Chapter XXV: Vice Work (2)

In order to accomplish this stretching as rapidly as possible it is necessary to use a light hammer, with sufficient force to be expended in condensing the metal at its surface, and to so form the hammer that it shall expend its force upon the work with a dead blow, that is, with as little rebound as possible. These results are best accomplished with a ball pened hammer, such as shown in Fig. 2108 and weighing about 1/2 lb. The blows should fall dead; that is, the hammer should fall, to a great extent, by its own weight, the number rather than the force of the blows being depended upon; hence, the hammer marks will not be deep. This is of especial importance when pening has to be performed upon finished work, because, if the marks sink deeply, proportionately more grinding or filing is required to efface them; and for this reason the force of the blows should be as near equal as possible. Another and a more important reason, however, is that the effect of the pening does not penetrate deeply; and if much of the pened surface is removed, the effects of the pening will be also removed. The work should not be rested upon metal, but upon wood.

The following are examples of pening. Fig. 2142 represents a shaft bent as shown, the arms being too wide at A, which may be corrected by pening at B. If the error was in the arms themselves and not in the stem, the side faces of the arms would require to be pened. Thus in Fig. 2143 the distance A is too short, and the pening must be at B C.

Fig. 2144 represents a strap requiring to be closed across A, the pening being at C or D. But as pening at D would bend the crown and unpair the bed of the brasses, it is preferable to pene at C. In either case the jaws will close as denoted by the dotted lines.

Fig. 2145 represents another common form of connecting rod strap, and in this case the pening may be most quickly and effectively done at the crown as denoted by the dots; and as this would alter the inside curve, the brass or box fitting into it must be refitted. In case the pening should be overdone it is better to modify it by filing away some of the pened surface.

Cast iron is more rapidly affected by pening than either wrought iron or steel. One of the most useful applications of pening is in the case of moulding patterns, which in time may become warped from the rapping of the pattern in the mould, and this warping may be corrected by judicious pening, or suppose that a number of plates, such as represented in Fig. 2146, having been cast, it is found that the ends of the tongues A B curl up when cooling in the mould, then the tongues may be pened as at C D, throwing them down to the requisite amount, and thus moulding the pattern to accommodate the curling in cooling.

The riveting usually performed by the machinist is generally upon cold metal. The blows in this case should fall dead and the riveting be performed with a view to stretching the metal uniformly and evenly over the surface to be riveted.

An excellent example of cold riveting is given in the crank pin P in Figs. 2147 and 2148. C is the crank (both being shown in section). The end of the pin should be recessed as shown at A, so that it may be the more readily riveted outward to fill the countersink shown in the crank at B, B. The crank-pin is rested upon a piece of copper D interposed between it and the iron block E to prevent damage to the finished face of the crank-pin.

The riveting blows should be given with a ball-faced hammer, and delivered with a view to stretch the whole end face of the crank-pin evenly. Otherwise the riveted surface will be apt to split as shown. This usually occurs from not riveting the area at and near the circumference sufficiently, although it may occur from riveting that part of the area too much. The line of travel of the hammer should not be directly vertical, but somewhat lateral in a direction from the centre towards the circumference. If the countersink is a deep one, it is desirable to leave the crank-pin sufficiently too long, so that after the riveting has proceeded some time the surface of the metal which has become condensed and crystallized from the direct impact of the hammer blows, may be chipped away, leaving a surface that is swollen by the riveting without being so much condensed. This enables a much greater spreading of the metal without splitting it.

If in this class of work the riveted piece (as the crank-pin) is not driven in very tight before riveting, the riveting blows will be apt to jar the pin back. Hence, it is necessary to occasionally drive the pin home. The riveting should proceed equally all over, as if one side be riveted in advance of the other it tends to throw the pin out of true. When, however, the riveting begins to bed the pin, four equidistant places may be riveted home in advance so as to bring the pin home and hold it firmly.

THE CHISEL.--The machinist's cold chisel is made from the two forms of steel shown in Figs. 2149, 2150, and 2151, and of these the former is preferable because it has two broad flats diametrally opposite and these form a guide to the eye in holding the chisel on the grindstone, and aid in grinding the facets that form the cutting edge true. Furthermore, as the cutting edge is in the same plane as these flats they serve as a guide to denote when the chisel edge lies parallel to the work surface, which is necessary to produce true and smooth chipping.

