified. The holes or eyes should be punched straight, and the precautions formerly given under the head of punches should be observed.

A tapered drift pin of an oval section ⁷/₈ × ⁵/₈ inch at the largest end, also a smaller oval-shaped handle punch, should first be provided.

102. Cold Chisel.—Fig. 87. Forging, hardening, and tempering tool steel. Material: 6¹/₂ inches of ³/₄-inch octagonal tool steel.

First draw ¹/₂ inch of one end to a smooth, round taper about ³/₈ inch in diameter at the extreme end, then grind off the rough projecting edges until it is ¹/₂ inch in diameter. This end should not be cooled quickly, because it might harden somewhat, which would cause it to break easily. Starting 2 inches from the opposite end, draw the tool tapering to ¹/₈ inch thick and 1 inch wide, using the flatter on these tapered sides and edges. They should be made straight and smooth, with the edges perfectly parallel. Two views with dimensions are shown in Fig. 87.

Grind the cutting edge of the chisel to the desired angle, then harden and temper it as follows: Heat about 2 inches of the cutting end to a dull cherry red and plunge about 1 inch of this perpendicularly into water; withdraw it about ¹/₂ inch, and keep it in motion between the first and second cooling places until the end is perfectly cold. Remove the tool and quickly polish one side with emery cloth or sandstone, watching the varying colors as they make their appearance and move toward the edge; when the dark purple or blue color entirely covers the point, thrust it into the water again and leave it there until thoroughly cooled. Regrind cautiously, protecting the temper, and test its cutting qualities on a piece of cast iron or soft steel.

103. Hot Cutter.—Figs. 88 and 89. Punching, fullering, forging, hardening, and tempering. Material: 4 inches of 1¹/₄-inch square tool steel.

Punch and drift an eyehole 1³/₄ inches from the end, making all sides straight and smooth, as shown at a, Fig. 88. With a pair of ³/₄-inch fullers, form two depressions on opposite sides ¹/₄ inch from the eye, as at b, fullering the metal to ⁵/₈ inch thick. From this place draw the end tapering to 1¹/₂ × ¹/₈ inch, and trim it off at a right angle to the stock, as at c. Using a hot cutter and working equally from all sides, cut the tool from the bar 1¹/₄ inches from the edge of the eye. Draw the head end tapering to about ⁷/₈ inch from the eye, draw the corners to form a slightly octagonal section. Remove all projecting metal so as to produce a convex head. (See Fig. 89.) This will be referred to later as forming the head. Grind both sides of the cutting end equally to form an angle of 60 degrees, with the cutting edge parallel to the eye. Harden, and temper to a dark purple or blue.

104. Cold Cutter.—Figs. 90 and 91. Punching, forging, hardening, and tempering. Material: 4 inches of 1¹/₄-inch square tool steel.

Punch and drift an eye 2 inches from the end a, Fig. 90. Draw this end tapering on the sides parallel with the eye, forming convex surfaces and terminating in 1 × ³/₁₆ inch. (See sketches b and c.) Cut the tool off at c, 1¹/₄ inches from the eye, and form the head.

Grind the cutting end equally from both sides to form an angle of 60 degrees, and a convex cutting edge similar to that shown at d. Harden, and temper to a dark purple or light blue. The finished tool is shown in Fig. 91.

105. Square-edged Set.—Fig. 92. Punching and forging. Material: 3¹/₂ inches of 1-inch square tool steel. Heavier or lighter stock may be used if desired.

Punch and drift an eye 1¹/₄ inches from the end, then, using a pair of ³/₈-inch fullers, form depressions about ¹/₈ inch deep across the corners, as at a, Fig. 92. Cut the tool off 1¹/₂ inches from the eye, and form the head to ³/₄ inch at the end. Heat and anneal in warm ashes; when it is cold, grind the face smooth, straight, and at right angles to the stock.

106. Hardy.—Fig. 93. Fullering, forging, hardening, and tempering. Material: 3 inches of 2 × ⁷/₈-inch tool steel.

Using steel 2 inches wide with a thickness equal to the dimension of the hardy hole, fuller and draw a slightly tapered shank 1³/₄ or 2 inches long, to fit loosely into the anvil. The broken lines at a, Fig. 93, indicate the drawn shank. Cut off the stock 1¹/₂ inches from the shoulders at b. Heat and drive the drawn end into the hardy hole so as to square up the shoulders and fit them to the anvil. Then draw the heavy end tapering gradually from the sides, terminating ¹/₈ inch thick and 2 inches wide. Grind this tool similar to the hot cutter; harden, and temper to a purple or blue.

