PLAN ANGLE WITH SECTION ANGLES
| 140° | 79.5° | 69° | 58° |
| 120° | 78.5 | 67 | 55 |
| 100° | 77 | 63.5 | 49.5 |
| 90° | 76 | 61 | 45 |
| 70° | 72.5 | 53.5 | 29 |
| WILL GIVE ——— CUTTING EDGES | |||
| 80° | 70° | 60° | |
The graver will again serve to illustrate the use of this table; for although only one edge is employed at the same time in hand turning, it belongs properly to the double edged class. This will be very apparent if a graver is held point upwards side by side with a point tool, and the dotted lines are added in [Fig. 8], to make the similarity of form more evident. Now Holtzapffel has said of the graver when employed for its original purpose of engraving, that "no instrument works more perfectly," pointing out that, while both the edges are engaged in cutting the same shaving, both the lower faces of the edges are respectively inclined at the smallest possible angle from the sides of the V-shaped groove. [Fig. 10] has already been used to illustrate the best position of the slide-rest tool, and if the illustration be turned round until the letters Q, R, read horizontally, and this line be taken to represent a flat surface with the graver acting upon it, it will be seen that the shaving is removed in exactly the same manner in both cases; the only difference being that the section of the shaving is triangular in one case and rectangular in the other. But so far as the tool is concerned the action is identical in each case, thus proving that every point tool may be so made and placed as to merit Holtzapffel's eulogium on the graver, and that this simple tool is in fact the type of all double-edged tools.
The graver being made from a square bar has of course a plan angle of 90°, and using it to illustrate the table, we will suppose that it is desired to give it two cutting edges of 60° each. Referring to 90° under the heading of "plan angle," 45° will be found on this line in the column over "cutting edge" 60°; denoting that the section angle of the point, i.e., the slope at which the graver is ground, must be 45° to give the desired edges. In the same way, if the section angle were 61° the cutting edges would be 70°. But taking the plan angle of 120°, the table shows that this would produce the same cutting edges of 60° with the larger section of 55°; and from this we have the important rule that, in obtaining cutting edges of any given degree of acuteness the larger the plan angle is made, the larger also may be the section angle. Thus pointed tools though constructed on the principle of the graver are an improvement on it in its simple form; for by making both plan and section angles as wide as possible, it is obvious that the strength and durability of the point will be much increased. It is, therefore, always better to give slide-rest tools a large plan angle, as in [Fig. 12]; and plan 120°, with section 55°, will be found a very useful and durable tool for surfacing purposes with wrought iron. When there are rectangular corners to cut in and out of, of course the plan angle cannot be more than 90°, and then it is well to sacrifice a little of the acuteness, as the section of 45° makes the point rather too weak. It is also worthy of remark as a mathematical fact, that unless the plan angle exceed 60°, it is impossible to obtain two cutting edges of that degree of acuteness; and in any case, such a plan angle would be radically bad, because it could not be used on the double-edged principle without undercutting the shaving. It is somewhat remarkable, in connection with this point, that while Holtzapffel, vol. ii. p. 536, recommends prismatic cutters, he should add a footnote which indirectly but most conclusively corroborates Prof. Willis' condemnation of that particular form, by admitting that the proper degree of acuteness cannot be given to both edges.
As the practical result of a circular edge is to cut in two opposite directions,—the edge passing gradually from one to the other,—so round-nosed tools belong properly to the double-edged class, and are open to great objections unless carefully formed on this principle.
Illustration No. 5.(13, 14)
This is illustrated in [Fig. 13], representing an oblique section of a round bar; and supposing the section to be made at an angle of 45°, it is obvious that the highest part of the edge at S will be exactly of this angle, while the lower point at T will be 135°, and the side points at U and V will be 90° each. Thus, between the point S and the points U and V on each side respectively, the edge will gradually pass through a range of 45°, consequently no two adjacent points on the same side will be of the same angle, and the highest point S may be too acute to stand while the lowest, U or V, is too blunt to cut.
Whenever, therefore, it is intended to round the nose of the tool, it should be first formed as a double-edged point tool, with a section angle agreeing as nearly as practicable with the intended degree of acuteness in the edge, so as to secure the highest points from being too weak, and the table given above will show what plan angle must be used, in combination with this section, to secure any part from being too blunt.