In these experiments, the conversion of the concavity into a convexity depends on two separate illusions, one of which springs from the other. The _first_ illusion is the erroneous conviction that the surface of the table is looking upwards as usual, whereas it is really inverted; and the _second_ illusion, which arises from the first, is, that the _nearest_ point of the object appears _farthest_ from the eye, whereas it is _nearest_ to it. All these observations are equally applicable to the vision of convexities, and hence it follows, that the conversion of relief, caused by the use of an inverting eye-piece, is not produced directly by the inversion, but by an illusion arising from the inversion, in virtue of which we believe that the remotest side of the convexity is nearer our eye than the side next us. In order to demonstrate the correctness of this explanation, let the hemispherical cavity be made in a stripe of wood, narrower than the field of the inverting telescope with which it is viewed. It will then appear really inverted, and free from both the illusions which formerly took place. The thickness of the stripe of wood is now distinctly seen, and the inversion of the surface, which now looks downward, immediately recognised. The edge of the cavity now appears _nearest_ the eye, as it really is, and _the concavity, though inverted, still appears a concavity_. The same effect is produced when a convexity is placed on a narrow stripe of wood. Some curious phenomena take place when we view, at different degrees of obliquity, a hemispherical cavity raised into a convexity. At every degree of obliquity from 0° to 90°, that is, from a vertical to a horizontal view of it, _the elliptical margin of the convexity will always be visible_, which is impossible in a real convexity, and the elevated apex will gradually sink till the elliptical margin becomes a straight line, and _the imaginary convexity completely levelled_. The struggle between truth and error is here so singular, that while one part of the object has become concave, the other part retains its convexity! In like manner, when a convexity is seen as a concavity, the concavity loses its true shape as it is viewed more and more obliquely, till its remote elliptical margin is encroached upon, or eclipsed, by the apex of the convexity; and towards an inclination of 90° the concavity disappears altogether, under circumstances analogous to those already described.