107. Flatter.—Fig. 94. Upsetting, forging, and punching. Material: 4³/₄ inches of 1¹/₂-inch square tool steel.

In forming the face of a flatter, the metal should be upset. This may be accomplished by ramming, but when so done, excess metal is formed just above the wide portion, causing considerable fullering and forging. If a piece of steel 4³/₄ inches long and 1¹/₂ inches square is cut off, and one end is drawn slightly tapering, it may, when heated, be placed in a square hole of the right size in the swage block, with the drawn end supported on something solid, leaving 1¹/₂ inches projecting. The hot steel can then be hammered down with a couple of sledges, until the face is formed to ³/₈ inch thick or about 2 inches square, as at a, Fig. 94.

Punch and drift an eyehole 1¹/₄ inches from the face, then draw and form the head. Anneal in warm ashes. When it is cold, the face should be ground perfectly straight, smooth, and at a right angle to the body, with the surrounding edges slightly round, as shown, or they may be left sharp and square if desired.

A round-edged set hammer may be made in this manner, but as the face should not be so large, less metal is required.

108. Small Crowbar.—Fig. 95. Drawing, swaging, welding, and tempering steel. Material: 16 inches of ³/₄-inch square mild steel, also a small piece of tool steel.

Draw 11 inches to the following dimensions: the first 4 inches to ³/₄-inch octagon, then beginning with ³/₄-inch round gradually reduce to ¹/₂-inch round at the end. This should be smoothly forged and swaged.

Form a depression ¹/₄ inch deep on one side of the square portion 2 inches from the end; from this, draw the metal to ¹/₂ × ³/₄ inch; by using a hot cutter where the depression was made, split and raise up a scarf fully ³/₄ inch long, as shown in the sketch. Prepare a piece of tool steel 2¹/₂ × ³/₄ × ¹/₂ inches; on one end of this draw a long, thin scarf and roughen it with a hot cutter, so it can be held in place securely. (See Fig. 95.)

Heat the bar cautiously where the scarf was raised, to avoid burning it; slightly cool the tool steel and put it into place. By holding the piece of steel against a hardy, swage, or fuller, the scarf can be hammered down tightly over the tool steel, which should hold it securely for heating. Place the pieces in the fire and heat them to a red; remove and thoroughly cover them with borax; replace them and raise the heat to a bright yellow or welding heat.

While the first light blows for the welding are being delivered, the end should be held against something to prevent the steel from being displaced; when positive that welding is proceeding, make the blows heavier and complete the operation.

When the pieces are securely joined, cut off the corner opposite to the steel face, and draw the bar tapering from this side, to a sharp, flat edge 1 inch wide. Bend this through its smallest dimensions to an inside radius of about 3¹/₂ or 4 inches and with the edge extending ¹/₂ inch to one side of the bar, as in Fig. 95. File or grind the outside surface and edge of this; then harden, and temper to a blue.

109. Eye or Ring Bolts.—An assortment of eyes is shown in Figs. 96, 97, and 98. All eyes should possess two essentials: the necessary strength and a good appearance; therefore the method of making should be chosen to fulfill those requirements. Generally the eyes that have the most strength require the greatest amount of labor.

A, Fig. 96, is an open eye which is very easily made, because bending is the only operation required. The method of making this form of eye has already been explained in section 69.

B is a welded eye. It is made by forming first a flat, pointed scarf on the end of the bar and bending it through its smallest diameter where the drawing was begun. This bend should be no less than 70 degrees on the outer side. Determine the length of the material needed for forming a ring of the required diameter, then subtract the diameter of the material from the determined length. Using this result, place a center-punch mark f that distance from e, and bend the piece at f in the same direction as e.

Form the metal between the bends into a circle, and place the scarf in position for welding, as at B. During the heating for welding, if the circle heats more rapidly than desired, it should be cooled off and the heating then continued. The welding should be done as quickly as possible and swaged if required.

The eye bolt, shown in Fig. 97, is similar to a solid forged eye. It is formed and welded with a specially forged scarf called a butterfly scarf.

Determine the amount of material needed to form a ring of the required diameter, and add to that a sufficient allowance for upsetting and welding, which would be approximately equal to the diameter of the material used. An invariable rule for that allowance cannot be given, because the results of the upsetting are seldom the same.

Place a center-punch mark the estimated distance from one end of the bar; then upset the end ¹/₈ inch larger than its original diameter, next upset it at the mark to a similar dimension, and bend it there to an angle of no less than 70 degrees. Now with the bend lying flat on the face of the anvil, draw out a thin, narrow scarf with a small ball peen hammer, not any wider than the thickness of the metal. The scarf may be drawn also by holding the outer portion of the bend on a sharp corner of the anvil and by drawing with overhanging blows. This scarf is shown in the upper view of Fig. 97 as it should appear.

The butterfly scarf should now be formed on the opposite side from the one just finished, by holding each side of the end at an angle of about 45 degrees on the edge of the anvil; this scarf may be drawn with overhanging blows. The extreme end should also be drawn thin in a similar manner, while it is held at a right angle with the edge of the anvil. All outer edges of this scarf should be thin and sharp.