The width of the chisel may be made greater, as in Figs. 2152 and 2153, for brass or cast-iron work than for wrought iron or steel for the following reasons. On account of the toughness and hardness of wrought iron and steel the full force of a 1-3/4 lb. hammer, having a handle 13 inches long, may be used on a chisel about 7/8 inch wide without danger of causing the metal to break out below the chipping line, but if such a chisel be used with full force blows upon cast iron or brass the metal is apt to break out in front of the chisel, the line of fracture often passing below the level it is intended to chip down to. Hence if a narrow chisel is used lighter blows must be delivered. But by using a broader chisel the force of the blow is distributed over a longer length of cutting edge, and full force blows may be used without danger of breaking out the metal.

The cutting end of the chisel should be kept thin, as in that case it cuts both easier and smoother. The total length of a chisel should not when new exceed 8 inches, for if made longer it is not suitable for heavy or smooth chipping, as it will bend and spring under heavy blows, and cannot be held steadily. The forged part should not exceed about 2-1/2 or 3 inches in length, as a long taper greatly conduces to springiness, whereas solidity is of great importance both to rapid and smooth work. The facets forming the cutting edge should be straight in their widths, as at B in Fig. 2154, and not rounded as at A, so that the face next to the work may form a guide in holding the chisel at the proper angle to maintain the depth of the cut. This angle depends upon the nature of the material to be cut; the facets forming an angle one to the other of about 65° for cast steel and about 50° for gun metal or brass. The more acute these angles the nearer the body of the chisel lies parallel with the work and the more effective the hammer blows. Thus in Fig. 2155 chisel C is the position of the chisel for wrought iron, and position D is for steel. The angles should always be made, therefore, as acute as the hardness of the material will permit. If they are too acute the cutting edge will be apt to bend in its length, while if not sufficiently acute they will not cut keen enough; hence the object is to make them as acute as possible without causing the cutting edge to bend in its length. For copper and other soft metals the angle may be about 30° or 35°, the chisel end being kept thin so that it may not become wedged between the work and the chipping, which will bend but little, and is, therefore, apt to grip the wedge end of the chisel. The cutting edge should be slightly rounded in its length, which will strengthen it and also enable a fine finishing clip to be taken off, as in Fig. 2156, the width of the chip not extending fully across the chisel width so that the corners are not under duty and are not, therefore, liable to break, or dig in and prevent smooth chipping. In some practice the edge is made straight in its length, as shown in Fig. 2149, which is permissible in heavy chipping when a cape chisel has been used, but in any event an edge rounded in its length is preferable. If the edge is hollow in its length, as shown in Fig. 2157, and magnified in Fig. 2158, the chip acts as a wedge to force the corners outwards as denoted by the arrows, causing them to break under a heavy cut, and, furthermore, a smooth cut cannot be taken when the corners of the chisel meet the work surface.

If the facets are ground under on one side, those on the other, as in Fig. 2159, the edge will not be parallel with the flats of the chisel, so that in holding it the flats will not form a guide to determine when the edge lies parallel to the work surface as it should do. The edge should also be at a right angle to the length of chisel, as denoted by the lines, as in Fig. 2160, for if not at a right angle the chisel will be apt to move sideways after each blow, and cannot be held steadily.

The chisel should be held as close to its head as possible, so that the hand will steady the head as much as possible, and should be pushed forward firmly and steadily to its cut, which will greatly facilitate rapid and smooth chipping, and for wrought iron and copper it is found better to occasionally moisten the chisel with oil or water, the former being preferable.

Messrs Tangye, of Birmingham, have introduced the employment of chisel holders, such as shown in Fig. 2161, the object being to fit to each holder a number of short pieces of steel for chisels so that a number can be ground or forged at one time; obviously chisels of different shapes require different forms of handle.

When a heavy cut is to be taken the cape (Fig. 2162) chisel is used, first to carry through grooves or channels, such as shown in Fig. 2176 at A, B, and C, the distance apart of these grooves being slightly less than the width of the flat chisel, whose cut is shown partly carried across at D in the figure. The width of a cape chisel should gradually decrease from A to B in Fig. 2163, so that its side will be free in the groove it cuts, and the chisel head will be free to be moved sideways, and the direction of the groove may be governed thereby. If the chisel end be made parallel, as at C in Fig. 2164, it will have no play in the groove and the head cannot be moved; hence if the groove is started out of line, as it is apt to be, it will continue so.

The round-nosed chisel, Figs. 2165 and 2166, may be straight from H nearly to the point G, but should be bevelled at and near G, so that the chisel head may be raised or lowered to govern the depth of the cut. Its round nose should also be wider than the metal higher up, so that the chisel head may be moved sideways to govern the direction of the cut as in the cape chisel. The cow mouth chisel, Figs. 2167 and 2168, should be bevelled from G to the point to enable the governing of the depth of the cut, and should be of greater curvature than the corner it is to cut out, so that its corners cannot wedge in the work.

