By the use of the spherometer to measure the surface curvatures of the mirror faces, it is easy to show that the surface of the magic mirrors is actually less convex, or even slightly concave, over those parts where the substance of the mirror is thick, as compared with those parts where the mirror is thin. For example, the curvature of the rectangular mirror, Plate VI., as measured from left to right over the convex surface, is, on the average, about 0·2 dioptries (or its radius of curvature is about 5 metres), but when measured at points over the vertical bamboo stems, its curvature falls to less than 0·05 dioptrie, and in some parts is absolutely flat, or even slightly concave. Makers of mirrors and lenses for large telescopes are accustomed to test the perfection of their figure by a process known as Foucault’s, in which the observer, after allowing light to fall from a single well-defined point upon the (concave) mirror at nearly normal incidence, places his eye at the point where the reflected rays converge to a focus, and then sees the whole surface of the mirror uniformly bright, save only such spots as differ in curvature from the rest. In the case of convex mirrors it is needful to interpose a large auxiliary convex lens to reconcentrate the otherwise divergent beam. Applying this method of investigation, the author finds that it is quite easy in many cases to see in the front face the pattern that the mirror bears on its back. Lastly, the author has made one absolutely direct proof of the inequalities of curvature of the front surface. He took the mirror depicted in Plate I., and having taken a mould of its face in a composition of gutta-percha, he deposited a firm layer of copper in the mould by the electrotyping process. The type so made was silvered and polished, when it was found to reflect from its face the image of the bird that was on the back of the original mirror; the image was, however, less regular than that from the mirror’s own face. Here, then, was a magic mirror without any pattern on its back. In repeating the experiments on heating, the author found a very singular effect to be produced by warming (with a flame) the back of a thin piece of mirror glass while it reflected from its face a grating of luminous lines thrown upon it by a lamp as described above. As the flame was passed rapidly across the back, the whole pattern appeared to heave, as though a wave had passed along it. [Illustration: PLATE VI.]