Bend the metal into a circle and place the scarfs in position, as shown at C, having all edges overlapping slightly and hammered down into close contact. Heat the work for welding, observing the precaution given in the explanation of the former eye. In welding, deliver the first few blows uprightly on each side, then weld the edges of the scarfs with the ball of the hammer. A few careful experiments with these scarfs will show what is required, and with practice no more labor will be needed than is required for the previous eye. The finished product will be more substantial and presentable.

D, Fig. 98, is generally called a ship-smith eye, because it is commonly used in ship work where strength is essential. Special swages, convex lengthwise, are usually provided for shaping the concave curves where they are formed and welded. The eye should be circular between the places indicated by f in sketch D, and the lines from f to where it is welded should be as nearly straight as possible, to increase the strength.

In estimating the material, take two thirds of the length for a ring of the required diameter, and add to that the proper allowance for the stock which forms the portion from f to the weld, and also an amount sufficient for the scarf. This scarf is drawn similar to the one for the welded eye in Fig. 96, but it should be made convex through its smallest dimension with a top fuller, whose diameter is equal to that of the metal. This is done while the metal is held in a bottom swage of corresponding size. When the scarf is finished, bend the eye into shape and bring the scarf close up to the stem of the eye.

Heat and weld with swages; if convex swages are not obtainable, others may be used by taking care to prevent marring the curves. This eye may also be welded with a large fuller while it is held over the horn of the anvil. If the curves are severely marred, the strength of the eye is lessened.

A solid forged eye is shown at E. When eyes like this are drop-forged in special dies, as they generally are, they do not require much skill, but when made entirely by hand they require considerable experience.

In forging an eye of this kind, the volume of material needed must first be determined, making some extra allowance for the usual waste. A convenient size of material should then be selected (round is preferable) and the amount required for the eye marked off. The round stem should be drawn down to size and the part for the eye forged to a spherical shape, then flattened, punched, and enlarged to correct dimensions.

110. Calipers.—The calipers shown in Fig. 99 may be easily made from the dimensions given; ³/₄ × ¹/₈-inch stock should be used for the main piece, and ¹/₂ × ¹/₈-inch stock for the legs.

111. Stock Calculation for Bending.—In the expansion and contraction of metals during the operation of bending, there is a fixed line, where the metal is left undisturbed; in other words, where it is not increased or decreased in length. So all measurements taken to determine the length of material required for producing any bent shapes should be taken from that fixed or undisturbed location, in order to attain accurate results.

All materials which have a symmetrical cross section, such as round, square, octagonal, oval, or oblong, have the above line at their true centers, no matter which way they are bent. While the metal remains undisturbed at the center of any of the above sections, the rest of it undergoes a change; the inner portion, in the direction of bending, will contract and become thicker, and the outer portion will expand and become thinner.

Other conditions arise, however, to modify these rules. If the heat is unevenly distributed, or if the stock is not of a uniform thickness, the results will not be exactly as estimated. When a heavy ring is formed of oblong material and bent through its larger diameter, as shown in sketch A, Fig. 100, and the product is to be finished to a uniform thickness, the expansion of the outer portion will make it necessary to use somewhat thicker material, to provide for the decrease of metal which will take place. The inner half, then too thick, could be reduced to the required size, but this operation always alters natural conditions of bending, and changes the general results. These conditions are not very noticeable and do not require special attention when small-sized materials are operated upon, but they must be observed when large oblong or square stock is formed into a ring requiring exact dimensions.

In all cases of this kind, the required length must be established from the undisturbed center and the ends cut at an angle of 85 degrees. If the material is to be welded, it should be scarfed on opposite sides and lapped when bent.

When hoops or bands of flat or oblong material are bent, scarfed, and welded through the small diameter, then both scarfs should be formed on the same side while straight, and bent as shown at B, Fig. 100; the scarfs then will fit more readily than if they were formed on opposite sides. Sometimes, in instances of this kind, only one end is scarfed, and the piece is bent in a similar manner, with the unscarfed end on the outside and just lapping enough to cover the heel of the inner scarf.

Another form of ring requiring a calculation of the area as well as of the length is one of a wedge-shaped section, as shown at C, Fig. 100. Here the area of the required section is found and the material supplied with the proper thickness and area. The length also must be computed, then cut, scarfed, and welded, as previously explained; after this the ring may be drawn to the form desired.

The circumference of a circle may be found by multiplying its diameter by 3.1416 (p). (See tables, pages 205-206.) For rings or bands the length of the center line, c, Fig. 100, should be found. Example: If a equals 5 inches and b equals 2 inches, c will equal 7 inches, and the length of stock for the ring will be 7 × 3.1416 = 21.991 inches,—practically 22 inches. 3¹/₇ may be used for the value of p instead of 3.1416.

Questions for Review