The oil groove chisel, Figs. 2169 and 2170, should be wider at the cutting edge than at A for reasons already stated, and of less curvature than the bore of the brass or bearing it is to cut the oil groove in.

The diamond point chisel, Figs. 2171 and 2172, may be made in two ways. First, as in Figs. 2173 and 2174, for shallow holes, and as in Figs. 2171 and 2172 for deep ones. In shallow holes the chisel can be leaned over, as in Fig. 2176 at _y_, whereas in deep ones it must be held straight so that the chisel body may not meet the other side of the hole, slot, or keyway. The form shown in Fig. 2172 is the strongest, because its point is brought into line with the body of the steel, as shown by the line Q. The side chisel, Fig. 2175, for cutting out the sides of keyways or slots, should be bevelled from W to the cutting edge for the reasons already given, and straight from W to V, the line V W projecting slightly above or beyond the body U. An application of the cow mouth chisel is shown at L, and one of the side chisel is shown at Z in Fig. 2176. All these chisels are tempered to a blue color.

The chisel that is driven by hammer blows may be said to be to some extent a connecting link between the hammer and the cutting tool, the main difference being that the chisel moves to the work, while the work generally moves to the cutting tool. In many stone-dressing tools the chisel and hammer are combined, inasmuch as that the end of the hammer is chisel shaped; an example of this kind of tool being given in the pick that flour millers use to dress their grinding stones. On the other hand we may show the connection between the chisel and the cutting tool by the fact that the wood-worker uses the chisel by driving it with a mallet, and also by using it for a cutting tool for work driven in the lathe. Indeed, we may take one of these carpenter's chisels and fasten it to the revolving shaft of a wood-planing machine, and it becomes a planing knife; or we may put it into a carpenter's hand plane, and by pushing it to the work it becomes a plane blade. In each case it is simply a wedge whose end is made more or less acute so as to make it as sharp as possible, while still retaining strength enough to sever the material it is to operate upon.

In whatever form we may apply this wedge, there are certain well-defined mechanical principles that govern its use. Thus when we employ it as a hand tool its direction of motion, under hammer blows, is governed by the inclination of the face which meets the strongest side of the work, while it is the weakest side of the material that moves the most to admit the wedge and therefore becomes the chip, cutting, or shaving. In Fig. 2177, for example, we have the carpenter's chisel operating at A and B to cut out a recess or mortise, and it is seen that so long as the face of the chisel that is next to the work is placed level with the straight surface of the work the depth of cut will be equal; or in other words, the line of motion of the chisel is that of the chisel face that lies against the work. At C and D is a chisel with, in the one instance, the straight, and in the other the bevelled face toward the work surface. In both cases the cut would gradually deepen because the lower surface of the chisel is not parallel to the face of the work.

If now we consider the extreme cutting edge of chisel or wedge-shaped tools it will readily occur that but for the metal behind this fine edge the shaving or cutting would come off in a straight ribbon, and that the bend or curl that the cutting assumes increases with the angle of the face of the wedge that meets the cutting, shaving, or chip.

I may, for example, take a piece of lead, and with a penknife held as at A, Fig. 2178, cut off a curl bent to a large curve, but if I hold the same knife as at B it will cause the shaving to curl up more. Now it has taken some power to effect this extra bending or curling, and it is therefore desirable to avoid it as far as possible. For the purpose of distinction we may call that face of the chisel which meets the shaving the top face, and that which lies next to the main body of the work the bottom face. Now at whatever angle either face of the chisel may be to the other, and in whatever way we present the chisel to the work, the strength of the cutting edge depends upon the angle of the bottom face to the line of motion of the chisel, and this is a principle that applies to all tools embodying the wedge principle, whether they are moved by a machine or by hand.

Thus, in Fig. 2179 we have placed the bottom face at an angle of 80° to the line of tool motion, which is denoted by the arrow, and we at once perceive its weakness. If the angle of the top face to the line of tool motion is determined upon, we may therefore obtain the strongest cutting edge in a hand-moved tool by causing the bottom angle to lie flat upon the work surface.

But in tools driven by power, and therefore accurately guided in their line of motion, it is preferable to let the bottom face clear the work surface, save at the extreme cutting edge. The front face of the wedge or tool is that which mainly determines its keenness, as may be seen from Fig. 2180, in which we have the wedge or tool differently placed with relation to the work, that in position A obviously being the keenest and less liable to break from the strain of the cutting process.

