Fig. 1845. Fig. 1846.
Fig. 1847.
The three-cutter die would in this case cut the perfectly circular form of [Fig. 1847].
Fig. 1848.
Now, suppose both of the dies to have been made or set to some certain diameter—in fact, presume them to be made by taking a ring of steel having a round hole of the required diameter, say 1 inch, and removing the metal shown by the dotted lines, [Fig. 1848], and leaving only the four cutting points in one case (and the three in the other). Then it is evident that our dies are both of the same diameter, and likewise both of the assumed diameter, or 1 inch; then it is fair to presume that the plugs or sections just cut by either one of the dies should enter a round hole of the same diameter as the dies; but it is obvious that only two, [Figs. 1840] and [1847], will do so, all the rest being considerably too large, from their irregularity of form, notwithstanding the fact that the diameter of any of those cut by four cutters is never more than that of the die, while any one of the equal radii, taken at equal distances on any of the forms cut by the three-cutter die, will not exceed the radius of the die. Now, six of the pieces being too large when referred to the standard of a round hole of the size of the die, while two are of the correct size, it is obvious that if the four-die, for example, which cut [Fig. 1846], were reduced enough to make [Fig. 1843] just enter the standard, that, [Fig. 1840], which is now just correct in size and form, would, when cut, be altogether too small. The same would be the case also with the three-cutter die.