The inconvenience which arises from too high a relief in the medal, or in the bust, might be remedied by some mechanical contrivance, by which the deviation of the diamond point from the right line (which it would describe when the tracing point traverses a plane), would be made proportional not to the elevation of the corresponding point above the plane of the medal, but to its elevation above some other parallel plane removed to a fit distance behind it.  Thus busts and statues might be reduced to any required degree of relief.

156.  The machine just described naturally suggests other views which seem to deserve some consideration, and, perhaps, some experiment.  If a medal were placed under the tracing point of a pentagraph, an engraving tool substituted for the pencil, and a copperplate in the place of the paper; and if, by some mechanism, the tracing point, which slides in a vertical plane, could, as it is carried over the different elevations of the medal, increase or diminish the depth of the engraved line proportionally to the actual height of the corresponding point on the medal, then an engraving would be produced, free at least from any distortion, although it might be liable to objections of a different kind.  If, by any similar contrivance, instead of lines, we could make on each point of the copper a dot, varying in size or depth with the altitude of the corresponding point of the medal above its plane, than a new species of engraving would be produced:  and the variety of these might again be increased, by causing the graving point to describe very small circles, of diameters, varying with the height of the point on the medal above a given plane; or by making the graving tool consist of three equidistant points, whose distance increased or diminished according to some determinate law, dependent on the elevation of the point represented above the plane of the medal.  It would, perhaps, be difficult to imagine the effects of some of these kinds of engraving; but they would all possess, in common, the property of being projections, by parallel lines, of the objects represented, and the intensity of the shade of the ink would either vary according to some function of the distance of the point represented from some given plane, or it would be a little modified by the distances from the same plane of a few of the immediately contiguous points.

157.  The system of shading maps by means of lines of equal altitude above the sea bears some analogy to this mode of representing medals, and if applied to them would produce a different species of engraved resemblance.  The projections on the plane of the medal, of the section of an imaginary plane, placed at successive distances above it, with the medal itself, would produce a likeness of the figure on the medal, in which all the inclined parts of it would be dark in proportion to their inclination.  Other species of engraving might be conceived by substituting, instead of the imaginary plane, an imaginary sphere or other solid, intersecting the figure in the medal.