If we now turn our attention to that class of chisel or wedge-shaped tools in which the cutting edge is not a straight line, but may be stepped or curved--as, for example, the carpenter's plane blade--we shall find that so long as the blade stands at a right angle to the surface it is operating upon, as in Fig. 2183 at B, the shape of surface it cuts will exactly correspond to the shape of its cutting edge; but so soon as the tool is inclined to its line of motion its cutting edge will, if curved, produce a different degree of curvature on the work.

Suppose, for instance, that we have in the figure a piece of moulding M and a plane blade B, and the length of the cutting edge is denoted by A, Fig. 2182; now suppose that the blade is inclined to its line of motion (as in the case of carpenters' planes) and stands at C, Fig. 2183: we then find that the cutting edge must extend to the length or depth D, and it is plain that the depth of the curve on the moulding is less than the depth of the cutting edge that produces it; the radius E being less than of D, so that if we place the cutter C upright on the moulding it will appear as shown in Fig. 2181. If, therefore, we are required to make a blade that will produce a given depth of moulding when moved in a straight line and presented at a given angle to the work, we must find out what shape the blade must be to produce the given shape of moulding, which we may do as follows:

In Fig. 2184 let A be a section of the moulding, and if the blade or knife is to stand perpendicular, as shown at B, Fig. 2183, and if it is moved in a straight line in the direction of the length of the work, then its shape would necessarily be that shown at B, Fig. 2184, or merely the reverse of A. In the position mentioned it could be used only as a sweep applicable to some few uses, but not adapted to cutting. To become a cutting tool it must be inclined and stand at some angle of less than 90° to its line of motion.

Thus in Fig. 2185 D B E represents the bottom of the moulding and line of motion of the cutter, and A B the cutter perpendicular to it, the highest point of the cutting edge, as _c_ of Fig. 2184, being at _c_, Fig. 2185. The height or thickness of the moulding cut would be the space between the lines E B D and _e_ _c_ _f_, but the cutter assuming the position B C at an angle of 30° from A B, the point _c_ is brought to _d_; consequently the highest line of the moulding would now be _g_ _d_ _h_, and its thickness less. This is further exhibited in Fig. 2186, where _a_ represents the original depth section of Fig. 2184 that would be formed by knife B of Fig. 2184 when standing perpendicular; and G shows the depth with the same knife when placed as B C, Fig. 2185, or at 30° inclination, and H shows the depth that would be cut with the same knife or cutter at 45°. It is now evident that every change in the inclination of the same cutter would effect a change in the shape of moulding which it cuts, and to produce a given style of moulding the shape of the cutter must be decided by its inclination, or the angle at which it is used.

The method of projecting a given section of moulding in order to exhibit the form that the curve of the opening should assume on the face of the knife, is shown in Fig. 2187. Upon a horizontal line A B C D draw a section of the required style of moulding, as shown at A E B. To the right of this draw a line, as F C, to meet the base line A B C D, and as F C represents the cutter, it must stand at the same angle that the proposed cutter is to have--in this particular example 30° from the perpendicular. From the highest point of the section A E B draw a horizontal line E G, meeting F C in G. From points G and C draw lines, as C J and G H, of any convenient length, at right angles to F C. At any distance from G H draw K L parallel to G H, and upon K L trace the section of moulding A E B, as K M L. Draw lines from the extreme edges K and L of K M L, as K N, L J, perpendicular to K L, cutting G H and meeting C J at N and J. E G being parallel to A B C D, G will be the point on the cutter where the top E of the moulding will come on the highest point of the cutting edge, and C G will be the entire length of cutting edge or height of opening measured on the face of the cutter F C. C J being drawn from the lowest point C of the cutter and G H being drawn from G, the highest cutting point, both lines at right angles to G C, then their distance from each other, as P O, must obviously represent the extreme height of opening in the cutter in its new position or front view, and K L, representing the width of moulding transferred to N J by the parallel lines K N and L J, will show the width of opening in the cutter. Having now the height and width, it only remains to project an indefinite number of points and trace the curve through them. Divide A B into a number of parts, and to avoid confusion mark the points of division thus obtained upon A B--1, 2, 3, 4, &c. Divide K L in an exactly similar manner and into the same number of parts, and mark the divisions I., II., III., IV., &c. Erect perpendiculars from points 1, 2, 3, 4, &c., meeting the curve A E B, and from the points thus found on A E B draw horizontal lines to F C; from the termini of these horizontals on F C draw the remaining lines parallel to and between G H and C J. From the divisions _i._, _ii._, _iii._, _iv._, &c., on K L, let drop the perpendiculars, cutting the other series of lines at right angles. A point of the curve will then be at the intersection of the line from 1 on A B, with line I on K L; another at the intersection of the line originating at 2 with that from II, and so on, and the proper curve is found by tracing from N through the intersections to P, and from P to J. Then K N being one side of the cutter and L J the other, N P J is the curve that the opening or cutting edges must have to cut the profile A E B, with the cutter set at F C, or 30°.

The same method is shown in Fig. 2188, except that in this case, instead of dividing A B and K L, the divisions are made directly on the peripheries A 6 B and K VI. L by stepping round with the dividers. The cutter F C is shown in this case at an angle of 45°, in order that the change in form which the curve assumes with the cutter at different angles may be clearly seen by comparing the curve N P J of Fig. 2187 with the same in Fig. 2188. The two figures are similar in other respects, and as the lettering is the same on each, the description of Fig. 2187 will apply equally to Fig. 2188.

There remains one more case of cutters moving in right lines, and that is where, besides having an inclination backward, as at F C, Fig. 2187, making a vertical angle to the line of motion, they are placed at an angle across the guiding piece also, or "skewing," thus making an angle to the line of motion on a horizontal plane as well as on a vertical one. Thus, suppose an ordinary carpenter's plane to have the cutter or "iron" turned partly round and placed so that the cutting edge, instead of lying at a right angle across the body, crosses it at some other angle. Fig. 2189 represents an ordinary carpenter's plane with the blade so placed. Here the edge, or rather side, D B, of the blade inclines back at an angle, as A B D, which is 45° in this case, to the perpendicular line A B on the side of the plane. For convenience call A B D the vertical angle. The lower or cutting edge E B of the blade also crosses the bottom of the plane at an angle E B C--30° in this instance--to a line B C, crossing the bottom at right angles. Now, it is evident that this latter angle E B C will influence the form of the cutter, if, instead of being a flat plane, as represented for clearness in Fig. 2189, it had a cutting edge of curved outline for cutting mouldings or similar work. But in either case the angle that D B or one side of the blade makes to E B, or the cutting edge--that is, the angle D B E--must be found in order to cut off the blank for the cutter or knife at the right "slant."

The method given in Figs. 2187 and 2188 of determining the form of cutter to produce a moulding of given profile now undergoes a modification where there are two angles to be taken into consideration instead of one. As an example, suppose a cutter is required that is to be fixed in such a position in its carrier or block that the handle A B D, or "vertical angle," of Fig. 2189 is, say, 45°, and the angle E B C, or "horizontal angle," of Fig. 2189 shall be 30°. Required the angle at which the bottom of the blank for the cutter must be cut off; or the angle that the side D B and lower edge B E of Fig. 2189 would make to each other, measured on the face of the cutter, and required the outline of cutting edge to be traced on the face of cutter to cut the section of moulding A E B, Fig. 2190: draw a horizontal line, as A B C D, and erect a perpendicular, as C R. From C draw C F, making an angle to C R equal to the "vertical angle," or angle A B D, Fig. 2189, which is 45° in this case. Draw a profile of the required moulding, as A E B, with its back A B coincident to the horizontal line A B C D. Draw a horizontal line from the highest point of the profile, as E, to meet F C in G. Draw parallel lines C J and G H, from C and G respectively, of any convenient length and making right angles to F C. At right angles to G H and C J, and parallel to F C, draw K H J to represent one side or edge of the cutter, but the angle of the lower end or angle D B E of Fig. 2189 must now be determined; to do this, draw an indefinite horizontal line, A B C, Fig. 2191, and from any point, as B, drop a perpendicular B D; now, from B set off on A B C the distance C _b_ of Fig. 2190, obtaining point E, and from E extend a perpendicular above and below A B C, as F E H. From E on E F set off distance G _b_ of Fig. 2190, obtaining J on E F. From B draw a line, making the same angle to B D that the angle E B C is in Fig. 2189, or 30° in this case, and cutting E H in K. Set off distance E K from E on A C, obtaining L; draw L J. Now, on Fig. 2190, with centre at H, and radius L J of Fig. 2191, describe arc _w_ _x_, and from J as centre, on Fig. 2190, and B K of Fig. 2191 as radius, describe arc _y_ _z_. Through the intersection _v_ of arcs _y_ _z_ and _w_ _x_, J L M must be drawn, making the proper angle to the side J H K of the cutter; this angle is 69° in this case, as found by construction. From H draw H N parallel to J L, and from H draw H O at the same angle to H N that B K is to B D, Fig. 2191, or angle E B C, Fig. 2189. Place a duplicate of A E B, with its base coincident to H O and corner A at H, as H P R. From R draw R N at right angles to H R and cutting H N at N; through N draw S N L parallel to K H J. Then while K H J represents one edge of the cutter, S N L will be the other, and J L the cutting edge before the opening is cut out. Divide the curves E B and P R similarly, obtaining points 1, 2, 3, &c., and I., II., III., &c., respectively. From points 1, 2, 3, &c., lines are to be drawn parallel to E G, meeting G C, continued from G C parallel to G H, and meeting H J, and from H J parallel to H N, meeting N L. From points I., II., III., &c., lines are to be drawn perpendicular to H R, meeting H N and continued from H N, parallel to H J, to J L, thus intersecting the first series. Lines from points 1, 2, 3, &c., then determine the height of different points of the curve, and those from I., II., III., &c., their location laterally; hence, by tracing through the intersections of 1 with I., 2 with II., &c., the curve H T L is obtained. The two outside lines K H J and S N L may now represent the edges of a piece of steel of which the cutter is to be made, and H T L will be the contour of cutting edge that must be given it in order that when, fixed for use at the angles named, it will form the required moulding A E B.

If the chisel, knife, or cutter revolves in a circle, instead of in a right or straight line, the problem is again different, and the shape of cutting edge necessary to produce a given shape of moulding is again altered. Let Fig. 2192, for example, represent the bar or head of a wood moulding machine, the bar or head revolving in the direction of the arrow, and the moulding being moved beneath it in a straight line endways as denoted by the arrow at N.

In order that the nut that holds the cutter to the head may clear the top of the moulding the highest cutting point of the cutter must not come nearer to the corner of the head than 1/4 inch. This is shown in the end view of a 2-1/2 inch cutter head in Fig. 2193, the circle B representing the path of revolution of the nut. In larger heads the nut will clear better.

Now we may consider that the cutter simply revolves about a circle whose diameter is the largest that can be described on the end of the square bar that drives it.

If, for instance, we look at the end of the bar as it is presented in Fig. 2195, we see that the circle just fills the square, and that if we cut off all four corners, leaving the bar round, as denoted by the circle, the chisel will revolve in the same path as before. Now suppose we place beneath the revolving chisel a piece of square timber, and raise this timber while holding it horizontally, as would be done by raising the work table. It will cut the work to the shape shown in the two views in the figure, enabling us to observe the important point that the only part of the work that the chisel has cut to its finished shape is that which lies on the line A A. This line passes through the axis on which the bar and cutter revolve, and represents the line of motion of the work in feeding upward to the chisel.

If now we were to move the work endways upon the table, we should simply cause the moulding to be finished to shape as it passes the line A; because all the cutting is done before and up to the time that the chisel edge reaches this line; or in other words, each part of the chisel edge begins to cut as soon as it meets the moulding, and ceases to cut as soon as it reaches this line. We may now draw this circle and put on it a chisel in two positions, one at the time its lowest cutting point is crossing the line A and the other at the time the highest point on its cutting edge is passing the line, these positions being marked 1 and 2 in Fig. 2196; the depth of moulding to be cut being shown at S. Now, since the chisel revolves on the centre of the circle, the path of motion on its highest cutting point C will be as shown by the circle B, and that of the lowest point or end E of its cutting edge will be that of the circle D, while the depth of moulding it will cut is the distance between C and E, measured along the line A A, this depth corresponding to depth shown at S.

Clearly when the chisel has arrived at position 2, the moulding will be finished to shape, and it is therefore plain that it takes a length of cutter-edge from C to F to cut a moulding whose depth is S, or what is the same thing, C E.

But to solve the question in this way, we require for every different depth of moulding to make such a sketch, and the square bar that drives the chisel is made in various sizes, each different size again altering the length or depth of chisel edge necessary for a given depth of moulding.

But we may carry the solution forward to the greatest simplicity for each size of square bar, and for any depth of moulding that can be dressed on that size of bar, by the following means:--In Fig. 2197 we have the circle and the line A as before; the depth from C to E being the greatest depth of moulding to which the square bar is intended to drive the chisels; while point C is the nearest point to the square bar at which the top of the moulding must be placed. Line _a_ represents a chisel cutting at its highest point; line _b_ a chisel cutting the moulding to final shape at 1/4 inch below C, on the line A; line _c_ a chisel cutting the moulding to final shape at a distance of 1/2 inch below point C and measured on the line A; lines _d_, _e_, _f_, _g_, _h_, and _i_ represent similar chisel positions, the last meeting the point E, which is the lowest point at which the chisel will cut. Suppose, now, we set a pair of compasses one point at the centre A of the circle, and strike the arc _j_; this arc will represent the path of motion of that part of the chisel edge that would finish the moulding to shape at C; similarly arc _k_ represents the path of motion of that part of the chisel edge that cuts the moulding to final shape on the line A, and at a distance of 1/4 inch below C, and so on until we come to arc _r_, which represents the path of motion of the end of the chisel. All these arcs are carried to meet the first chisel position C _a_, and from these points of intersection with this line C _a_ we mark lines representing those on a common measuring rule. The first of these from C we mark 1/4, the next 1/2, the next 3/4, and so on to 2, these denoting the measurement or depth of chisel necessary to cut the corresponding depth of moulding. If, for example, we are asked to set a pair of compasses to the depth of cutting edge necessary to cut a moulding that is an inch deep, all we do is to set one leg of the compasses at C, and the other at line 1 on the line C _a_; or if the moulding is to be 2 inches deep, we set the compasses from C to 2 on line C _a_. We have here, in fact, constructed a graduated scale that is destined to be found among the tools of every workman who forms moulding cutters, and if we examine it we shall find that the line that is marked 1/4 inch from C is not 1/4 inch but about 5/16 inch; its distance from C being the depth of chisel edge necessary to cut a moulding that is 1/4 inch deep.

Again, the line marked 1 measures 1-3/16 inch from C, because it requires a chisel edge 1-3/16 deep to cut a moulding that is one inch deep. But if we measure from _c_ to the line marked 2 we find that it is 2-1/4 inches from C, and since it represents a chisel that will cut a moulding two inches deep, we observe that the deeper the moulding is the nearer the depth of cutting edge is to the depth of moulding it will produce. This occurs because the longer the chisel the more nearly it stands parallel to the line A, at the time when its point is crossing the line A. Thus, line _i_ is more nearly parallel to A than line _a_ is, and our scale has taken this into account, for it has no two lines equally spaced; thus, while that marked 1/4 is 5/16 inch distant from C, that marked 1/2 is less than 5/16 inch distant from that marked 1/4, and this continues so that the line marked 2 is but very little more than 1/4 inch from that marked 1-3/4. Having constructed such a scale we may rub out the circle, the arcs, the line A, and all the lines except the line from C to _a_ and its graduations, and we have a permanent scale for any kind of moulding that can be brought to us.

If, for example, the moulding has the four steps or members _s_, _t_, _u_, _v_, in the figure, each 1/2 inch deep, then we get the depth of cutter edge for the first member _s_ on our scale, by measuring from _c_ to the line 1/2 on line C _a_. Now the next member _t_ extends from 1/2 to 1 on the moulding, and we get length of cutter edge necessary to produce it from 1/2 to 1 on the scale. Member _u_ on the moulding extends from 1 to 1-3/4; that is to say, its highest point is 1 inch and its lowest 1-3/4 inch from the top of the moulding, and we get the length for this member on a scale from the 1 to the 1-3/4; and so on for any number of members.

After the depth of cutting edge for each member has thus been found, it remains to find the exact curve of cutting edge for each step, and, in doing this, the same scale may be used, saving much labor in this part also of the process, especially where a new piece of moulding must be inserted to repair part of an old piece that needs renewal in places only, as is often the case in railroad cars.

In Fig. 2197A we have a scale or rule constructed upon the foregoing principles, but marked to sixteenths, and it may now be shown that the same scale may be used in finding the actual curve as well as the depth of cutter edge necessary to produce the moulding of any member of it. Let the lower curves _s_, _t_, for example, represent the moulding to be produced, and the upper outline represent the blank piece of steel of which the cutter is to be made, the edges C, D being placed in line one with the other. We may then draw across both the moulding and the steel, lines such as E E, F F, G G, H H, I I, J J, all these lines being parallel to the edges C, D. To get the total depth of cutter edge for the moulding we measure with a common measuring rule the total height of the moulding, and supposing it to measure an inch, we set a pair of compasses to an inch on our cutter scale, and with them mark from the base _m_ of the steel, the line P giving total depth of cutter edge. We next measure with a common rule the depth of member _s_ of the moulding, and as it measures 1/2 inch we set the compasses to the 1/2 on the cutter scale, and with these compasses mark from line _m_ line B, showing the depth of member _s_. In order to find the exact curve for each member, we have first to find a number of points in the curve and then mark in the curve by hand, and it is for the purpose of finding these points that the lines E E, F F, G G, H H, I I, J J, have been drawn. These lines, it may be remembered, need not be equally spaced, but they must be parallel, and as many of them may be used as convenient, because the greater their number the more correctly the curve can be drawn.

The upper edge or base line, _m_ _m_, both of the steel and of the drawing, is that from which all measurements are to be taken in finding the points in the curve, which is done as follows: With an ordinary measuring rule we measure on the moulding and from line _m_ _m_ of the moulding as a base the length of the line F F below _m_ _m_, to the curve, which in this case measures say 5/16 inch; we then set a pair of compasses or compass calipers to the 5/16 on the cutter scale, and from base _m_ _m_ on the cutter steel, mark, on line F F, an arc, and where the arc cuts F F is one point in the curve.

Similarly we measure on the moulding, or drawing of the moulding, the length of line G G from line _m_ _m_ to the moulding curve, and find that it measures, say 7/16 inch, hence we mark from base line _m_ _m_ of the steel, on line G G, arc V, distant 7/16 according to the cutter scale. Similar measurements are taken at each vertical line of the drawing which represents the moulding, and by means of the corresponding divisions of the cutter scale, arcs are marked on the vertical lines on the cutter steel, and where the arcs cut the vertical lines are points in the curve, and through these points the curve may be drawn by hand. We may make a cutter scale from an ordinary parallel rule, marking one end to correct inches and the other end for a cutter scale. Measurements from the moulding may then be made on one end of the rule; measurements for the cutter may be taken from the other end of the rule, and the rule may be used at the same time to draw the parallel lines E E, &c. Or, as each size of cutter head requires a different cutter scale, we may make a rule out of a piece of box or other close-grained wood, say 3/4 inch square, using one side for each size of cutter head. One end of each face of this rule may be marked in correct inches and parts of an inch (the divisions being thirty-seconds of an inch), and the other end may be marked as a cutter scale, the divisions being found as described with reference to Fig. 2197.

An instrument, patented by R. Drummond, for finding the depth of cutting edge and also for finding the curves, is shown in Figs. 2198 and 2199. It consists essentially of a bar G bent at a right angle, thus making two arms. Upon one arm is a slide W (best seen in Fig. 2199) secured by a set-screw B, and having at A a pivot to carry a second bar H, which is slotted throughout its length to permit bar G to slide freely through it. Upon the other arm of G is a slide P secured by a set-screw C, and carrying a compass point E. The bar H carries an adjustable slide Z secured by a set-screw D and carrying the compass point F.

In using the instrument but three very simple operations are necessary. First, the two slides W and P are set to the numerals on the bar, which correspond to the size of the head on the moulding machine the cutter is to be used upon; thus in Fig. 2199 they are shown set to numeral 2, as they would be for a 2-inch cutter head. The instrument is next opened, its two bars occupying the position shown in Fig. 2199, and the two compass points are set to the height of the moulding or to any desired member of it, as the case may be. The bars are then opened out into the position shown in Fig. 2200, and the compass points at once give the depth of cutter edge necessary to produce the required depth of moulding.

It will be noted that the pivot A represents the centre upon which the cutter revolves, and that while the face of the bar H corresponds to the line of moulding formation answering to line A A in Fig. 2196, the face of bar G corresponds to the face C F of the cutter in Fig. 2196; hence the instrument simply represents a skeleton head and cutter, having motions corresponding to those of an actual cutter head and cutter.

THE FILE.--The file is a piece of hardened steel having teeth produced upon its surface by means of rows of chisel cuts which run more or less diagonally across its width at an angle that is varied to suit the nature of the material the file is to be used upon. The vertical inclination of the tooth depends upon the inclination of the face of the chisel with which it is cut, the two being equal, as is shown in Fig. 2201, which is an enlarged view of a chisel and some file teeth. In order that the tops of the teeth shall be sharp, and not rounded or curved, as in Fig. 2202, it is necessary that the edge of the chisel be kept sharp, an end that is greatly aided by the improved form of chisel shown in Fig. 2203. When a file possesses curved points, or caps, as they are technically termed, a few strokes upon a narrow surface will cause them to break off, reducing the depth of the teeth and causing the cuttings to clog in them. If, however, the file is used upon a broad surface these caps will remain, obviously impairing the cutting qualifications of the file, even when new, and as they soon get dulled the file loses its grip upon the work and becomes comparatively valueless.